“ -- I~ TEE Fv-J how: 5 iv: '.. ‘V4« ~- 0“ In- bu. . . V ‘1 on; a 't V l;- “b. :- '1 (I) A L ‘4 I)! ~. ~ Walter Zinn Each of these five types of postponement-speculation were analyzed in terms of total cost by the use of five normative cost models, which contained all logistics costs relevant to postponement-speculation decisions. Each model is a step-by-step procedure enabling managers to collect and organize data for a decision on a particular product. To test hypotheses relating postponement-speculation to product physical and demand characteristics, the cost models were replicated by a computer simulation. The simulator treated the product physical and demand characteristics as inputs. The relevant logistics cost structure was the algorithm. The output provided data to determine if distribution should be postponed or speculated on. A discriminant analysis was completed to isolate significant product physical and demand characteristics. In labeling postponement-speculation, they were product value, uncertainty of demand, and the number of brands. In packaging postponement-speculation, product value and uncertainty of demand. In assembly postponement-speculation, product value, cube reduction, and the number of product versions. In manufacturing postponement-speculation, product value, demand uncertainty, and the weight of ubiquitous materials. Finally, in time postponement-speculation, demand uncertainty. Copyright by WALTER ZINN 1986 To My family, in return for love and cheerleading ii on. a~ on. "V I h. . Iv. 2 I. ‘5 't ACKNOWLEDGMENTS Writing a dissertation is a complex --and lengthy-- task. A great deal of curiosity about the findings is required to complete it successfully. Equally required is the input of the candidate's committee, colleagues and, most importantly, family. Dr. Donald J. Bowersox, Chairman of the committee, was instrumental in all stages of the dissertation, from problem definition to editing the final version. Interest on this research first developed from reading his logistics book, and was inspired by his numerous writings on the importance of the topic. I also learned much from Dr.Bowersox's editing of earlier drafts of the dissertation; the writing style is greatly influenced by his dedication to clarity and precision. Drs. Forrest 8. Carter and Donald A. Taylor, committee members, provided important assistance. Dr. Carter has contributed much with his in-depth knowledge of methodology and statistics. His insightful methodological and substantive suggestions are greatly valued. Dr. Taylor, one of the most experienced committee members in the Department of Marketing and Transportation, was always willing to provide support and advice, especially during the early iii stages of the dissertation when the road sometimes looked rockier than it actually was. His eternal optimism is always a source of inspiration. Dr. David J. Closs, associate professor at Michigan State, gracefully agreed to apply his computer simulation expertise as a reviewer of the research models. Dr. Closs also volunteered a number of valuable contributions to the research. His scholarly participation is deeply appreciated. Drs. Luis V. Dominguez and Jerry Gotlieb, my colleagues at the University of Miami, were always willing to share ideas on day-to-day tactical decisions. Dr. Dominguez's reviews and constructive criticisms were especially helpful. The greatest debt is owed to my family. My son Bruno will have to grow up a little before he can understand some of the events around him. My older son, Marcelo, watched his father work on a doctoral degree for half of his life. His ability to grasp that something important was going on and that, consequently, Dad could not go to the park every Sunday was at one time remarkable and touching. Marianne, my beloved wife, endured the process on a daily basis. She put up with my long nights at the office, sporadic vacations, and a doubled share of housework in times of crisis. Her constant demonstrations of true partnership were a source of encouragement. Marianne wrote a thesis in her own right and, thus, knows the bumps and iv hurdles in the process. This explains her ability to make meaningful comments and --I have to admit-- criticism as well. This dissertation is a tribute to my family in Brazil. It is the recognition that my career choices required life at a great distance from Sao Paulo. Telephones, mail, and airplanes were used extensively in an attempt to shorten the distance, but we all know that it is not the same thing. Still, no one ever ceased to selflessly share my goal. I am very fortunate to have them, and it is only natural that we share the outcome of that goal. TABLE OF CONTENTS LIST OF TABLES 0 0 0 . . 0 0 0 . 0 0 . . 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0Viii LIST OF FIGURES 0 0 0 ..... 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 . 0 0 0 0 0 0 0 0 0 Xii GmSSARY00....00000000000000000000... ..... 0.00.00.000.0xv I. II. III. INTRODUCTION00.0000.00.00.00.00.00...00.0.0.0..0.0.1 General Overview...................................3 Basic Concepts.....................................4 Business Problem..................................16 Research Objectives...............................17 Research Questions................................18 Research Models and Scope.........................19 Methodology Overview..............................27 Potential Contributions...........................28 Limitations.......................................29 LITERATIJRE REVIEW000000.00.00.00.0000000000.00.00031 Previous Studies in Postponement-Speculation......33 Manufacturing and Distribution Decision Models....36 Production and Distribution Interface.............39 Simulation and Logistics..........................43 MODEL DEVELOPMENT AND RESEARCH DESIGN.............51 Normative Cost Models.............................51 common framework................................52 model A.........................................57 model B.........................................61 model C.........................................67 model D.........................................74 model E.........................................81 Computer Simulation...............................88 the simulator...................................89 application to model A..........................96 application to model B.........................105 application to model C.........................117 application to model D.........................129 application to model E.........................142 validation of inputs...........................144 vi IV. Research Hypotheses and Methodology .............. 154 research hypotheses...................... ..... .155 meth0d01ogy.........O............ 00000000000 ...157 DATA ANALYSIS. 0 . . . . 0 . . ........ 0 00000000000000000 . 163 Model A........................ .................. 163 validation.......... ..... ....... ......... ......164 application input/output.......................166 findings.......................................166 discussion ..................................... 172 Model B..........................................180 validation.....................................180 application input/output.. ........... .. ........ 183 findings.......................................183 discussion............ ..... .......... ...... ....189 Model C............................... ..... . ..... 198 validation.....................................198 application input/output ...... . .......... . ..... 200 findings................ ........ ... ...... ......201 discussion.....................................212 Model D...................... .............. ......217 validation......................... ..... .......217 application input/output.......................219 findings.......................................220 discussion.....................................230 Model E..........................................234 validation.....................................234 application input/output.......................237 findings.................................. ..... 237 discussion.....................................246 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS........250 Research Summary.................................246 postponement-speculation types ........... ......252 normative cost models..........................253 computer simulation............................254 research results...............................255 limitations....................................257 Conclusions......................................258 Managerial Implications......... ........ ... ...... 260 Questions for Further Research..... ............ ..263 LIST OF REFERENCES..0............. OOOOOOOOOOOOOO ......265 APPENDIX A.................. ........................ ..270 vii LIST OF TABLES Postponement-Speculation Types...................24 Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model A-variable List000000.0000.00000.0......100 A UUOOOOOOOIDGGWUW’D Variable Range and Value Levels.......102 Constant Values.......................102 Application Relationships.............103 Variable List - Packaging.............llo Variable List - Inventory.............111 Variable List - Transportation........112 Variable Range and Value Levels.......113 Constant Values.......................113 Application Relationships.............114 Variable List - Assembly..............122 Variable List - Customer Service......123 Variable List - Transportation......-.124 Variable List - Inventory.............125 Variable Range and Value Levels.......126 Constant Values.......................126 Application Relationships.............127 Variable List - Customer Service......134 Variable List - Manufacturing.........135 H64 u‘ ”I Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model >MMMMMMUUUUU » v V > v Variable List - Inventory.............136 Variable List - Transportation........137 Variable Range and Value Levels.......138 Constant Values............... ....... .138 Application Relationships....... ..... .139 Variable List - Customer Service......147 Variable List - Inventory.............148 Variable List - Transportation........149 Variable Range and Value Levels.......150 Constant Values.......................150 Application Relationships.............151 Observed and Expected Outputs for Extreme Products..................165 Group Means and Centroids. ......... ...168 correlation Matrix. . . 0 . 0 . 0 0 . 0 0 . 0 . 0 . 0 0 0 168 Discriminant Function Correlation ..... 168 Test of Significance - Independent variables..............00.........0...169 Discriminant Weights and Discriminant madings000.0..0..0....0.0.0....00..00169 Box's M Test of Equality of Group Covariance Matrices...................l69 Classification Matrix for Hold-Out sample.................O....00........17o Observed and Expected Outputs for Extreme Products..................182 ix Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model wwmm 0000 Group Means and Centroids.............l85 Correlation Matrix....................185 Discriminant Function Correlation.....185 Test of Significance - Independent variables00.0..000..........0...00.00.186 Discriminant Weights and Discriminant madings..0000.000........0..00..000.0186 Box's M Test of Equality of Group Covariance Matrices...................186 Classification Matrix for Hold-Out sample........0.................0.....187 Observed and Expected Outputs for Extreme Products........... ....... 200 Group Means and Centroids.............202 Correlation Matrix....................203 Discriminant Function Correlation.....203 Test of Significance - Independent variables..0....0000.............0...0203 Discriminant Weights and Discriminant Loadings.......0....0...0........0....203 Box's M Test of Equality of Group Covariance Matrices...................204 Classification Matrix for Hold-Out sample.0.0.0000......00.0.000..0.....0204 Observed and Expected Outputs for Extreme Products..................219 Group Means and Centroids.............221 CorrelatiOn Matrix.... ....... .........222 4.28 4.29 Model Model Model Model Model Model Model Model Model Model Model Model Model MMMEI Discriminant Function Correlation.....222 Test of Significance - Independent variab1e800......0....................222 Discriminant Weights and Discriminant madings......................0.......223 Box's M Test of Equality of Group covariance Matrices.............00....223 Classification Matrix for Hold-Out sample..0........0....................223 Observed and Expected Outputs for Extreme Products........... ..... ..236 Group Means and Centroids.............238 Correlation Matrix....................239 Discriminant Function Correlation.....239 Test of Significance - Independent Variables.0...........0.....0......00.239 Discriminant Weights and Discriminant Loadings0.000..00.0.00..00...0..0...00240 Box's M Test of Equality of Group Covariance Matrices...................240 Classification Matrix for Hold-Out sample........00....0...0...000000....240 Discriminant Weights............................256 xi 3.12A 3.13 3.13A 3.14 3.14A 3.15 3.15A LIST OF FIGURES Business Logistics Cost Trade-offs..... .......... 8 Postponement-Speculation Cost Trade-offs........13 Normative Model for Postponement-Speculation....55 Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model A UCOO¢G>§MMOUOOUU> Labeling Postponement-Speculation.....58 Direct Cost Per Product...............62 Labeling Postponement-Speculation.....64 Direct Cost Per Product...............68 'Labeling Postponement-Speculation.....70 Direct Cost Per Product...............75 Labeling Postponement-Speculation.....77 Direct Cost Per Product...............82 Labeling Postponement-Speculation.....84 Direct Cost Per Product...............87 Block Diagram.........................98 Subroutines...........................99 Block Diagram............. ...... .....108 Subroutines..........................109 Block Diagram .......... . .......... ...120 Subroutines..........................121 Block Diagram........................132 subroutines.....................00...133 xii Model Model Model Model Model Model Model Model Model Model Model Model Model Model Model Block Diagram ..... . ........ ..........145 subroutines..0.0........0.....000....146 Relationship Between Demand and the Incentive to Postpone................173 Relationship Between Uncertainty and the Incentive to Postpone............174 Relationship Between Number of Brands and Incentive to Postpone............175 Relationship Between Product Value and Incentive to Postpone............176 Relationship Between Demand and the Incentive to Postpone................190 Relationship Between Uncertainty and the Incentive to Postpone............191 Relationship Between Number of Package Sizes and Incentive to Postpone..0......0.000...0...0.......192 Relationship Between Product Value and Incentive to Postpone............193 Relationship Between Demand and the Incentive to Postpone................207 Relationship Between Uncertainty and the Incentive to Postpone............208 Relationship Between Number of Product Versions and Incentive to POStponeooooooooooooo00000000000000.0209 Relationship Between Cube Reduction and Incentive to Postpone............210 Relationship Between Product Value and Incentive to Postpone............211 xiii Model Model Model Model Model Model Model Relationship Between Demand and the Incentive to Postpone................226 Relationship Between Uncertainty and the Incentive to Postpone............227 Relationship Between the Weight Proportion of Ubiquitous Materials and the Incentive to Postpone........228 Relationship Between Product Value and Incentive to Postpone............229 Relationship Between Demand and the Incentive to Postpone................243 Relationship Between Uncertainty and the Incentive to Postpone............244 Relationship Between Product Value and Incentive to Postpone............245 xiv 9. 10. GLOSSARY us' 5 's 8: Activities performed by one firm to distribute its products. Channel of Distribution: An interorganizational structure with the common objective of participating in the distribution of products. Prinpiple pf Postponement: The differentiation and the movement of goods are delayed until a customer order is received. Pringiple of Specnlation: The differentiation and the movement of goods are done in anticipation of a customer order. Principle pf Ppstponenent-Speculatipn: Goods are moved and differentiated at the time and location where it minimizes the total cost of distribution. 'm 05 o - a ' : Goods are moved at the time when it minimizes the total cost of distribution. Eotn Postponement-Speculation: Goods are differentiated at the location where it minimizes the total cost of distribution. b ' st men - u a ' : Goods are labeled at the location where it minimizes the total cost of distribution. Labeling does not affect transportation costs in the distribution process. WM: Goods are packaged at the location where it minimizes the total cost of distribution. ss mb 0 nt- e ' : Goods are assembled at the location where it minimizes the total cost of distribution. In assembly, all parts originate at the same source. 11. 12. 13. 14. 15. Manufac ur n t o e - ul : Goods are manufactured at the location where it minimizes the total cost of distribution. In manufacturing, parts originate in multiple sources. : All costs, fixed and variable, that will be eliminated if the product is eliminated from the firm's product line. Incremental Cost: The difference in cost between two alternatives. Simulation: The process of replicating a system with the purpose of testing hypotheses about that system. fiinnlntpt: Computer algorithm containing the mathematical relationships needed to simulate a system. 16. Model: A normative cost structure that facilitates the computation of all relevant costs for a decision in postponement-speculation. 17. Applipntipn: The adaptation of the simulator to the specific conditions of one of the five postponement- speculation models. xvi ":vs ‘-45 o ' I D" ,R‘ l' i4 a o,:;. ...-d. ~ln. .- ' ... ovh. - u.“ D-“ 65“ ‘A-. v.3. O“ CHAPTE I NTRO U T ON The role of business logistics in the American Economy has been increasingly recognized in the past twenty-five years. Estimates of the share of the gross national product by distribution and distribution related activities have traditionally been centered around 20 percent (Bowersox, 1978, p. 4), although more recent calculations have set that share at 11 percent (Delaney, 1986). Irrespective of the accuracy of these estimates, no evaluation of total logistics expenditures has put it at less than 400 billion dollars a year (Delaney, 1986). During the same period, managers and researchers have realized the strategic importance of business logistics costs and services to the success of the business enterprise in the marketplace. One of the earliest successful attempts to conceptually integrate all logistics functions in one theoretical framework that could be used as a competitive tool was by Smykay, Bowersox and Mossman (1961). In 1962, Drucker (1969) stressed the potential importance of business logistics systems in competitive strategy when referring to it as the frontier of modern management, and the one area in the firm where much could still be accomplished in terms of .a I. F! vi [n I I.” II. It. 2 cost reduction and customer service. More recently, Shapiro (1984), addressed the crucial role of logistics in a firm's competitive strategy by examining the impact several alternative strategies on the logistical system. The importance of distribution for the national economy and for a firm must not be underestimated. In this context, the issue of productivity has been a major concern for those interested in the field of physical distribution. The productivity of business logistics, as measured by the proportion of the GNP spent in logistics activities, has improved since the economic deregulation of the transportation industry (Delaney, 1986). The need for further improvements at the macro and firm levels is emphasized in the literature. To increase productivity, managers and scholars of business logistics have concentrated on a number of concepts with the potential to improve the efficient use of system resources like inventory reduction methods, transportation consolidation, and warehousing automation. In this dissertation the first chapter is an introduction divided into nine sections. The first provides a general overview of the research. It is followed by an explanation of the theoretical foundations. The next three sections discuss the business problem, the research objectives and the research questions. The last four sections present the research models and scope, an overview gun..- vu- - -— ”In: U h...” Inn: V1... ..fl ‘6', a n 0. h. u I .“ ll. 0 u' f!- \v .’ I I I. 3 of the methodology, potential contributions, and research limitations. GENERAL OVERVIEW The principle of postponement-speculation, the basic theoretical construct in this dissertation, is a major concept for the improvement of productivity in business logistics. It focuses on the issue of timing--the proper time to move goods, and the proper time to put them in their final form before consumption. The objective is to minimize the total cost of the business logistics system for a predetermined level of customer service. The objective of this study is to develop models enabling managers to decide whether it is more cost efficient to ship products through the distribution system before or after the receipt of a customer order. Similarly, models are developed to help managers decide whether to ship products in an unfinished or finished (ready to be sold) state. Furthermore, several product and demand characteristics, like the level of demand or the value of the product, are tested to measure their impact on a manager's decision to anticipate or to postpone distribution of a particular product. The relevance of the principle of postponement- speculation to the management of logistics systems is 4 threefold. First, it enables a firm to find new ways to reduce inventory levels while keeping its level of customer service constant. Second, it reduces a firm's dependence on the accuracy of sales forecasting to maintain a predetermined level of customer service. Third, the principle of postponement-speculation can be a competitive resource. Once an efficient logistical system is implemented, it becomes very difficult and time consuming for competitors to emulate it. In this research, the approach to the principle of postponement-speculation is based on two phases. First, a normative cost model shows, step-by-step, what costs to include when a manager must decide whether to postpone or speculate on the distribution of a product. As a part of this phase, the reporting forms necessary to compute all costs are developed. Second, a number of hypotheses relating the decision to postpone or to speculate on the distribution of a product to several product physical and demand characteristics are tested with the help of computer simulation. AS CO C This research project is anchored in two marketing and business logistics concepts. The first is the total cost approach, a paradigm of the study of business logistics, 5 upon which the entire discipline is founded. The second is the principle of postponement-speculation, which addresses the issue of timing in the commitment of resources for the distribution of a particular product. Both concepts are further explained in this section. The Total Cost Approagh to Business Lpgistics The Council of Logistics Management (COLM) defined logistics as: the process of planning, implementing, and controlling the efficient, cost effective flow and storage of raw materials, in-process inventory, finished goods, and related information from point of origin to point of consumption, for the purpose of conforming to customer requirements (1985). The activities related to business logistics have always commanded managerial attention. However, the concept of integrating them systematically is recent. One of the earlier works in the field demonstrated how increases in transportation costs could be offset by reductions in other logistics costs (Lewis, Culliton and Steel, 1956). Such an integrated approach has been termed the total cost approach. This approach is based on the application of systems theory to cost minimization in business logistics. The concept of a system refers to interrelationships among parts of a whole working toward a common objective. Parts can not perform independently. The performance of one system component affects the others. The variation in the performance of one component given a change in the performance of another component of the system is called a trade-off. Further, the performance of the whole system is not contingent on the optimization of each individual component. Rather, the level of performance of each individual component must be managed so as to optimize the level of performance of the whole system. In the case of business logistics systems, the goal is to minimize the total cost, as opposed to individual cost categories. Some costs are sub-optimized so that the over-all cost of distributing a given product is minimized. Lambert and Stock (1982, p. 183) identify six cost categories in business logistics systems. The interrelationships of these categories, as well as the integration of business logistics in the marketing mix of the firm, are presented in Figure 1.1. Each cost category is discussed below. The customer service level represents the extent to which ordered goods are available where and when needed by the customer. It is the contact point between marketing and business logistics. The availability of goods at the point of purchase affects their demand, as does the delivery time and the extent to which products arrive undamaged. A low level of customer service increases a company's cost of lost sales. Ultimately, customer service must be justified by an increase in profits or in a level of demand that outweighs CV the cost of the service. The second cost category is transportation. The relationship of transportation to the other business logistics costs is based on cost and service trade-offs, mostly speed and consistency (Bowersox, 1978, p. 44). Fast transportation increases the level of customer service and reduces warehousing and inventory carrying costs. It also affects manufacturing costs by making possible low-inventory production systems. The desired level of service and the lowest total cost in the system determine the level of transportation service required. Cost minimization of the transportation function should be limited by the service level constraint. Warehousing costs vary with the number of warehouses in the system. Since these costs tend to be relatively fixed in the short-run, other logistics costs are expressed as a function of the number of warehouses in the system in defining the lowest total cost for the system (LeKashman and Stolle, 1965, p. 334: Bowersox, 1978, p. 253). Warehousing costs can also vary as a function of the facility's size, level of automation, and the characteristics of demand. The cost of operating a warehouse must also be justified in terms of reductions in other business logistics costs. £I§QBE—1Ll BUSINESS LOGISTICS COST TRADE-OFFS Place-Customers service Ievels (cost or lost sales) Inventory carrying costs Transportation costs Production Order Warehousmg lot quantity processmg costs costs ”‘0 'n'Otmation (throughput costs costs not storage) Objective: Minimize total cost: Total costs - Transportation costs 4- Warehousing costs 4- Order processing and information costs + Production Iot quantity costs 4» Inventory carrying costs + Cost oI lost saIes Source: Adapted from Lambert and Stock, Stzntggig s . Richard D. Irwin, Inc., Homewood, Illinois, 1982, p. 35. 9 Moreover, storing goods closer to a given market increases the level of customer service. Warehouses also reduce transportation costs by facilitating the consolidation of shipments. Similarly, plants can optimize production costs with the use of plant warehouses. However, inventory carrying costs generally increase with every increase in the number of warehouses. Order processing and information costs are incurred for communication within business logistics systems. Four subsets of activities compose the communication function: (1) order processing, (2) communication of the business logistics system with other sectors of the firm, (3) transmittal of commands to the system, and, (4) monitoring and control. Order processing and information systems are fundamental in business logistics systems. A sophisticated system facilitates centralized decision making. It can also be a decisive factor in customer service because rapid order processing reduces delivery time. Production lot quantity costs refer to the contact between manufacturing and business logistics. Minimization of production costs generally results in higher inventory carrying costs. Also, transportation costs are affected by the size and frequency of production runs and by plant warehousing capacity. Inventory carrying costs are usually one of the largest items in the total cost of physical distribution in the lO firm. Firms normally underestimate their inventory related costs. Inventory carrying costs are those that vary with the level of inventories in the system. Inefficiencies in the distribution system often result in poor customer service levels or larger than necessary stocks. Specifically, the functions of inventories in the system are to provide a balance between supply and demand, to provide regional specialization of the product assortment, to enable plants to operate at optimum scales, and to provide a buffer against demand and lead time uncertainties. T P ' c' os o e nt- Speculation The principle of postponement links physical distribution efficiency to the ordering of steps in the manufacturing-marketing value added process. Postponement involves changes in the form, identity, or place of goods. That is, the principle proposes that changes in form and identity occur at the latest possible point in the marketing flow (form postponement), and that changes in inventory location occur at the latest possible point in time (time postponement) (Alderson, 1950). The principle serves two purposes. The first is to reduce the cost of sorting in the distribution channel, by permitting sorting to occur as much as possible while the product is maintained in a relatively undifferentiated 11 state. The second is to reduce marketing risk through reduced dependence on anticipating future demand patterns (Alderson, 1950). Fundamental to the principle is what is referred to as the limits of postponability (Alderson, 1950). Factors such as manufacturing lead time, economies of scale requirements, and customer service constraints limit the extent of postponement opportunities in the marketing process. Practical limits to postponability are formalized through a second principle concerned with speculation (Bucklin, 1962). The principle of speculation suggests that goods should move through the distribution channel at the earliest possible point in the marketing process. Similarly, form should be differentiated early in the process. There are several cost incentives for the firm to speculate on time or form: economies of scale in distribution, fewer stock-outs, and transfer of risk to distributors or retailers. The two principles combine to derive a general principle called postponement-speculation. In postponement- speculation, advantages of postponement are balanced with advantages of speculation to determine if a speculative inventory is justified in the distribution channel. Important to understanding the general principle is the notion that speculation is the limit of postponement and vice-versa (Bucklin, 1962, p. 69). Thus, from an operational viewpoint, the general principle can be used to 12 reflect degrees on an anticipation/delay spectrum. Figure 1.2 details the operation of the principle. Delivery time is used as a measure for time postponement- speculation. Curve DB shows the seller's average cost to deliver one unit of a product relative to delivery times, with a speculative inventory. Curve AD' shows the seller's average cost to deliver one unit of a product, without a speculative inventory. Clearly, very short delivery times can be accomplished only with a speculative inventory. The lowest cost for the seller, with or without a speculative inventory, is given by DD'. The seller's cost of delivery decreases as delivery time expands. As this happens, the seller can afford to reduce safety stocks, increase turnover, and reduce warehousing costs. As soon as Point I is reached, it is cheaper to drop the speculative inventory altogether. The buyer's average cost of buying one unit of a product will increase as delivery time is allowed to increase (Curve C). The reason is that longer delivery times have to be accompanied by higher safety stocks to compensate for the increase in lead time uncertainty and demand fluctuations. The total cost for buyers and sellers is given by DD' C. The point of minimum total cost in the channel of» distribution is M, with N days (hours) for delivery. The + (11/ D D 13 Average Costs per Unit (Dollars) DDHCL I -- -----—--3 DO p- -——--—-- l l l _ I O T 2 Delivery I Time ”Indirect Channel ——- I Direct Channel —-- Source: Bucklin and Halpert, "Exploring Channels of Distribution for Cement with the Principle of Postponement-Speculation." Marketing_and_fisenemie pggglppngnt. Peter D. Bennet, ed., Chicago: American Marketing Association, 1965, p. 698. ;,~‘..- 1 l v ‘9' it {In (D ... .5- ’I \. J 14 key assumption concerning behavior by channel participants towards that point of minimum cost is enunciated in the concept of substitutability, also introduced by Bucklin. According to the concept, under competitive conditions, channel institutions interchange distribution activities so as to minimize the total cost in the channel. The assumptions of the principle of postponement- speculation are as follows: The number of buyers and sellers is large enough to ensure active price competition. Manufacturers are located close to each other, and significantly distant from customers, who also are close together. Buyers buy in quantities large enough to eliminate savings from sorting. Seasonal variations do not influence production and consumption. Finally, the presence of an intermediary inventory does not affect production costs. An illustration clarifies the operation of the principle of postponement-speculation. Let us assume that a product--widgets--is being distributed to a market, and that the assumptions mentioned in the above paragraph apply. The three functions presented in Figure 1.2 are used to determine if a speculative inventory will appear between the buyers and the sellers in the channel of distribution for widgets to a particular market. A fourth function is derived from the sum Of all functions. 15 The first function, curve DB, shows the seller's cost to deliver one unit of widget to the market, as a function of delivery time, if a speculative inventory between buyers and sellers is used. The slope of the function is negative because longer delivery times would correspond to lower delivery costs per unit. The reason is that a longer delivery time would allow the seller to reduce the level of safety stocks, and to contract for slower forms of transportation. The second function, curve AD', demonstrates the seller's cost of delivering one unit of widget to the market without using a speculative inventory between the buyer and the seller. As shown in Figure 1.2, very short delivery times are not possible without a speculative inventory. The slope of this function is also negative. However, it is a steeper function than curve DB because short delivery times over long hauls require very fast transportation systems. The third function, curve C, is positively sloped because longer delivery times would force the buyer to increase safety stocks. Faster delivery times would allow the buyer to postpone purchasing widgets until the exact number of models and units needed is known. The total cost for buyers and sellers in the channel is given by curve C+DD'. It is the sum of the buyers' total cost (curve C) and the sellers' total cost (curve DD') derived from the minimum cost points from curves DB and AD'. 16 The point of minimum total cost in curve C+DD' determines whether a speculative inventory will or will not appear in the channel. In Figure 1.2, the minimum cost for buyers and sellers to distribute one unit of widget to the market is M dollars, and the delivery time is N days. THE USI O The potential application of the principle of postponement-speculation to business logistics systems is large. As explained above, the postponement of the distribution of goods, in time or form, may reduce the cost of sorting and the level of marketing risk in the channel of distribution. Changes in the business environment have added new demands on business logistics systems. The increase in the number of different products and multiple brands available in the market has increased the cost of sorting in the marketing process. Changes in consumer preferences are a constant source of uncertainty in the marketing and distribution of goods. Moreover, new manufacturing technologies and just-in-time procurement have increased customer service requirements. The design of business logistics systems has been traditionally speculative in nature: products are distributed on the basis of expected demand. Demand is most at mums :5 17 commonly anticipated through sophisticated forecasting techniques, which can be costly and not problem free. Informant bias can distort techniques based on human expectations. Most techniques are based on the assumption that the past will repeat itself, an assumption not always justified. The alternative approach to anticipate demand in different markets is the postponement of movement or differentiation of goods until the customer order is received. A study that demonstrates a systematic approach to the postponement of distribution will therefore contribute to the reduction in the anticipatory nature of most distribution systems and, consequently, reduce the dependence of such systems on the hazards of demand forecasting. RES ARCH C S This research looks at the principle of postponement- speculation as a way to alleviate the problem of the dependence of business logistics systems on demand forecasting, and to improve the productivity of business logistics systems. These aims are accomplished through two research objectives. The first objective is to devise a systematic approach to postponement-speculation decisions. Such an approach includes a normative model that makes fl‘n V¥U u 18 explicit all costs involved and their relationships. The second objective is to understand the impact of several product physical and demand characteristics on postponement-speculation decisions. ESEAR 8 To fulfill the objectives stated above, the research addresses three specific questions. The first two questions are related to the first objective, a systematic approach to postponement-speculation decisions. 1.What are the specific logistical costs involved in the decision to postpone or to speculate, in time or form, the distribution of a given product? 2.How should these costs be measured and integrated in a managerial decision framework? The third question is related to the second objective, an understanding of the impact of product physical and demand characteristics on postponement-speculation decisions. 3.What is the relative importance of different physical and demand characteristics on the decision to postpone or to speculate the distribution of a particular product? Each of these questions is designed to cover one aspect of this research, and all are interconnected in such a way ‘that the overall purpose of this study is achieved-- to enable researchers and managers to use the principle of ea“? 693L- O In.‘ 1"» O 0“ Ian. WV; u .“'l NAb.I "IA! our“ 0 (In 5 u a} l.- in“: lg... s.‘ Q ‘i u 4!- -I l t '1’! v f 19 postponement-speculation in the design of logistical systems. The first research question arises from the need to understand the relationship of the costs to the principle. The second question concerns the integration of all relevant costs in a framework that managers and researchers can use in the design of logistical systems. The third question introduces a different aspect of the research: what is the importance of demand related variables such as the volume of sales or the variability of demand in the decision to postpone or to speculate on the distribution of a product? Similarly, what is the importance of physical characteristics such as weight and cube in the decision to postpone or to speculate on the distribution of a product? This section presents the models developed for this research. Five models are introduced--one for time postponement-speculation, and four for form postponement- speculation which correspond to four different levels of ‘postponement: labeling, packaging, assembly and manufacturing . The section includes two parts. The first outlines the scope of the models, while the second presents a conceptual and nontechnical overview for each of the models. “up. Uvb 2...- ‘ 1 mm blind. fine. ’A ' L. S, :.,. OVA-‘ En M a: V} A one“, ' I a... b "... :‘z:~ -.:-.‘ ‘ ‘ u'.’l~. |."‘ 31':¥ 1‘ ... Si.“\ ‘5‘. ‘. t‘ " 5“: .I’ 1 u‘. ‘.\ ~_ ‘1 20 co f d s This research adopts the point of view of a large manufacturer with a diversified product line. Models are developed to aid the firm in deciding whether to postpone or to speculate on the distribution of a product, in time or form, on the basis of the minimum cost alternative. There is one decision per product, as opposed to one decision per firm, because costs are product specific. Three additional delimitations of the scope of the models must be made explicit. First, all models assume a status quo of speculation in the distribution system. Products are given their final form and shipped to field warehouses in anticipation of demand. Such an assumption simulates most business logistics systems now in operation. Second, the segment of the distribution system to be modeled is the manufacturer-warehouse segment. The warehouse-customer segment is a question for further research, since it involves the manipulation of products by another firm in the channel of distribution. This will introduce some additional complexities to the problem, such as the possibility that product tampering may occur. Finally, the five models of postponement-speculation are static. Costs are computed for a single point in time. In the past, single period models have been helpful in designing minimum cost business logistics systems. 21 Rese r o s As mentioned earlier, five models are presented in this dissertation. Despite their distinctions, these models have a common underlying framework. Three issues are addressed by way of introducing the research models to the reader, three issues are addressed. The first issue is the common framework for the models. It consists of an eight-step procedure to calculate the cost of speculation and estimate the cost of postponement for every product in the product line. The second issue is to clarify the idiosyncrasies of each of the five models. Finally, the third issue concerns the use of each of these models as inputs to a computer simulation procedure that will enable this research to address the third research question in this dissertation, namely the determination of the most important physical and demand characteristics to decide whether a product's distribution should be postponed or speculated on. Common Framework The common framework to the five postponement- speculation models to be introduced is an eight-step normative cost model based on two cost concepts: direct costing and incremental costing. 22 Direct cost is defined as being directly traceable to one particular product. Such costs would be eliminated in case the product is also eliminated from the firm's product line. This would include variable costs plus non-allocated fixed costs. Incremental costs are defined as the difference in cost between two alternatives. Thus, the normative cost model is based on direct and incremental costs. Next, the common framework to the five postponement- speculation models is briefly introduced. A complete description of the framework is presented in Chapter III. The common framework comprises eight steps. In the first, the market to be studied is defined. In the second step, the period of analysis must be defined, since the normative cost models are static. The products supplied to the market in the period of analysis are defined in the third step. The level of customer service required in the analysis is defined in the fourth step. In the fifth step, the direct cost per product in the alternative of speculation is computed. In the next step, the direct cost per product in the alternative of postponement is estimated. The seventh step is computed as the difference in cost for the alternatives of postponement and speculation. The last step is the outcome of the model, where the least cost alternative is chosen. There is one outcome per product in the period selected for analysis. 23 The Five Models The common framework introduces the basic logic to be used in deciding whether to postpone or speculate on the distribution of a product. The four models for form postponement and the model for time postponement have distinctive characteristics that differentiate them from each other. Table 1.1 summarizes the discussion on the five models, the costs involved in the distribution of a product in each one, and the type of firm that would be most appropriate to the application of each model. Each model is identified with a letter. The labeling postponement-speculation model is Model A, the packaging postponement-speculation model is Model B, the assembly postponement-speculation model is Model C, the manufacturing postponement-speculation model is Model D, and the time postponement-speculation model is Model B. The major characteristics of each model are presented below. Each model is presented in full detail in Chapter III of this dissertation. Model A, labeling postponement-speculation, shows a trade—off between two basic alternatives. In the first one, speculation, labeling of the products is done at the plant level, based on the forecasted demand for each brand of the product at each market. In the second alternative, products 24 momsocouoa cownsafiuuowo no woman: omuoa a nu“: mauwm muosooum mcausuoouscos mcamsonouoz mumoo Oswauuoo >uouco>CH cowumauoucw a oswmmooouo uoouo osao> afics noes saws maufim cofiuouuommcmua oaws m moaom umoa no umou Amcwuzuoouscoav ocwmmoooum oaowuouma mswosocouos msouwsowns no cowuuomoum no“: a mumoo unwauuou >uouco>cH saw: muosooum Haou non» mauwm c0auouuommsous ocwusuoousca: o ooanaommoc: oommucm moaoo umoa uo umoo aw ooosoou aauoouo ow onso Axunaoomov mswmmoooum omocs uosooum o Haom was» usuam mcwmsocoumz manna coaaoo cuwa mausooun mumoo mcwhuuoo >uouco>cH ucouomuwo Haoo vac» mahwm cowuouuommcoua >anaomm< o mouoo uooa uo umou .ocwmoxoomv mswmmoooum mswmsocouMS monam ovmxooa Houo>oo mumoo ocwhuumo auouco>cH uoocs uosooum a ”How pun» mauwm cowumuuommcoua ocwmoxoam m Amcaaonoav ocwmmoooum moans ocmua Houo>oo ocflmsosouos woos: uosooua o Haoo vac» mauwm mumoo osfiauuno >uouco>cn mcaaonma 4 mauwu ooumououcH oo>Ho>cw mumoo cofiuoasoodm Hoooz tucoaocomumom I" to 25 are shipped to the warehouses without labels, and labeling is done at the warehouse level, after the brand has been ordered. The model assumes that the product under analysis is marketed under different brands. Model B, packaging postponement-speculation, follows the same logic. It assumes that one particular product is marketed in different package sizes. In the speculation alternative, products are sent packaged from the plant to the warehouse. In the postponement alternative, products are sent bulk to the warehouse, and packaged in response to customer orders. Model C, assembly postponement speculation, weighs the alternatives of full assembly at the plant level, as opposed to shipments of unassembled goods to the warehouse level, where products are to be assembled. Model D, manufacturing postponement-speculation, does not differ in logic from the previous ones. In speculation, products fully manufactured at the plant are shipped to the warehouse in anticipation of customer orders. On the other hand, in postponement, product parts are sent to the warehouse where products are manufactured. At this point, it is important to clarify the basic distinction between models C and D. In assembly postponement-speculation all products shipped to the warehouse come from a single location. In manufacturing postponement-speculation parts arrive at the warehouse from several original locations. 26 In Model B, time postponement-speculation, speculation refers to a decentralized inventories system wherein products are shipped to warehouses as they are produced. In time postponement, products are shipped to the warehouse only after demand has been generated, and, therefore, inventories are centralized. The final issue discussed in this part is computer simulation. Computer Simulation Question three of this research studies the relationship between the cost of postponement-speculation and product physical and demand characteristics. With that focus, the normative cost models are reproduced in a computer simulation. There are five applications of the simulator, each corresponding to one of the normative cost models. The inputs to the simulator are a number of variables such as the level of demand or the value of the product. The mathematical relationships in the simulator are defined according to existing business logistics theory. The output of the simulator determines the decision to postpone or to speculate on the distribution of a product, based on minimum cost computations. Before the simulator is used to test the relationships hypothesized between cost and physical and 27 demand characteristics, it is validated. Validation procedures are detailed in Chapter III. MEIEQDQLQ§X_QEEB¥IEE This research generates twenty hypotheses relating the cost of postponing or speculating on the distribution of a product, to the product's physical and demand characteristics. For the five models, there are a total of twenty such hypotheses. Each model has an independent set of product physical and demand characteristics. In order to generate data for the test of hypotheses, product physical and demand characteristics are chosen as input variables to the simulator, and a range defined for each. Within that range, a number of value levels is determined. The input variables are applied to the validated simulator, and a dichotomous (postpone or speculate) output is obtained. To test the hypotheses and also to decide on which of the input variables is more important to the decision to postpone or to speculate on the distribution of a product, a discriminant analysis is performed, with postponement- speculation as the dependent variable and the simulation input variables as the independent variables. The absolute size of the discriminant weight is used to determine the relative importance of each independent variable, while the 28 sign of the discriminant weight is used to accept or to reject a hypothesis. The first contribution of this study is the normative cost models themselves. They aid manufacturing companies to optimize decision making in postponement-speculation. The second potential contribution evolves from the first. Better postponement-speculation decisions can contribute to productivity improvement in physical distribution systems. Third, the research adds to the few instances of empirical work in this area available for managers and academicians. Fourth, at a theoretical level, the research tests a number of hypotheses relating product physical and demand characteristics to the cost of postponing or speculating on the distribution of a product. The results not only indicate directionality, but also quantify the strength of the relationships. Fifth, the study presents a methodology enabling managers to predict whether the distribution of a product should be postponed or speculated on in the context of a specific firm. 29 Sixth, it may represent a stimulus for researchers to develop studies concerning the theoretical advancement and new potential applications of the principle of postponement- speculation. Finally, at the application level, the study may be a starting point for practitioners and researchers to develop similar studies in related areas not addressed in this research, such as distribution channels. Léfllléllgflfi This research has three general limitations. First, in an effort to maintain the problem within manageable proportions, the models are kept at the firm level, and therefore other channel institutions involved in the distribution process are excluded. Second, decisions in the business community are not made on the sole basis of cost. Investment is also a factor. For instance, a decision to postpone in time will most likely require the rearrangement of warehousing facilities. However, the analysis of investment alternatives has been extensively addressed in the business logistics, finance, and economics literatures. Third, there is the limitation generally attributed to static simulation models: the absence of a time dimension causes the research to leave out the longitudinal effects of 30 the decision under study. The remainder of this dissertation is organized as follows. Chapter II contains a review of the literature on the principle of postponement-speculation and on computer validation methodology. Chapter III presents in detail the normative cost models, the computer simulation, the research hypotheses, and the methodology to generate the data and to test the research hypotheses. Chapter IV presents the analysis of the results. The conclusions and implications, and the suggestions for further research are in the last chapter. Appendix A contains the raw data, so that the research can be replicated by the reader. A literature review of an area where so little has been written about should go beyond those articles dealing specifically with the issue under study. It should also address some subject areas where the issue could have, or even should have, been considered. As stated in Chapter I, this dissertation focuses on the importance of the principle of postponement-speculation for increasing the efficiency of physical distribution systems. The underlying logic for the principle is the notion of timing. When, in the performance cycle, should a product be moved through the distribution system: prior to or after the receipt of the customer's order? Similarly, it relates to the extent to which products will be moved through the distribution system in a semi-finished or ready- to-be-sold state. At what level in the channel, plant or warehouse, should the product be given its final form? To some extent, these questions were asked before in the business logistics literature. Yet, they also concern related business disciplines such as marketing and 31 32 production. Ballou (1973, p. 362) points out that the interface between logistics and production lies in the areas of production scheduling and management of finished goods inventories. Clearly a decision to link production of an item to the receipt of a customer order will affect, if not determine, the scheduling of production. Nevertheless, a review of recent literature in the production-logistics interface, especially what concerns some approaches proposed by operational researchers, reveals an implicit assumption that distribution systems are speculative; i.e., goods are moved to the finished goods inventory once produced, and are produced to stock based on the assumption of an accurate sales forecast. The review of the production-logistics interface extends to an assessment of the most popular production systems, such as just-in-time production, materials requirements planning and flexible manufacturing systems, in an effort to understand the interrelationships between each and the principle of postponement-speculation. Finally, one other pertinent body of literature is the issue of computer simulation, especially what concerns validation. Validation of a simulation model is a fundamentally important step in establishing its credibility, and must be adequately addressed if results are to be called empirical. 33 Therefore, the literature review is organized in four sections. The first reviews the historical development and the previous studies in the principle of postponement- speculation. The second reviews production and distribution decision models from the operations research literature. The third section takes a broader, conceptual, look at the production logistics interface, especially the impact of different production systems on postponement-speculation decisions. Finally, the fourth section reviews the utilization of computer simulation in business logistics from two different perspectives: an examination of past applications of computer simulation in business logistics problems and how the models were validated: and a general overview of general validation procedures proposed by authors in computer simulation. The original article by Alderson (1950, p. 3) defined the principle of postponement as it is currently referred to in the literature. The two major writings on the subject that followed Alderson took opposite directions. Bucklin (1965) extended the time postponement principle to include its opposite--speculation--and applied it to understand the formation and change of channels of distribution structure. Subsequently, Bucklin (1966) included the principle as one 34 of the touchstones of his overall theory of channel structure. Bowersox (1978, p. 281-3) extended the principle of postponement in its applicability as an instrument to improve physical distribution and marketing channel efficiency. Instead of describing the formation of a theoretical channel structure, the principle became a managerial alternative to counter the anticipatory nature of most logistical systems. Several other authors made reference to the principle. Christopher (1985) stressed the strategic importance of form postponement in reducing inventory levels and pointed to the growing role of flexible manufacturing systems in generating form postponement opportunities. Heskett (1977) restated the importance of the principle of postponement as an effective way to provide a large number of items from a smaller number of standardized components that are mass produced and distributed. Sharman (1984), without utilizing the term "postponement," made reference to the "point at which a product becomes earmarked for a particular customer" as a key input in the design of logistics systems. The point is labeled as the order penetration (OP) point. Moving the 0P up or down the distribution system provides different cost vs. service alternatives. The author hypothesized, but did not test, that the greater the level of competitive 35 pressure, "the greater the incentive to provide better service by moving the 0P point downstream and increasing the models available from stock." Such hypothesis ignores the equally relevant effect of form postponement on delivery time and product quality. Shapiro (1984) analyzed the impact of different levels of postponement—speculation and the breadth of the product line as determinants of four alternatives for designing the firm's logistical strategy. The argument is based on the concept of time postponement-speculation, although form posponement-speculation was used in the definition of the term. Such conflicting statements can be explained by the author's implicit assumption that made-to-stock inventories are always decentralized and made-to-order inventories are always centralized, which clearly is not true. A number of practical applications of the principle of postponement have been reported in the literature. Cox and Goodman (1956) looked at the principle as a way to improve efficiency in the channel of distribution for homebuilding materials. Stainton (1978) reported an interesting application of the principle of postponement-speculation to solve a production scheduling problem for a manufacturer of canned soup. Because most demand for the firm's products took the form of numerous private labels, accurately forecasting the demand for each label proved a problem. One alternative considered was redesigning the manufacturing 36 plant so that the labeling process could be postponed until the order was received. Stainton failed to report whether the alternative was adopted. The proliferation of real-time ordering systems, as well as overnight delivery systems, led some distributors of electronic components to reduce the number of stocking locations in favor of a greater centralization of inventories (Temin, 1985). The principle of postponement-speculation was used to explain the emergence of a direct channel structure for the distribution of cement between 1959 and 1963 in California (Bucklin and Halpert, 1965). Similarly, Adams applied the principle to explain long term institutional change in the appliance industry (1977). This section reviews papers in operations research that have addressed the problem of manufacturing and distribution programming. The review shows that the operations research literature developed mathematically sophisticated solutions for the problem of scheduling production and distribution, but failed to consider alternatives that could be generated with the principle of postponement. In general, these models explicitly or implicitly assume that products will be moved in anticipation of demand, and that firms speculate 37 in form. Damon and Schramm (1972) present a joint production, finance and marketing model where non-linear programming is employed to optimize decision making in the firm. Two models are compared, simultaneous decision making and sequential decision making, by which marketing decisions are input to the other two areas. The marketing sector of the model is a demand function whereby sales are a function of past sales, price and advertising levels. Welan's (1977) later criticism of the model was directed to the form of the demand function, but did not alter its anticipatory nature. Folie and Tiffin (1976) selected a similar approach. An algorithm is developed to optimize the production and distribution of two brands of snack-foods manufactured by the same firm. One of the brands is sold in six package sizes and the other in three. The products are manufactured in seven plants, three of them common to the two brands. Different factories have different packaging and cooking capacities. The aim of the algorithm is to minimize cost, but there is no consideration of postponing packaging from the manufacturing to the warehouse level. Three additional examples of manufacturing distribution opitimization problems are worth mentioning. As in previously discussed problems, no postponement alternative is considered. Moore (1980) suggests a computer modeling approach to the determination of an optimum number and 38 location of distribution centers, given variations in demand, product mix and in-house or contracted manufacturing. Mairs et.al. (1978) attempt to allocate sales demand centers to manufacturing facilities with the help of mixed integer programming. The objective is to minimize manufacturing and distribution costs, where distribution costs are a function of transportation cost factors. Williams (1981) has compared seven heuristics for minimizing joint production and distribution costs. Form is assumed to be speculated at the manufacturing level, and demand is assumed to be deterministic (no uncertainty). Consequently, because backlogging and lost sales are not computed in the comparison, the practical uses of the heuristics are seriously constrained. Huge (1979) presents an alternative approach. Rather than a cost optimizing model, management of manufacturing lead times is suggested as a way to coordinate marketing's need to respond to demand uncertainty and production's need to minimize cost. The shorter the lead time'for assemblies and component parts, the faster the firm's ability to respond to needed variations in product scheduling with minimum impact on manufacturing and distribution costs. Lead times can be accelerated within the firm in the manufacturing of sub-parts, or external to the firm in the negotiation of lead times with vendors, where system inventories are shifted to suppliers. 39 P O S IB ON CE The interdependence of the production and distribution functions for the firm's overall management has led to mutual expectations for the performance of each function. Such dependence often causes organizational conflict. Shapiro (1977), has detailed eight areas of potential conflict between the marketing and manufacturing functions of the firm. The principle of postponement-speculation could help in at least two of those areas. The first stresses the importance of sales forecasting to schedule production. The role of form postponement in compensating the need for sales forecasting by adding flexibility to the production scheduling process was mentioned already. The second area is the breadth of the product line, where economies of scale must be balanced against the idiosyncratic needs of individual consumers. Form postponement can allow for a broader product line without overbearing production capacity and inventory carrying costs. Interestingly, Shapiro's brief mention of Martin Starr's (1965) suggestion that products be manufactured from interchangeable modules is itself a special case of form postponement. The relationship between the production and distribution functions in the firm are further affected by 40 the firm's choice of the production operation system. Three of the most popular systems, Materials Requirements Planning (MRP), Kanban (JIT) and Flexible Manufacturing Systems (FMS) are briefly reviewed in terms of their postponement- speculation implications. The objective of MRP systems and their outbound counterpart, Distribution Requirments Planning (DRP) is to minimize the level of inventories in the firm or channel of distribution (Stenger and Cavinato, 1979: Aggarwal, 1985). Needs for parts and raw materials are determined by accurately forecasting the demand of finished products, with needs for parts and subassemblies treated as derived demand (Stenger and Cavinato, 1979, p. 1). Forecasting, therefore, is required but once at the system output level. Consequently, MRP/DRP logic is inherently speculative. It has been increasingly adopted by U.S. manufacturing firms, especially large ones with complex production processes (Anderson et.al., 1982). MRP/DRP systems affect time postponement decisions because centralized inventories allow for the unification of the demand forecast for several markets. Therefore, the dependence of MRP systems on the accuracy of sales forecasting can be reduced. Similarly, MRP/DRP systems are impacted by form postponement-speculation because the variations in the demand can be equally consolidated. On the other hand, some manufacturing operations are performed 41 at the warehouse level, thereby increasing the level of in- process inventories. Kanban or just-in-time production systems are based on a different set of principles. As in MRP systems, in- process inventories are greatly reduced and safety stocks totally eliminated. In addition, because production lots are rather small, fast machine setup times are needed. The final two system characteristics of relevance to postponement-speculation decisions are the frequency and consistency of delivery times required from suppliers, and the long-term relationships that must be developed between manufacturers and suppliers (Jackson and Morgan, 1983). The relevance of JIT systems for postponement- speculation decisions is twofold. First, lack of safety stocks and relatively small delivery lot sizes force inventories up the channel. JIT systems, then, are based on an assumption of time postponement in the channel of distribution. Second, the fact that production lot sizes are small and that machine setup times are short, present an opportunity to postpone form. Common parts among different products could be produced under a JIT system, while product idiosyncrasies are added at the warehouse level. This is particularly important if it is recognized that JIT systems operate less well when load fluctuations exceed 10 percent (Aggarwal, 1985, p. 9). 42 The emergence of Flexible Manufacturing Systems is a recent phenomenon. The proliferation of robotic systems has been responsible for great improve ments in manufacturing's ability to turn out a great diversity of products at low unit costs. Flexibility is the key factor in these systems. Production cells can switch the product being manufactured in less than ten minutes (Production Engineering, 1984). This ability to turn out a great variety of products opens new perspectives in the integration of marketing and manufacturing. With FMS, inventories no longer build up to accomodate economies of scale in production. In that regard, the principle of postponement—speculation and the concept of flexible manufacturing systems may also effectively reduce marketing risk from demand uncertainty. Still, there are differences. FMS requires the centralization of production, and inventories are therefore likely to build up at the warehouse and retail levels, while form postponement-speculation maintains the level of inventories low throughout the channel of distribution. Also, while FMS and the principle of postponement- speculation are effective at reducing marketing risk with nmnufacturing and assembly operations, the principle of Postponement-speculation provides additional risk reducing oPportunities by postponing labeling and packaging. 43 §IMHLAIIQH_AED_LQ§1§II§§ Computer simulation is one of the most widely utilized quantitative techniques in the design of logistical systems. Although it will not provide optimal or near-optimal solutions per se, it is a powerful tool to test hypotheses prior to the commitment of resources (Bowersox, 1978, p. 354). In this review, the role of computer simulation in the study of business logistics is examined from two different perspectives. First are the applications of computer simulation to logistics. Next is an examination of simulator validation techniques useful in this study. One of the earliest applications of simulation in the field of logistics is the Kuehn and Hamburger model, a static simulation program to help in the location of warehouses (Kuehn and Hamburger, 1963). The model inputs include factory locations, potential warehouse sites, the number of warehouses to be evaluated in each cycle, shipping costs, sales forecast for each customer, warehousing costs and customer sevice. The output involves the number and location of warehouses that will minimize distribution costs. Another application of static simulation is Shycon and Maffei's (1960) model. Developed in a study for H. J. Heinz Co., the findings include the optimum number of warehouses 44 needed for their national distribution system, and the capability to experiment with alternative warehouse locations. The authors claimed that the model would also be effective in other cost minimization studies, in product mix decision making studies and in studies that included time as a variable (dynamic simulation). Two out of three more recent applications of computer simulation to logistics problems are dynamic in nature. Walter (1981) developed a static computer simulation to test an industry cost model designed to help analyze the effects of several alternative packages on the total cost of the firm. The model includes the specific costs to be considered in the decision, the system relationships, and the computer algorithm. Although briefly mentioned, model validation procedures are difficult to reproduce as reported. McDermott, Stinson and Koprowski (1979), used a dynamic simulation approach to analyze the distribution system for a consumer electronics products firm with two overseas plants. The objective of the model is to minimize total cost, with special focus on shipping costs -- a critical factor in their particular system. The model is validated by comparing expected and past actual data for the firm studied. More recently, Closs and Law (1984) applied simulation ‘to compare the performance of logistics systems with respect 'to environmental uncertainty and alternative inventory 45 management policies. The issue of validation has long been a concern in the area of computer simulation. Although different authors present different approaches to validating simulations, the basic logic is similar, as are recommended tests and precautions. The remainder of this chapter reviews the literature on some procedures to validate computer simulations. Schmidt and Taylor (1970) suggest that the distribution of data inputs be validated with goodness-of-fit tests to see if actual input distribution fits the expected distribution. The Kolmogorov-Smirnov test or the chi-square test are presented as adequate for this purpose, and an alpha level of 5 percent is suggested. In addition, the simulator must be checked for logic errors by comparing computer and hand calculations for a number of runs. Simulated and real system output comparisons confer additional credibility to the model. Kleijnen (1974) proposes a more comprehensive validation program. As in Schmidt and Taylor, program debugging with hand calculations, comparison with historical data, and goodness-of-fit tests to input data should be performed. Furthermore, the simulator should be run several times with deterministic values or very low variances to see if the behaves as the theory prescribed. 46 In addition, a five step validation procedure is forwarded by Teorey (1975). 1. Testing of the authenticity of the random number generators and random variate generators. 2. Verification of distributional properties of the independent variables (exogenous variables or factors) established for the model. 3. Proper choice of dependent variables (endogenous or response variables) to observe in the model and the actual system. 4. Choice of statistical tests on both independent and dependent variables. 5. The ability to predict system performance due to future changes in the actual system configuration. Teorey's steps are specifically designed for static models. Two points are key in Teorey's validation criteria. One, if several models are used in the same project, checking the random number generator once suffices. Two, the level of confidence in the model can be improved with a test of normality. In such a test, the simulation is replicated N times until the distribution of outputs takes the form of a normal distribution. Once normality is assured, parametric tests for the mean (student's test) and the variance (Snedecor's F-test) can be used to compare simulated to real system data. The number of replications (N), should be large enough to establish 95% confidence of normality. Geoffrion (1976) reports on the validation procedure used in a dynamic simulation project at Hunt-Wesson Foods, Inc.. The simulation was validated at two levels. In the technical validation level, modellers were faced with two questions. Is the data input consistent with what was 47 intended? Does the algorithm manipulate the data as intended? The paper offers no insights on approaching the questions. In the managerial validation level, confidence in the model was achieved by comparing simulated and actual historical system data. In addition, Geoffrion suggests running restricted cases where the variance of the inputs is limited to see if the model behaves as predicted with manual calculations or by simple inspection. Finally, several versions of the same case should be changed in a systematic way to see if theory or managerial insight can predict output. A distinction between building confidence in the model as well as in the simulator is proposed by Lehman (1977). Although earlier authors have validated models and simulators, Lehman provides and defines terms to distinguish the two. The process by which the model is checked for its accuracy in reproducing relationships from the actual system is named "validation," while the accuracy of the computer algorithm to reproduce the model is termed "verification." This work differentiates itself from earlier works for its scientific approach, as opposed to managerial applicability. Indistinguishability tests is the basic validation procedure suggested by Lehman. These tests are based on the well known Turing test, whereby an evaluator is simultaneously exposed to actual and simulated data, and tries to identify them. The model is considered valid if the 65-! '1' '-.‘a. l. ‘7 i ..-.A ..- A. ,. ..lE 48 evaluator is unable to distinguish them. Bowersox et. al. (1979) provide a thorough application of validation procedures to a logistics related dynamic simulation. Validation of the model is achieved by addressing two general issues: validation of the model itself and validation for a specific application. Validation of the model itself, which has also been termed "verification" or technical validation else in the literature, is established by addressing Emshoff and Lisson's (1970) four questions: 1. Do the basic programming techniques used to implement the model operate correctly? 2. Do the physical distribution activities, as implemented in the model, operate as intended, and are the activities satisfactory to analysts and decision makers? 3. Does the model converge to a steady-state condition and remain there over time? In particular, do the initial starting conditions or different random number streams have any significant effect on model performance? 4. Do the values of the target variables respond logically to changes in parameters and exogenous factors? Some of the procedures adopted to establish model validity can also be useful in static simulations. The simulator was evaluated with manual tracing of individual orders that were compared to the simulated outcome. Very high and very low values were assigned to inputs to check their effect on the outcome. Furthermore, experts were asked to assess face validity on the model's assumptions, the expected performance, and the clarity of the reports to 49 be generated. Application validity is addressed with a test of model fit to the expectations of analysts and decision makers, with a test of fit to real system historical data, and a test for the impact of start-up conditions on simulation output. Sargent (1979) contributed to the issue of validation of simulations with a general review of existing techniques and a framework for their application. At least three areas should concern the modeller; the correctness of the model's underlying assumptions, the correctness of the parameters and the statistical distributions, and the adequacy of the input-output transformations. The author provides a list of validation procedures to be considered by the modeller. In his view, a simulation model is developed for a specific purpose, and it is against that purpose that the model should be checked for validity. Therefore, no overall procedure can be applied in every case. The modeller must select from a pool of techniques the ones that will maximize the credibility for his model. Of the twelve techniques suggested, all but two were not reviewed elsewhere in this chapter. First, results of one model could be compared to results of another model already validated. Second, a model could be evaluated by using live graphics to test its operational validity. 50 In a subsequent review article, Sargent (1982) included the internal validity test. It is similar to Teorey's notion of a test of normality. The model should be replicated to check for the amount of stochastic variability of the output. High levels of variation will reflect a lack of model stability, and deem results as questionable. In summary, a wide range of techniques are available to verify and to validate computer simulation models. The overall logic of the process starts with a test of randomness and frequency distribution for input data, and a test of the simulator's adequacy to capture all aspects of the analyst's model. Finally, the model's accuracy in reproducing the system it claims to reproduce must be demonstrated. QEAEIEB_IIL ARCH S GN The purpose of this chapter is to present the normative cost models, the computer simulation, the research hypotheses, and the methodology. The chapter is structured in three sections. The normative cost models, a step-by-step procedure to enable managers to collect and organize data for a decision on postponement-speculation, are introduced in the first section. In the second, the computer simulation is introduced. It includes the simulator and its five applications, needed to generate the data to test the research hypotheses. In the third section, methodology, the research hypotheses and the hypothesis testing methodology are presented. IEE_EQBMAIIEE_QQ§I_MQDEL§ As suggested in the first chapter, the five normative cost models introduced in this section are independent. However, they follow the same logic, and, therefore, a common framework for all models is presented first. The section on the normative cost models is divided in six 51 52 parts. The common framework appears in the first part, while the next five parts present the five models. A number of assumptions are addressed in the common framework. First, the framework is built from a manufacturer's perspective. The manufacturer is assumed to have a sufficient level of channel power to decide on the level of postponement-speculation that will minimize its total cost to distribute one unit of product. Second, the outcome of the normative cost models is one decision per product as opposed to one decision per firm. Third, the segment of the distribution network to be modeled is the plant-warehouse. One plant and three warehouses are assumed. Fourth, the status quo for all decisions is assumed to be speculation, to reflect the majority of logistical systems presently in operation. Consequently, in the time postponement-speculation model, form postponement is assumed; while in the form postponement-speculation models, time speculation is assumed. Finally, the models are designed to be static. Costs are computed for a single period in time. A decision in form postponement-speculation can occur at four different processing levels; labeling, packaging, assembly, and manufacturing. These four levels, together with time postponement-speculation, provide the basis for 53 developing the five normative cost models. Although not all costs are relevant to every model, the cost categories included in the analysis are the following: customer service level (cost of lost sales), processing (labeling, packaging, assembly, or manufacturing), inventory carrying costs, warehousing, and transportation. Order processing and information costs are assumed constant in this study. Costs are to be computed at the plant and the warehouse levels. In the case of speculation, the status quo alternative, costs can be measured. In the case of postponement, costs have to be estimated. The objective is to determine which alternative, postponement or speculation, is the lowest cost approach to distributing a product. The approach to the models is based on direct cost. A direct (or variable) costing system is considered better for management information systems because it minimizes the problem of allocating fixed costs, and the distortions that result from it. In a direct costing system, the criterion for assigning costs to a cost segment, product in this case, is all variable costs plus fixed costs directly attributable to that segment. The test to determine which costs are "directly attributable" to the product is to consider the costs that would be eliminated if the segment (product) is eliminated. The other cost concept of relevance to the normative cost models is the idea of incremental costing: that is, 54 only costs that are directly affected by the decision to postpone or to speculate on the distribution of a product are considered in the models. The common framework to the five postponement- speculation models to be introduced is an eight step normative cost model based on two cost concepts: direct costing and incremental costing. By definition, direct costs can be directly traceable to one particular segment (product) and would be eliminated if the product is also eliminated from the firm's product line. This includes variable costs plus non-allocated fixed costs. Incremental costs are defined as the difference in cost between two alternatives. Thus, the normative cost model is based on direct and incremental costs. Next, the eight steps of the common framework to the five postponement-speculation models are presented, step by step. Figure 3.1 summarizes the common framework: 1.Define Market to be Studied - the market must be defined in the number and location of delivery points in the system, as well as the number of plants and warehouses utilized in supplying that market. 2.Define Period of Analysis - the normative cost model has been presented as a static model. The period of analysis must be defined to guide the calculation and estimation of costs. 55 W NORMATIVE MODEL FOR POSTPONEMENT SPECULATION DEFINE MARKET TO BE STUDIED l DEFINE PERIOD OF ANALYSIS l DEFINE ALL PRODUCTS SUPPLIED TO THE MARKET IN THE PERIOD l DEFINE REQUIRED CAPABILITY AND AVAILABILITY DETERMINE STATUS QUO. (DIRECT COST PER UNIT OF PRODUCT. FOR ALL PRODUCTS) ESTIMATE DIRECT COSTS AFTER (PER UNIT 0F PRODUCT. FOR ALL PRODUCTS) l CALCULATE DIRECT PRODUCT COST (PER PRODUCT . FOR ALL PRODUCTS) l POSTPONEOR SPECULA‘IE 56 3. Define All Products Supplied to the Market in the Period - all products to be distributed in the defined period of analysis to the defined market under study must be clearly identified. The model will produce one outcome--postpone or speculate--for each product. 4. Define Required Capability and Availability - capability and availability are two measures of customer service. The former refers to the absolute time and consistency involved from the moment a customer places an order to the time of the actual delivery of goods. The latter refers to the extent to which ordered goods are available in the vendor's inventory. The level of customer service has a significant impact on the cost of delivering goods. 5. Determine Status Quo - the status quo is defined as the direct cost of distribution per period, for each product, under the alternative of speculation. 6. Estimate Direct Costs After Postponement - if the status quo is assumed to be speculation, direct costs under the alternative of postponement must be estimated. There is one estimation per product, per period. In this estimation, it is important to consider the level of customer service defined in step four. 7. Calculate Direct Product Costs per Product, For all Products - the direct cost per product is the difference between the measured costs of speculation 57 (step 5) and the estimated costs of postponement (step 6). 8. Postpone or Speculate - the outcome of the model. There is one outcome per product, per market being studied in the period of analysis. The question addressed in this model is as follows: Should or shouldn't the firm postpone the labeling of a product to the warehouse level? The criterion for approaching this question is the least cost alternative between labeling at the plant and labeling at the warehouse. In the alternative of postponement, goods are moved to the warehouse in a package, but without a label identifying the product's brand. The label is added at the warehouse when the product is sold. In order to consider the advantages of postponement, the firm must sell the product in more than one brand. Figure 3.2 presents the system to be modeled. In Model A, the following cost categories are involved: labeling, inventory, and warehousing. Each is discussed below. Labeling costs are affected in two ways. One, labeling equipment has to be purchased for each of the three warehouses. The fixed cost is equal to the total investment multiplied by the hurdle rate. The hurdle rate is defined as 58 W MODEL A - LABELING POSTPONEMENT-SPECULATION SPECULATION - labeling a: plant. non-consolidated invenuory a: warehouse: AREI-IOUSE I mung-I FM" TEE-FE muse 3‘ _ p71,...m POSTPONEMEN'T - Labeling at warehouses. consolidated inventory at warehouaes WAREHOUSE 1 _ pa 1 mouse 2 1 mm PR 1 AREI-IOUSE 3 2 PR 1 PR 1 -product 31.... 36 - brands 59 the rate of return on the investment for best alternative use of the money. The capital costs at the plant level are assumed to be sunk, since the status quo is assumed to be speculation, and labeling equipment at the plant level is in place already. Two, in the alternative of postponement, labor costs are higher, because labor is needed in three different warehouses, and the equipment operates at a lower scale, which tends to be more labor intensive. Savings per unit of product in the alternative of postponement are equal to the difference in labor/hours to label one unit at the plant and one unit at the warehouse, multiplied by the labor cost per hour. The cost of direct materials is assumed constant. The base stock, the level of inventory needed to operate in a risk free environment, is not affected by the decision to postpone or to speculate because the overall level Of demand remains the same. Inventory carrying cost savings from postponement derive from reductions in‘the safety stock, which is the additional level of inventory needed for the firm to cope with the uncertainty of demand variability and the variability in the lead time for the supply of raw materials. Savings in safety stock in the alternative of postponement are estimated in the following manner. The first step is to determine the number of standard deviations of demand kept as safety stock for the product. Since the level of inventory availability is to be 60 kept constant, that safety stock protection level is used in the estimation of the safety stock after postponement. In the second step, the level of safety stock after postponement is given by the number of standard deviations of demand kept as safety stock, multiplied by the standard deviation of the total demand for the product being analyzed, multiplied by the product value, multiplied by the percentage used by the firm as the inventory carrying cost. In the third step, the cost of safety stock in the alternative of speculation is given by the number of units kept as safety stock for each brand, multiplied by the product value, multiplied by the percentage used by the firm as inventory carrying cost. Finally, in the fourth step, the costs for all individual brands are added to obtain the product total. Savings from postponement are arrived at by the cost difference in the two alternatives. In warehousing costs, two categories are examined. Handling costs are not accounted for separately in the postponement-speculation decision because additonal handling in the alternative of postponement is included in the labeling cost. Storage costs are affected because safety stocks are. If the firm uses public warehouses, the reduction in storage cost equals the reduction in safety stock in units, multiplied by the warehousing charge per unit. If the public warehouse charges a period fee, that must be treated as a period cost. If company operated 61 warehouses are utilized, the reduction in storage costs in the alternative of postponement can only be computed if there is an alternative use for the additional space available. If that is the case, the storage space cost per square foot is multiplied by the number of square feet saved with postponement to derive the value of savings. Figure 3.3 presents a framework for calculating the cost advantage or disadvantage of postponement relative to speculation. The figure includes all logistics costs involved in the decision. A negative sign means that the cost of speculation is lower than the cost of postponement for a particular cost category, while a positive sign means the opposite. The net effect of labeling postponement is the sum total of all costs. A positive sign in the bottom line means that the firm should label the product at the warehouse level (postponement), while a negative sign means that the firm should label the product at the plant level (speculation). Mod B - c a ' st 0 - e ' n The question addressed in this model is as follows: Should or shouldn't the firm postpone the packaging of a product to the warehouse level? The criterion for approaching the question is the least cost alternative between packaging at the plant or at the warehouse. 62 IEIQQBE_212. DIRECT COST PER PRODUCT Variable Costs Labeling cost at warehouse - Labeling cost at plant + Inventory carrying cost + Warehousing cost + Variation in variable cost per unit due to potponement Unit variation in variable cost x total demand for product W Warehousing fixed cost in the period - Labeling equipment fixed cost in the period - - MODEL A + or - + or - + or — 63 In the alternative of postponement, goods are moved to the warehouse in bulk, with a low cost protective package for transportation purposes. The package is added at the warehouse when the product is sold. The cost of labeling the product once it is packaged is included in packaging costs. A problem to estimate costs in the alternative of postponement is the need to define a unit, since the product is shipped in bulk. The criterion is to define a unit as the amount of product contained in the smallest package size offered to the market. Figure 3.4 presents the system to be modeled. In Model B, the following cost categories are involved: packaging, inventory, warehousing and transportation. Each is discussed below. The impact of postponement on the packaging cost is threefold. One, packaging costs at the plant level are eliminated, and savings are computed as the average number of hours to package one unit of product, multiplied by the labor cost per hour. Two, there are additional packaging costs at the warehouse level. It includes the packaging equipment costs multiplied by the hurdle rate (a fixed cost), and the additional labor cost to package the product at the warehouse level (a variable cost). Three, if necessary, an additional packaging cost is needed at the plant level for protective purposes in the transportation process. The protective package must be removed at the warehouse. The costs related to additional 64 W MODEL B - PACKAGING POSTPONEMENT-SPECULATION SPECULA’TION - Packaging at plant. mn-cmuolldated inventory a: warehouse». packaged msponation mouse 1 mmfs I I AREIIOUSEZ m Emma-l mamas] % mum-.1 POSTPONEMENT - Packaging at warehouses. canolidand inventory a: waxehouaea. bulk Wm ARH'IOUSE I PR1 ARE-IOUSE 2 PR 1 ARE-IOUSE 3 PR 1 PR 1 - product Pl ..... P6 - package sizes 65 protective packaging are additional labor and packaging materials, which are variable costs. The base stock is not affected by the decision to postpone or to speculate because the overall level of demand remains the same. Inventory carrying cost savings from postponement derive from reductions in the safety stock. In the alternative of postponement, savings from the reduction in safety stock are estimated in the following manner. The first step involves determining the number of standard deviations of demand kept as safety stock for the product. Since the level of inventory availability is to be kept constant, that safety stock protection level is used in the estimation of the safety stock after postponement. In the second step, the level of safety stock after postponement is given by the number of standard deviations of demand kept as safety stock, multiplied by the standard deviation of the total demand for the product being analyzed, multiplied by the product value, multiplied by the percentage usedrby the firm as the inventory carrying cost. In the third step, the cost of safety stock in the alternative of speculation is determined by the number of product units kept as safety stock for each package size, multiplied by the product value, multiplied by the percentage used by the firm as inventory carrying cost. Finally, in the fourth step, the costs for all package sizes are added to reach the product total. Savings from postponement are arrived at by the cost 66 difference in the two alternatives. In warehousing costs, two categories are examined. Handling costs are not accounted for separately in the postponement-speculation decision because additional handling in the alternative of postponement is included in the packaging cost. Storage costs are affected because safety stocks are affected. If the firm uses public warehouses, the reduction in storage cost is equal to the reduction in safety stock in units, multiplied by the warehousing charge per unit. If the public warehouse charges a period fee, it should be treated as a period cost. If company operated warehouses are utilized, the reduction in storage costs in the alternative of postponement can only be computed if there is an alternative use for the additional available space. If that is the case, the storage space cost per square foot is multiplied by the number of square feet saved with postponement to get the value of savings. The last cost category in Model B is transportation. If the firm utilizes for-hire transportation, the carrier supplies the cost estimates in the two alternatives are. If the fleet is company operated, line haul costs for both alternatives is determined by the cost per ton/mile to haul the product, multiplied by the product's weight, multiplied by the average distance from plant to warehouse. The cost of loading and unloading is measured by the number of hours needed to load or unload one unit of product, multiplied by 67 the labor cost per hour. If new equipment is needed to haul the product in bulk, the cost is estimated by the net investment in new equipment multiplied by the hurdle rate. The difference in cost between the two alternatives is given by the difference between shipping goods packaged or in bulk. Figure 3.5 presents a framework for the calculation of the cost advantage or disadvantage of postponement relative to speculation. The figure includes all logistics costs involved in the decision. A negative sign means that the cost of speculation is lower than the cost of postponement for a particular cost category; a positive sign means the Opposite. The net effect of packaging postponement is the sum total of all relevant costs. A positive sign in the bottom line means that the firm should package the product at the warehouse level (postponement); a negative sign means that the firm should package the it at the plant level (speculation). Model C - ss 1 st - e at n The question addressed in this model is the following: Should or shouldn't the firm postpone the assembly of a product to the warehouse level? The criterion for addressing this question is the least cost alternative between assembly at the plant or at the warehouse. 68 EIQQBE_;L§ DIRECT COST PER PRODUCT - MODEL B V os s Packaging cost at warehouse Packaging cost at plant Packaging cost (protective) Inventory carrying cost Warehousing cost Transportation cost 4-+-+| + l Variation in variable cost per unit due to potponement + or - Unit variation in variable cost x total demand for product + or - W Warehousing fixed cost in the period - Packaging equipment fixed cost in the period - Transportation fixed cost in the period - s 'n ' d - t o ' ' O a u t + or - 69 In the alternative of postponement, the product is moved unassembled to the warehouse, where it is assembled once sold. In this model, all unassembled parts originate at the same point: the plant. This is the major difference between Model C and Model D, manufacturing postponement- speculation, where the final product is assembled from parts KP that‘come fromIVariedmsources. The cost of labeling and packaging the product after it assembly is included in the assembly cost. Figure 3.6 presents the system to be modeled. In Model C, the following cost categories are involved: customer service, assembly, inventory, warehousing, and transportation. Each is discussed below. The only customer service variable affected by the decision to postpone or to speculate on the distribution of a product is order cycle time. Postponement increases the order cycle time, because time is needed to assemble the product after the order is received. The extent to which the level of demand is affected by the increase in order cycle time is a function of the sales elasticity of service. The impact of the increase in order cycle time on the cost of postponement is estimated by the cost of lost sales, which is equal to the estimated decline in demand multiplied by the contribution margin of the product being considered for postponement. The impact of postponement on assembly costs is threefold. One, assembly coSts at the plant level are eliminated, and savings are computed as the average number 70 new MODEL C - ASSEMBLY POSTPONEMENT-SPECULATION SPECULATION- Assembly a: plant. non-consolidated inventorya at warehouses. assembled amputation “m I m 4[minnow-z 2 AREI'DUSE 3 POSTPONEMENT - Assembly a: walehouses. consolidated inventory at warehouses. assembled Importation AREI‘IOUSE I PR 1 AREI-IOUSE 2 PR 1 AREI-IOUSE 3 PR 1 PR 1 - product Vl.... V6 - product versions 71 of labor hours needed to assemble one unit of product, multiplied by the labor cost per hour. Two, there are assembly costs at the warehouse level. They include the cost of the equipment multiplied by the hurdle rate (a fixed cost), and the additional labor cost to assemble the product at the warehouse level (a variable cost). Three, if necessary, there is an additional packaging cost needed at the plant level, for transportation to the warehouse. The protective package must be removed at the warehouse level. The costs of additional protective packaging are additional labor and packaging materials, which are variable costs. Additional packaging costs, when needed, are included as assembly costs. The base stock is affected by the alternative of postponement because it has to be adjusted to the decline in demand caused by the increase in order cycle time. Inventory carrying cost savings from postponement derive from reductions in the safety stock. In the alternative of postponement, savings from the reduction in safety stock are estimated in the following manner. The first step is to determine the number of standard deviations of demand kept as safety stock for the product. That level of safety stock protection is used in the estimation of the safety stock after postponement. In the second step, the level of safety stock after postponement is given by the number of standard deviations of demand kept as safety stock, multiplied by the 72 standard deviation of the total demand for the product being analyzed, multiplied by the product value and by the percentage used by the firm as the inventory carrying cost. It is important to note that savings in inventory carrying cost are limited to the proportion of the product's value that is common to the different versions of the product, and that the value of the product utilized in the computation of savings due to postponement must be adjusted for this factor. In the third step, the cost of safety stock in the alternative of speculation is given by the number of product units presently kept as safety stock for each version, multiplied by the product value, multiplied by the percentage used by the firm as inventory carrying cost. Finally, in the fourth step, the costs for all product versions are added to find the product total. Savings from postponement are arrived at by the cost difference in the two alternatives. Two categories of warehousing costs are examined. Handling costs are not accounted for separately in the postponement-speculation decision because additonal handling in the alternative of postponement is included in the assembly cost. Storage costs are affected because inventories are affected. If the firm uses public warehouses, the reduction in storage cost is equal to the reduction in inventory in units, multiplied by the warehousing charge per unit. If the public warehouse charges 73 a period fee, it must be treated as a period cost. When company operated warehouses are used, storage cost reduction in the alternative of postponement can be computed only if an alternative use for the additional available space is found. If that is the case, the storage space cost per square foot is multiplied by the number of square feet saved with postponement to determine the value of savings. The last cost category in Model C is transportation. If the firm utilizes for-hire transportation, the cost estimates in the two alternatives are supplied by the carrier. If the fleet is company operated, line haul costs for both alternatives is determined by the cost per ton/mile to haul the product, multiplied the product's weight, multiplied by the average distance from plant to warehouse. The cost of loading and unloading is measured by the number of hours needed to load or unload one unit of product, multiplied by the labor cost per hour. The difference between the two alternatives in the cost of transportation is given by the reduction in cube that is accomplished by shipping unassembled products to the warehouse, in the alternative of postponement. Figure 3.7 presents a framework for the calculation of the cost advantage or disadvantage of postponement relative to speculation. The figure includes all logistics costs involved in the decision. A negative sign means that the cost of speculation is lower than the cost of postponement 74 for a particular cost category, while a positive sign means the opposite. The net effect of assembly postponement is the sum total of all relevant costs. A positive sign in the bottom line means that the firm should assemble the product at the warehouse level (postponement), while a negative sign means that the firm should assemble the product at the plant level (speculation). Modal Q - Manufacturing Pgstpoaemeat-Speculation The question addressed in this model is as follows: Should or shouldn't the firm postpone manufacturing of a product to the warehouse level? The criteria for addressing this question is the least cost alternative between manufacturing at the plant or at the warehouse. In the alternative of postponement, product components are moved from different sources to the warehouse, where the product is manufactured once sold. In this model, manufacturing components do not come from the same sourcing point. In the alternative of postponement, it is assumed that non-ubiquitous materials come from the plant, while ubiquitous materials come from sources close to the warehouses. Ubiquitous materials are defined as components that are equally and easily available at the plant and at the warehouses at a similar, and low, cost. It is also assumed that the firm will inventory only negligible amounts 75 IGURE 3.7 DIRECT COST PER PRODUCT - MODEL C 'a sts Assembly cost at warehouse Assembly cost at plant Inventory carrying cost Warehousing cost Transportation cost Cost of lost sales I +-++-+ I Variation in variable cost per unit due to potponement + or — Unit variation in variable cost x total demand for product + or - 'O s s Warehousing fixed cost in the period - Assembly equipment fixed cost in the period - Transportation fixed cost in the period - Togal fixeg cost in age pariog A - ec o s e st t O O is 'cs s r od + or - 76 of ubiquitous materials. The cost of labeling and packaging the product after it is manufactured is included in the manufacturing cost. Figure 3.8 presents the system to be modeled. In Model D, the following cost categories are involved: customer service, manufacturing, inventory, warehousing, and transportation. Each is discussed below. The only customer service variable affected by the decision to postpone or to speculate on the distribution of a product is order cycle time. Postponement increases the order cycle time, because time is needed to manufacture the product after the order is received. The extent to which the level of demand is affected by the increase in order cycle time is a function of the sales elasticity of service. The impact of the increase in order cycle time on the cost of postponement is estimated by the cost of lost sales, which is equal to the estimated decline in demand multiplied by the contribution margin of the product being considered for postponement. The impact of postponement on manufacturing costs is threefold. One, at the plant level, manufacturing costs are eliminated, and savings are computed as the average number of labor hours needed to manufacture one unit of product, multiplied by the labor cost per hour. Two, manufacturing costs exist at the warehouse level. They include the cost of the equipment multiplied by the hurdle rate (a fixed cost), and the additional labor cost to manufacture the product at 77 EIQQBE 3,8 MODEL D - MANUFACTURING POSTPONEMENT-SPECULATION SPECULATION - Manufacturing at plant. inventory at warehouses. long transportation of ubiquitous materials iAREIDUSE I PR1 AREIIOUSE 2 PR I AREI-IOUSE 3 PR 1 POST PONEMENT - Manufacturing 1 warehouses. inventory at warehouses. short transportation of ubiquitous materials AREHOUSE I * NU AREHOUSB 2 7 ~ - PLANT SOURCE I NU AREHOUSE 3 2 ~ . NU NU - non-ubiquitous materials PR 1 - product 78 the warehouse level (a variable cost). Three, there is an additional packaging cost at the plant level, when it is needed for transportation to the warehouse. The protective package must be removed at the warehouse level. The costs of additional protective packaging are additional labor and packaging materials, which are variable costs. Additional packaging costs, when needed, are included in manufacturing costs. The base stock is affected by the alternative of postponement, because it has to be adjusted to the decline in demand caused by the increase in order cycle time. Inventory carrying cost savings from postponement are derived from reductions in the safety stock. In the alternative of postponement, savings from the reduction in safety stock are estimated as follows. The first step is to determine the number of standard deviations of demand kept as safety stock for the product. That level of safety stock protection is used in the estimation of the safety stock after postponement. In the second step, the level of safety stock after postponement is given by the number of standard deviations of demand kept as safety stock, multiplied by the standard deviation of the total demand for the product being analyzed, multiplied by the product value and by the percentage used by the firm as the inventory carrying cost. It is important to note that savings in inventory carrying cost are very limited in this model, because ubiquitous 79 components in the product's value are of little importance. In the third step, the cost of safety stock in the alternative of speculation is determined by the number of product units presently kept as safety stock, multiplied by the product value, multiplied by the percentage used by the firm as inventory carrying cost. Savings from postponement are arrived at by the cost difference in the two alternatives. In warehousing costs, two categories are examined. Handling costs are not accounted for separately in the postponement-speculation decision because additonal handling in the alternative of postponement is included in the manufacturing cost. Storage costs are affected because inventories are affected. If the firm uses public warehouses, the reduction in storage cost is equal to the reduction in inventory in units, multiplied by the warehousing charge per unit. If the public warehouse charges a period fee, it should be considered a period cost. If company Operated warehouses are utilized, the reduction in storage costs in the alternative of postponement can only be computed if there is an alternative use for the additional available space. If such is the case, the storage space cost per square foot is multiplied by the number Of square feet saved with postponement to get the value of savings. The last cost category in Model D is transportation. If the firm utilizes for-hire transportation, the cost 80 estimates in the two alternatives are supplied by the carrier. If the fleet is company operated, line haul costs for both alternatives is determined by the cost per ton/mile to haul the product, multiplied the product's weight, multiplied by the average distance from plant to warehouse. The cost of loading and unloading is measured by the number of hours needed to load or unload one unit of product, multiplied by the labor cost per hour. The transportation of ubiquitous materials to the warehouse in the alternative of postponement is assumed to be performed by for-hire carriers. The difference between the two alternatives in cost of transportation is given by the reduction in product weight that is accomplished by shipping only non-ubiquitous components to the warehouse, in the alternative of postponement. Figure 3.9 presents a framework for the calculation of the cost advantage or disadvantage of postponement relative to speculation. The figure includes all logistics costs involved in the decision. A negative sign means that the cost of speculation is lower than the cost of postponement for a particular cost category, while a positive sign means the opposite. The net effect of manufacturing postponement is the sum total of all relevant costs. A positive sign in the bottom line means that the firm should manufacture the product at the warehouse level (postponement), while a negative sign means that the firm should manufacture the 81 product at the plant level (speculation). Model E - Time Postponemeat-Speculatlgn The question addressed in this model is the following: Should the firm centralize (plant or plant warehouse level) inventories for a product, or should inventories remain decentralized (warehouse level)? The criteria for addressing this question is the least cost alternative between the two alternatives. In the alternative of postponement (inventory centralization), products are moved to the warehouse only after the sale. In the alternative of speculation (inventory decentralization) products are moved to the warehouse in anticipation of the sale, based on a demand forecast. As in previous models, speculation is assumed to be the status quo. In the alternative of postponement, products are shipped to a for- hire carrier which will provide local delivery service. Figure 3.10 presents the system to be modeled. I The following cost\categories are involved: customer service, inventory, warehousing, and transportation. Each is discussed below. The only customer service variable affected by the decision to postpone or to speculate on the distribution of a product is order cycle time. Postponement increases the order cycle time, because time is needed to ship the product after the order is received. The extent to 82 EIQQBE_1L2 DIRECT COST PER PRODUCT - MODEL D yariabla Costs Manufacturing cost at warehouse - Manufacturing cost at plant + Inventory carrying cost + Warehousing cost + Transportation cost + Cost of lost sales - Variation in variable cost per unit due to potponement + or - Unit variation in variable cost x total demand for product + or - mam Warehousing fixed cost in the period - Manufacturing equipment fixed cost in the period - Transportation fixed cost in the period - ota ' cost ' ' - 83 which the level of demand is affected by the increase in order cycle time is a function of the sales elasticity of - service. The impact of the increase in order cycle time on the cost of postponement is estimated by the cost of lost sales, which is equal to the estimated decline in demand multiplied by the contribution margin of the product being considered for postponement. The base stock is affected by the alternative of postponement because it has to be adjusted to the decline in demand caused by the increase in order cycle time. Inventory carrying cost savings from postponement derive from reductions in the safety stock. In the alternative of postponement, savings from the reduction in safety stock is estimated in the following manner. The first step is to determine the number of standard deviations of demand kept as safety stock for the product. That level of safety stock protection is used in the estimation of the safety stock after postponement. In the second step, the level of safety stock after postponement is given by the number of standard deviations of demand kept as safety stock, multiplied by the standard deviation of the total demand for the product being analyzed, multiplied by the product value and by the percentage used by the firm as the inventory carrying cost. In the third step, the cost of safety stock in the alternative of speculation is given by the number of product units presently kept as safety stock at each warehouse, 84 w MODEL E - TIME POSTPONEMENT-SPECULATION SPECUIATION - Truckload tramportstion. inventory at warehouses AREHOUSE 1 PR 1 PLANT AREI-IOUSE 2 _ pa 1 AREHOUSE 3 PR 1 POST PONEMENT . Icss-tlun-truckload u'ansponation. inventory at plant AREHOUSE j PLANT AREHOUSE 2 7 PR 1 AREHOUSE 3 l I’R l - product 85 multiplied by the product value, multiplied by the percentage used by the firm as inventory carrying cost. , Finally, in the fourth step, the cost for all warehouses is added to reach the product total. Savings from postponement are given by the cost difference in the two alternatives. In warehousing costs, handling and storage are examined. Although variable handling costs per unit remain constant in both alternatives, the total handling cost in the alternative of postponement has to be adjusted for the decline in demand caused by the increase in the order cycle time. Storage costs are affected because inventories are affected. If the firm uses public warehouses, the reduction in storage is equal to the reduction in inventory in units, multiplied by the warehousing charge per unit. If the public warehouse charges a period fee, that must be treated as a period cost. If company operated warehouses are utilized, the reduction in storage costs in the alternative of postponement can be computed only if there is an alternative use for the additional available space. If that is the case, the storage space cost per square foot is multiplied by the number of square feet saved with postponement to get the value of savings. If new handling equipment is needed, the fixed cost is determined by the cost of the equipment multiplied by the hurdle rate. The last cost category in Model E is transportation. If the firm utilizes for-hire transportation, the carrier 86 supplies the cost estimates in the two alternatives. If the fleet is company operated in the plant- warehouse segment, .line haul costs for both alternatives is determined by the cost per ton/mile to haul the product, multiplied by the product's weight, multiplied by the average distance from plant to warehouse. The cost of loading and unloading is measured by the hours needed to load or unload one unit of product, multiplied by the labor cost per hour. The transportation of the product to customers in the alternative of postponement is assumed to be performed by for-hire carriers. The difference between the two alternatives in this model is given by the increase in the proportion of less-than-truckload shipments in the alternative of postponement. Figure 3.11 presents a framework for the calculation of the cost advantage or disadvantage of postponement relative to speculation. The figure includes all logistical costs involved in the decision. A negative sign means that the cost Of speculation is lower than the cost of postponement for a particular cost category, while a positive sign means the opposite. The net effect of time postponement is the sum total of all relevant costs. A positive sign in the bottom line means that the firm should inventory the product at the plant level (postponement), while a negative sign means that the firm should inventory the product at the warehouse level (speculation). 87 EIEHBE_2&11 DIRECT COST PER PRODUCT Va ' e s s Inventory carrying cost + Warehousing cost + Transportation cost - Cost of lost sales - Variation in variable cost per unit due to postponement Unit variation in variable cost x total demand for product Perm Warehousing fixed cost in the period - Transportation fixed cost in the period - ' t ' he 'Od - MODEL E + or - + or - 88 COMP S ON The first section of this chapter presented the normative cost models. As discussed in Chapter I, the models are reproduced in a computer simulation. Its purpose is to test hypotheses relating the decision to postpone or to speculate on the distribution of a product to selected product physical and demand characteristics. The computer simulation is based on a simulator introduced in this section. The simulator is the actual computer algorithm containing the mathematical relationships needed to generate the simulation's output. The simulator is applied five times, once for every one of the normative cost models. Every application contains several adaptations to accommodate the idiosyncrasies of each model. Each of the five applications of the simulator is treated independently. Data is not transferred between applications, although the range for the input variables, as well as the constant values, are the same whenever that data can be supported by theory. This section on computer simulation is structured in seven parts. The first introduces the simulator. The second part introduces the first application of the simulator, the application to Model A. In parts three to six, the applications of the simulator to the remaining models are 89 discussed. Finally, empirical support for the inputs is presented in the last part. The Slmalator The simulator contains the mathematical relationships needed to simulate the normative cost models. This part starts by clarifying the simulator's assumptions, and is followed by a description of the four subroutines that compose the simulator. The emphasis is on the relationships common to the five applications. Despite their particularities, the applications of the simulator have a number of commonalities explained below. First, the simulator is built from the point of view of a manufacturer who has to decide whether to postpone or to speculate on the distribution of a product. Second, the status quo is assumed to be speculation. More specifically, whenever the simulator is applied to one of the form postponement-speculation models, time speculation is assumed. Similarly, whenever the simulator is applied to the time postponement-speculation model, form speculation is assumed. Finally, the output in all applications is dichotomous: the firm will either postpone or speculate on the distribution of one or more products. The simulator has a provision for the very few cases where the output is 90 indifferent: that is, the cost of the postponement and the speculation alternatives to the distribution of a product are identical. These cases are dropped from the analysis. The objective of the application of the simulator to the normative cost models is to decide whether products should be inventoried or processed at the plant at the warehouse. In the case of the time postponement-speculation model, products can be inventoried at the plant level (postponement), or at the warehouse level (speculation). In the case of the form postponement models, the term "processing" refers to the four different degrees of form postponement-speculation: labeling, packaging, assembly, and manufacturing. In form postponement-speculation, products can be processed either at the plant level (speculation), or at the warehouse level (postponement). The simulator needed for postponement-speculation decisions is based on the normative cost models which, in turn, are based on the total cost approach to business logistics. In the total cost approach, the different cost factors in the firm that are affected by business logistics decisions are managed as an integrated system. The goal of business logistics management is to minimize the total cost of that system, as opposed to minimizing the cost of one particular cost factor. The cost factors that constitute the business logistics system were explained in Chapter I. They are grouped in six 91 cost categories: order processing and information, customer service, transportation, warehousing, lot quantity costs, and inventory carrying costs. For the analysis of the impact of postponement- speculation decisions in business logistics systems, the simulator is composed of four subroutines extracted from the six cost groups of the total cost approach. The four subroutines are customer service, inventory, processing, and transportation. The processing subroutine includes lot quantity costs, while warehousing costs are included in the inventory subroutine. Order processing and information costs are assumed constant in this study. In the remainder of this part, each of the simulator subroutines is explained separately. Customer Service The subroutine customer service is included in the simulator to account for those cases where the decision to postpone the distribution of a product will imply in an increase in delivery time and, therefore, in a decline in the level of demand. The decline in demand is given by a constant, DECDEM, of value equal to 5% of the original demand in units. ADEMAND is the adjusted level of demand after postponement. 92 The reduction in the level of demand increases the cost of lost sales. The unit cost of lost sales, also a constant, ‘ is fixed at 35% percent of the product value. Processing The subroutine processing computes the cost increase resulting from the decision to postpone the distribution of a product in one of the four form postponement-speculation models. In the application of the subroutine to a particular model, the term "processing" should be substituted for the word "labeling," "packaging," "assembly," or "manufacturing," depending on the model run on the simulator. Three variables are key to this subroutine: plant variable processing cost, warehouse variable processing cost, and warehouse fixed processing cost. Plant fixed processing costs are assumed sunk. The plant variable processing cost is a function of the level of demand. For each of the applications of the simulator, additional variables are introduced in the computation of this cost. The relationship between plant variable processing cost and the level of demand is a negatively sloped exponential curve, whereby higher levels of demand result in a lower processing cost per unit. Although in many cases a non-linear relationship can be 93 assumed to be linear, in this particular case a non-linear equation is needed because the range of the variable demand » is very large, and, therefore, the error around the mean values will be large as well. The warehouse variable processing cost is calculated from the same equation as the plant variable processing cost, the only difference being that the level of the demand is divided by three. It reflects the fact that there are three warehouses in the system and that one third of the demand is assumed to be processed at each warehouse. Warehouse fixed processing cost is a function of the demand level. It is a positive linear relationship because higher levels of demand require a larger investment in equipment capable of handling a high volume of output. Inventory The subroutine inventory computes the effect of the decision to postpone or to speculate on the distribution of a product on the level of inventory for that product. The inventory carrying cost under the alternative of speculation is determined by the sum of the base and safety stock levels, multiplied by the cost of carrying one unit of product. The cost of carrying one unit of product is the same regardless of the alternative of postponement or 94 speculation. It is assumed to be equal to 1/4 of the product's value. The level of base stock is assumed to be equal to 1/11 of the level of demand. In the alternative of postponement, the level of demand is readjusted for the decline in demand, as explained in the customer service subroutine. The level of safety stock in the alternative of speculation is determined by the level of the demand, the desired level of protection chosen by management, and the level of demand uncertainty. The desired level of protection is a constant, equal to two standard deviations of the demand. Demand uncertainty is usually measured by the standard deviation of demand. This simulation does not provide historical values for the calculation of the standard deviation. Consequently, the standard deviation is estimated by the range of high and low levels of demand divided by four. The variable demand uncertainty is an index whereas the standard deviation is divided by the level of demand. The range for demand uncertainty index is from .03 to .15. The level of safety stock in the alternative of postponement is determined to be between 1 and 3 times less that of the level of safety stock under speculation. The amount of the savings is determined by the number of warehouses in the system and by other variables specific to each simulator application. In this study, the number of 95 warehouses in the system is a constant value of 3. - Transportation The subroutine transportation measures the effect of the decision to postpone or to speculate on the distribution of a product on its transportation costs. The calculation of the transportation cost per unit in the alternative of speculation is the same in any application of the simulator, while the transportation cost per unit in the alternative of postponement is specific to each application. The transportation cost per unit under speculation is described below. Transportation cost per unit is considered a function of the proportion of Less Than Truckload (LTL) shipments to the warehouse, and the cost of truckload (TL) and Less Than Truckload (LTL) transportation per unit. The proportion of LTL shipments is a positive linear function of uncertainty, whereby higher levels of demand uncertainty lead to a higher proportion of LTL shipments to the warehouses. The unit cost of TL transportation is a positive linear function of product value, whereby products with a higher unit value have higher transportation costs. The proportion of LTL shipments to the warehouse varies between 10 and 60 percent Of all shipments. The cost of TL transportation per unit is assumed to vary between 25 and 75 96 cents. The cost of LTL transportation per unit is a constant value equal to twice the cost of TL transportation. If the firm decides to postpone the distribution of a product to the warehouse level, transportation costs per unit are expected to increase in the time postponement- speculation model, and to decrease in the form postponement- speculation models. The remaining parts of this section introduce the application of the simulator to Models A through E, respectively. Each application contains a graphic representation and a block diagram for the computer program. It also contains tables with information on the simulator inputs and mathematical relationships. In addition, the application assumptions and the mathematical relationships that are specific to one application are further explained in each part. A c ' o e 'mu to to e The objective of the application of the simulator to Model A, the labeling model, is to decide whether products should be labeled at the plant level (speculation), or at the warehouse level (postponement). This application of the simulator has two subroutines, labeling and inventory. The cost trade-off in the case of postponing the labeling function to the warehouse level is 97 an increase in the cost of labeling products due to reduced economies of scale, and a reduction in inventory carrying . costs due to the consolidation of inventories of the same product sold under different brand names. Application Assumptions Two general assumptions in this model should be made explicit. First, additional handling and storage space needed at the warehouse level due to postponement are included in the fixed and variable labeling costs. Second, the labeling equipment can be used for all brands of one product only. Figures 3.12 and 3.12A show the block diagram for the computer program. Table 3.1 presents the variable list and the unit of analysis for each variable. Table 3.2 shows the range and the value levels for the inputs. In Table 3.3, the constant values to be used as inputs are listed. In Table 3.4, the mathematical relationships used in this application of the simulator are presented. The remainder of this part discusses the criteria used to arrive at the relationships in Table 3.4. 98 w MODEL A - BLOCK DIAGRAM 99 W MODEL A - SUBROUTINES 100 TABLE 3.1. VARIABLE LIST Variable name Definition Unit WLABELF Fixed labeling cost at the Dollars per warehouse level period, for all warehouses WLABELV Variable labeling cost at the warehouse level PLABELV Variable labeling cost at the Dollars per plant level unit of product DEMAND Demand level for a product Units per period UNCERT Uncertainty of demand Index.One std. variability deviation of demand BSTOCK Base inventory Units of product STDVU One standard deviation of Units of product demand NWHSES Number of warehouses supplying Constant.Units the market NBRANDS Number of brands that product is sold DESPRO Level of inventory protection Number of std. deviations of demand. Constant SSTOCKP Safety stock if postponement Units of product SSTOCKS Safety stock if speculation Units of product ICC Inventory carrying cost Dollars per unit ICCI Inventory carrying cost Constant. 101 TABLE 3.1. Continued Variable name Definition Unit PVALUE Product value - manufacturers Dollars per unit sales price INVS Total inventory if speculation Total dollars INVP Total inventory if postponement Total dollars LABELCS Total labeling cost if Total dollars speculation LABELCP Total labeling cost if Total dollars postponement TCS Total cost if speculation Total dollars TCP Total cost if postponement Total dollars 102 TABLE 3.2. VARIABLE RANGE AND VALUE LEVELS Variable Range Value levels DEMAND 600-48000 600 12000 24000 36000 48000 UNCERT ' .03-015 .03 .06 009 012 .15 NBRANDS 1-6 1 2 3 5 6 PVALUE 1.00-15.00 1.00 4.50 8.00 11.50 15.00 TABLE 3.3. CONSTANT VALUES Constant Value DESPRO 2.0 ICCI .25 NWHSES 3 103 TABLE 3.4. APPLICATION RELATIONSHIPS Variable Equation PLABELV = .618786 * (DEMAND * (1/NBRANDS) * (l/UNCERT)) ** -.337287 WLABELV = .618786 * ((DEMAND/3) * (1/NBRANDS) * (1/UNCERT)) ** -.337287 WLABELF = 6.284 + .15612 * DEMAND BSTOCK = DEMAND/11 STDVU = UNCERT * DEMAND SSTOCKS = STDVU * DESPRO SSTOCKP = STDVU * DESPRO/ (.6 + .13333 * NWHSES * NBRANDS) ICC = PVALUE * ICCI INVS = (BSTOCK + SSTOCKS) * ICC INVP = (BSTOCK + SSTOCKP) * ICC LABELCS = PLABELV * DEMAND LABELCP = (WLABELV * DEMAND) + WLABELF TCS = LABELCS + INVS TCP = LABELCP + INVP 104 Application Relationships Two of the mathematical relationships in this application should be explained in more detail to clarify the criteria used to determine the values in the equations. The first of these relationships is the equation to calculate the value of PLABELV, the plant labeling variable cost. It is considered a function of three variables: DEMAND, NBRANDS, and UNCERT. The relationship between PLABELV and DEMAND is a negatively sloped exponential curve, whereby higher levels of demand result in a lower plant variable labeling cost per unit. The relationship with NBRANDS and UNCERT is positively sloped and linear, because the higher the NBRANDS, the greater the number of adjustments needed to reset the labeling equipment to label the different brands. Similarly, the higher the level of UNCERT, the greater the number of resettings needed in each labeling machine to accommodate fluctuations in the level of demand for the different brands. The variable DEMAND is exponential, whereas variables UNCERT and NBRANDS are linear. Because the inverse of a linear function is exponential, the variables UNCERT and NBRANDS are inputed in the formula for PLABELV in their inverse form (1/NBRANDS, and 1/UNCERT). In this format, the three variables will fit the same equation without 105 distorting the relationship. The total variation for PLABELV and WLABELV is estimated at between one half and ten cents per unit of product. WLABELF, the warehouse fixed labeling cost, is estimated to vary from $100 to $7000 dollars per product per period. The second mathematical relationship to be addressed is SSTOCKP, the safety stock under the alternative of postponement. It is considered to be a function of SSTOCKS, whereby the savings in safety stock originated by a decision to postpone the labeling of a product to the warehouse level is a function of the number of warehouses in the system, and the number of brands that the product is being sold under. The higher the value of NWHSES and NBRANDS, the greater the savings in inventory carrying costs. The objective of the application of the simulator to Model B, the packaging model, is to decide whether to package goods at the plant level (speculation), or at the warehouse level (postponement). The subroutines included in this application of the simulator are the following: packaging, transportation and inventory. The cost trade-off in the decision to postpone the packaging of a product to the warehouse level, is an 106 increase in packaging costs due to a loss in economies of scale, a reduction in inventory carrying costs because of consolidation of inventories Of different package sizes of the same product, and a reduction in transportation costs, due to the fact that the product is shipped in bulk to the warehouses. Application Assumptions There are several assumptions to the application of the simulator to Model B. First, packaging costs are constant per package, regardless of size. Second, packaging equipment can be used for only one product. Third, the postponement of the packaging function to the warehouse level does not affect delivery time to the customer. Fourth, additional storage and handling costs at the warehouse level due to postponement are included in the fixed and variable packaging costs. Finally, transportation costs per unit of product are equal for all package sizes. Figures 3.13 and 3.13A show the block diagram for the computer program. Tables 3.5, 3.6, and 3.7 present the variable list and the unit of analysis for each variable. Table 3.8 shows the range and the value levels for the inputs. Table 3.9 lists the constant values to be used as inputs to the simulator. The mathematical relationships in the application are in Table 3.10. The remainder of this 107 part discusses the criteria used to arrive at the relationships in Table 3.10. Application Relationships In the application of the simulator to Model B, three variables call for greater detail: DEMANDT, PPACKV, and SSTOCKP. Variable DEMANDT represents the total demand, in units per period, for all package sizes. The model allows for each product to be sold in up to 5 package sizes (NSPACK). It assumes that package size 1 contains 1 unit of product, package size 2 contains 2 units of product, and so on. The level of the demand for each package size is a fixed function of the level of demand for package size 1. Determining the size and demand level for all package sizes adds a level of realism to the simulation by making smaller the demand for larger size packages. The plant variable packaging cost, PPACKV, is a negatively sloped exponential function of DEMANDT, and a linear positive function of PVALUE and NSPACK. The relationship with DEMANDT reflects the lower packaging costs per unit achieved at higher levels of demand. The relationship with PVALUE can be explained by the fact that more expensive products are sold in more elaborate packages, a practice leading to higher packaging costs per unit. The 108 mm MODEL B - BLOCK DIAGRAM BHMN 109 W MODEL B - SUBROUTINES £2, DATA: DATA: NSPACK mm UNCER'I‘ UNCERT 110 TABLE 3.5. VARIABLE LIST--PACKAGING SUBROUTINE Variable name Definition Unit PVALUE Product value, manufacturer's Dollars per unit sales price of product PPACKV Packaging cost at plant-- Dollars per variable package WPACKV Packaging cost at warehouse—- Dollars per variable package WPACKF Packaging cost at warehouse-- Dollars per fixed period XPACK Variable protective packaging Dollars per unit cost for bulk shipments of product NSPACK Number of package sizes DEMANDl Demand for package size 1 Packages per period DEMAND2 Demand for package size 2 Packages per period DEMAND3 Demand for package size 3 Packages per period DEMAND4 Demand for package size 4 Packages per period DEMANDS Demand for package size 5 Packages per period DEMANDT Total demand Units per period NPACK Total demand Packages per period PACKCS Total packaging cost--if Total dollars speculation PACKCP Total packaging cost--if Total dollars postponement 111 TABLE 3.6. VARIABLE LIST--INVENTORY SUBROUTINE Variable name Definition Unit BSTOCK Base inventory Units of product UNCERT Uncertainty of demand Index. One std. variability deviation of demand STDVU One std. deviation of demand Units of product DESPRO Level of inventory protection Number of std. deviations of demand SSTOCKP Safety stock if postponement Units of product STOCKS Safety stock if speculation Units of product ICCI Inventory carrying cost Constant ICC Inventory carrying cost Dollars per unit NWHSES Number of warehouses supplying Constant. Units the market INVS Inventory cost if speculation Total dollars INVP Inventory cost if postponement Total dollars 112 TABLE 3.7. VARIABLE LIST-~TRANSPORTATION SUBROUTINE --TOTAL COST Variable name Definition Unit TRCU ‘Transportation cost--packages Dollars per unit PLTL Proportion of units of product Percentage shipped at LTL rates CTL Cost of TL transportation Dollars per unit CLTL Cost of LTL transportation Dollars per unit TRCUB Transportation cost--bulk Dollars per unit TRCS Transportation cost if Total dollars speculation TRCP Transportation cost if Total dollars postponement TCS Total cost if speculation Total dollars TCP Total cost if postponement Total dollars 113 TABLE 3.8. VARIABLE RANGE AND VALUE LEVELS Variable Range Value Levels NSPACK 1-5 1 2 3 4 5 DEMANDl 600-8000 600 2500 4300 6200 8000 UNCERT .03-.15 .03 .06 .09 .12 .15 PVALUE 1.00-15.00 1.00 4.50 8.00 11.50 15.00 TABLE 3.9. CONSTANT VALUES Constant Value DESPRO 2.0 ICCI .25 NWHSES 3 114 TABLE 3.10. APPLICATION RELATIONSHIPS Variable Equation PPACKV = .477182 * (DEMANDT * (l/NSPACK) * (l/PVALUE)) ** -.257451 WPACKV = .477182 * ((DEMANDT/3) * (l/NSPACK) * (l/PVALUE)) ** -.257451 XPACK = PPACKV * 3 WPACKF = 164.5569 + .225738 * DEMANDT DEMAND2 = DEMANDl * .7 DEMAND3 ? DEMANDl * .5 DEMAND4 = DEMANDl * .4 DEMANDS = DEMANDl * .1 DEMANDT = DEMANDl + DEMAND2 * 2 + DEMAND3 * 3 + DEMAND4 * 4 + DEMANDS * S NPACK = DEMANDl + DEMAND2 + DEMAND3 + DEMAND4 + DEMANDS PACKCS = PPACKV * NPACK PACKCP = (WPACKV * NPACK) + (XPACK * DEMANDT) + WPACKF BSTOCK = DEMANDT/ll STDVU = UNCERT * DEMANDT SSTOCKS = STDVU * DESPRO SSTOCKP = STDVU * DESPRO/(.6 + .1333 * NWHSES * NSPACK) ICC = PVALUE * ICCI INVS = (BSTOCK + SSTOCKS) * ICC INVP = (BSTOCK + SSTOCKP) * ICC 115 TABLE 3.10- Continued. Variable Equation PLTL = -.025 + 4.1666 * UNCERT CTL = .214286 + .035714 * PVALUE CLTL = CTL * 2 TRCU = (PLTL * CLTL) + (1- PLTL) * CTL TRCUB = .65 * CTL TRCS TRCU * DEMANDT TRCP = TRCUB * DEMANDT TCS = PACKS + INVS + TRCS TCP = PACKP + INVP + TRCP 116 relationship with NSPACK is explained by the greater number of machine stops necessary to reset the equipment for different package sizes. The variable DEMANDT is exponential, and variables PVALUE and NSPACK linear. Beacause the inverse of a linear function is exponential, variables PVALUE and NSPACK are input in the equation for PPACKV in their inverse form (l/PVALUE, and l/NSPACK). In this format, DEMANDT, PVALUE, and NSPACK fit the same equation without distorting the relationship. The variable SSTOCKP, the safety stock in units under the alternative of postponement, is a function of SSTOCKS. The savings in safety stock made feasible by a decision to postpone packaging to the warehouse level, is a function of the number of warehouses in the system and the number of packages under which the product is sold. The higher the value of NWHSES and NSPACK, the greater the savings in safety stock. To keep the level of savings reasonable, they are limited within one to three times less than the original safety stock under the alternative of speculation. In this application of the simulator to Model B, the values attributed to some other variables must be clarified. XPACK, the extra packaging costs needed for protective purposes if a product is shipped in bulk, are expected to be small. It is considered to be equal to 30% of the plant variable packaging cost. The transportation cost per unit 117 of product in bulk is assumed to be 65% of the TL rate for the same product. The variable WPACKF, the warehouse fixed packaging cost, is estimated to vary from $300 to $11000 dollars per product per period, while PPACKV and WPACKV are estimated to vary between 3 and 35 cents per unit of product. I 1. a!‘ E !] 5' J ! ! fl 1e] ; The Objective of the application of the simulator to Model C, the assembly postponement-speculation model, is to decide whether to assemble goods at the plant level (speculation), or at the warehouse level (postponement). This application has four subroutines: customer service, inventory, assembly, and transportation. The cost trade-off in the decision to postpone assembly to the warehouse is an increase in assembly costs due to reduced economies of scale, an increase in cost of lost sales resulting from an increase in average delivery time to customers, a reduction in the cost of carrying inventories due to the consolidation of inventories of common parts of different product versions, and a reduction in transportation cost because products are shipped unassembled to the warehouses. 118 Application Assumptions This application of the simulator has a number of assumptions. As in previous applications, assembly equipment is used for all versions of one product. Additional assembly and storage space required at the warehouse level is included in fixed and variable assembly costs. Although the increase in delivery time affects the customer service level, delivery time consistency is assumed constant and, therefore, the decline in sales is relatively small. One other effect of the longer delivery time on the simulator is the fact that the decrease in demand also reduces the total variable cost in the alternative of postponement in the remaining subroutines. Figures 3.14 and 3.14A show the block diagram for the computer program. Tables 3.11 to 3.14 present the variable list and the unit of analysis for each variable. Table 3.15 shows the range and the value levels for the inputs. Table 3.16 lists the constant values to be used as inputs to the simulator. Table 3.17 presents the mathematical relationships in this application. The remainder of this part discusses the criteria used to arrive at the relationships in Table 3.17. 119 Application Relationships Three of the mathematical relationships in the application of the simulator to Model C warrant additional attention: the transportation cost of unassembled products, the plant variable assembly cost, and the level of safety stock in the alternative of postponement.. The transportation cost of unassembled products (TRCUNA) is a function of the transportation cost for assembled products (TRCUA) and the reduction in product cube that results from shipping them unassembled to the warehouse. The greater the reduction in cube, the greater the transportation savings from postponing assembly to the warehouse level. The reduction in cube is assumed to vary between 10% and 50% of the original cube. The plant variable assembly cost (PASSEMV) is a function of DEMAND and UNCERT. The relationship between PASSEMV and DEMAND is a negatively sloped exponential curve whereby a higher level of demand corresponds to a lower PASSEMV. The relationship of PASSEMV with UNCERT is positive and linear, whereas a higher level of uncertainty requires a greater number of machine changes from one version to another and, therefore, to a higher assembly cost. The variable DEMAND is exponential, while UNCERT is linear. Because the inverse of a linear function is exponential, UNCERT is input in the equation for PASSEMV in 120 W MODEL C - BLOCK DIAGRAM .a I 'a ' SUBROUTINE CALL ASSEMBLY SUBROUTINE w MODEL C - SUBROUTINES READINPUt READINPUT READINPU’I‘ READINPUI‘ DATA: DATA: DATA: DATA: DEMAND DEMAND Dma'wm UNCERT PVALUE UNCERT PVALUE PVALUE CUBER NVER f GET [ (DMPUI'EW WAN!) ADEMAND GDMPUTE ASSEMCS ASSEMCP 122 TABLE 3.11. VARIABLE LIST--ASSEMBLY SUBROUTINE Variable name Definition Unit PVALUE Product value, manufacturer's Dollars per unit sales price of product PASSEMV Variable plant assembly cost Dollars per unit of product WASSEMV Variable warehousing assembly Dollars per unit cost of product WASSEMF Fixed warehouse assembly cost Dollars per period ASSEMCS Total assembly cost if Total dollars speculation ASSEMCP Total assembly cost if Total dollars postponement 123 TABLE 3.12. VARIABLE LIST-~CUSTOMER SERVICE SUBROUTINE Variable name Definition Unit DECDEM Percent decline in demand DEMAND Demand level for a given product Units per period ADEMAND Adjusted demand Units per period CLS Cost of lost sales Proportion of product value TCLS Total cost of lost sales Total dollars 124 TABLE 3.13. VARIABLE LIST--TRANSPORTATION SUBROUTINE Variable name Definition Unit CUBER Percent reduction in transpor- Index tation cube required by one unit of product PLTL Proportion of units of product Percentage shipped at LTL rates CTL Cost of TL transportation Dollars per unit CLTL Cost of LTL transportation Dollars per unit TRCUA Transportation cost--assemb1ed Dollars per unit TRCUNA Transportation cost-~unassembled Dollars per unit TRCS Transportation cost if Total dollars speculation TRCP Transportation cost if Total dollars postponement TABLE 3.14. 125 VARIABLE LIST-- INVENTORY SUBROUTINE -- TOTAL COST Variable name Definition Unit NWHSES Number of warehouses supplying Constant. Units the market UNCERT Uncertainty of demand Index. One std. variability deviation of demand STDVUP One standard deviation of Units of product demand if postponement STDVUS One std. deviation of demand Units of product if speculation DESPRO Level Of inventory protection Constant. Number of std. deviations of demand SSTOCKS Safety stock if speculation Units of product PCOMP Proportion of common parts Index. Constant SSTOCKP Safety stock if postponement Units of product ICCI Inventory carrying cost Constant ICC Inventory carrying cost Dollars per unit BSTOCKP Base inventory if postponement Units of product BSTOCKS Base stock if soeculation Units of product NVER Number of versions of a product INVS Inventory cost if speculation Total dollars INVP Inventory cost if postponement Total dollars TCS Total cost of speculation Total dollars TCP Total cost of postponement Total dollars TABLE 3.15. 126 VARIABLE RANGE AND VALUE LEVELS Variable Range Value Levels PVALUE 1.00-15.00 1.00 6.00 11.00 15.00 DEMAND 600-48000 600 16500 32000 48000 CUBER .10-.50 .10 .23 .36 .50 UNCERT .03-.15 .03 .07 .11 .15 NVER 1-6 1 3 4 6 TABLE 3.16. CONSTANT VALUES Constant Values DECDEM 5 CLS .35 DESPRO 2.0 ICCI .25 NWHSES 3 PCOMP .50 127 TABLE 3.17. APPLICATION RELATIONSHIPS Variable Equation ADEMAND = ((100 - DECDEM) / 100) * DEMAND TCLS = (DEMAND - ADEMAND) * PVALUE * CLS PASSEMV = 5.04373 * (DEMAND * (l/UNCERT)) ** -.274455 WASSEMV = 5.04373 * ((ADEMAND/3) * (l/UNCERT)) ** -.274455 WASSEMF = 246.835445 + (.338608 * ADEMAND) ASSEMCS = PASSEMV * DEMAND ASSEMCP = (WASSEMV * ADEMAND) + WASSEMF PLTL = -.025 + 4.1666 * UNCERT CTL = .214286 + .035714 * PVALUE CLTL - CTL * 2 TRCUA = PLTL * CLTL + (1-PLTL) * CTL TRCUNA = TRCUA * (l-CUBER) TRCS = TRCUA * DEMAND TRCP = TRCUNA * ADEMAND BSTOCKS = DEMAND/11 STDVUS = UNCERT * DEMAND SSTOCKS 8 STDVUS * DESPRO SSTOCKP 8 STDVUP * DESPRO * (.6 + .2666 * PCOMP * NVER * NWHSES) 128 TABLE 3.17. Continued Variable Equation ICC = PVALUE * ICCI BSTOCKP = ADEMAND /ll STDVUP = UNCERT * ADEMAND INVS = (BSTOCKS + SSTOCKS) * ICC INVP = (BSTOCKP + SSTOCKP) * ICC TCS = ASSEMCS + TRCS + INVS TCP = TCLS + ASSEMCP + TRCP + INVP 129 its inverse form (1/UNCERT). In this format the two variables will fit the same equation without distorting the relationships. Variable PASSEMV varies between ten and seventy cents per unit of product, while variable WASSEMF, the fixed warehouse assembly cost, varies between $450 and $16500 per product per period. The safety stock level in the alternative of postponement, SSTOCKP, is calculated as a function of the safety stock under the alternative of speculation, and as a function of the number of warehouses, the proportion of common parts among the different versions of a product, and the number of versions available from a product. The last three variables have a positive linear relationship with SSTOCKP; that is, the higher their value, the higher the savings in inventory that result from postponing assembly to the warehouse level. The number of warehouses and the proportion of common parts are constants of 3 and .50, respectively. The number of versions varies between 1 and 6. W The objective of the application of the simulator to Model D, the manufacturing postponement—speculation model, is to determine whether to manufacture goods at the plant level (speculation), or at the warehouse level 130 (postponement). The key distinction between this application and that of the simulator to Model C is that in the latter all manufacturing inputs come from a single source, while in this application, inputs come from multiple sources. The key economic factor derived from multiple source supplies is the transportation and storage of ubiquitous materials. These are defined as low cost manufacturing inputs available at short distances from the plant as well as short distances from the warehouses. Consequently, ubiquitous materials are transported at a very low unit cost, and only negligible amounts of them will be stored by the firm. Application Assumptions The assumptions for the application of the simulator to Model D follow. The increase in delivery time assumed in the subroutine customer service does not affect delivery time consistency. Additional storage and material handling space, needed for manufacturing activities at the warehouse level, are already included in the subroutine manufacturing. Also, manufacturing equipment can be shared by no more than one product. Figures 3.15 and 3.15A show the block diagram for the computer program. Tables 3.18 to 3.21 present the variable 131 list and the unit of analysis for each variable. Table 3.22 shows the range and the value levels for the inputs. Table 3.23 lists the constant values used as inputs to the simulator. Table 3.24 presents the mathematical relationships in this application. The remainder of this part discusses criteria used to arrive at the relationships in Table 3.24. Application Relationships Three of the mathematical relationships in this application are explained further: the transportation cost per unit in the alternative of postponement, the plant variable manufacturing cost, and the inventory carrying cost savings from postponement. The transportation cost per unit in the alternative of postponement (TRCUP), is a function of the transportation cost for ubiquitous materials (TRCUBM), and the transportation cost for non-ubiquitous materials (TRCNUBM). TRCUBM is a constant fixed at 5 cents per amount of material needed in one unit of product. TRCNUBM is a result of savings from the transportation cost in the alternative of speculation, given the proportion of ubiquitous materials in the weight of one unit of product. The higher the proportion, the higher the savings in transportation costs. These savings are obtained from trucking capacity that 132 w MODEL D - BLOCK DIAGRAM 133 WA MODEL D - SUBROUTINES 134 TABLE 3.18. VARIABLE LIST-~CUSTOMER SERVICE SUBROUTINE Variable name Definition Unit PVALUE Product value, manufacturer's Dollars per unit sales price of product DECDEM Percent decline in demand Index DEMAND Demand level for a product Units per period ADEMAND Adjusted demand Units per period CLS Cost of lost sales Proportion of product value TCLS Total cost of lost sales Total dollars 135 TABLE 3.19. VARIABLE LIST--MANUFACTURING SUBROUTINE Variable name Definition Unit NWHSES Number of warehouses Constant. Units WMFGF Fixed warehouse manufacturing Dollars per cost period WMFGV Variable warehouse manufacturing Dollars per unit cost of product PMFGV Variable plant manufacturing Dollars per unit cost of product MFGCS Manufacturing cost if Total dollars speculation MFGCP Manufacturing cost if Total dollars postponement TABLE 3.20. 136 VARIABLE LIST--INVENTORY SUBROUTINE Variable name Definition Unit BSTOCKS Base inventory if speculation Units of product BSTOCKP Base inventory if postponement Units of product UNCERT Uncertainty of demand Index. One std. variability deviation of demand STDVUS One standard deviation of Units of product demand if speculation STDVUP One standard deviation of Units of product demand if postponement DESPRO Level of inventory protection Constant. Number of std. devia- tions of demand SSTOCKS Safety stock if speculation Units of product SSTOCKP Safety stock if postponement Units of product ICCI Inventory carrying cost Constant ICCS Inventory carrying cost if Dollars per unit speculation of product ICCP Inventory carrying cost if Dollars per unit postponement of product VUBIQM Value of ubiquitous materials Constant. in one unit of product proportion of product value INVS Inventory cost if speculation Total dollars INVP Inventory cost if postpOnement Total dollars TABLE 3.21. 137 VARIABLE LIST--TRANSPORTATION SUBROUTINE Variable name Definition Unit WUBIQM Weight of ubiquitous materials Proportion of in one unit of product product weight PLTL Proportion of units of product Percentage shipped at LTL rates CTL Cost of TL transportation Dollars per unit CLTL Cost of LTL transportation Dollars per unit TRCUS Transportation cost per unit Dollars per unit if speculation TRCUBM Transportation cost per unit-- Dollars per ubiquitous materials amount needed in one unit Of product TRCNUBM Transportation cost per unit-- Dollars per nonubiquitous materials amount needed in one unit of product TRCUP Transportation cost per unit Dollars per unit if postponement TRCS Transportation cost if Total dollars postponement TRCP Transportation cost if Total dollars speculation TCS Total cost if speculation Total dollars TCP Total dollars Total cost if postponement 138 TABLE 3.22. VARIABLE RANGE AND VALUE LEVELS Variable Range Value Levels PVALUE 1.00-15.00 1.00 4.50 8.00 11.00 15.00 DEMAND 600-48000 600 12000 24000 36000 48000 WUBIQM .30-.80 .30 .42 .55 .68 .80 UNCERT .03-.15 .03 .06 .09 .12 .15 TABLE 3.23. CONSTANT VALUES Constant Values DECDEM 5 CLS .35 NWHSES 3 DESPRO 2.0 ICCI .25 VUBIQM .10 139 TABLE 3.24. APPLICATION RELATIONSHIPS Variable Equation ADEMAND = ((100 - DECDEM)/ 100) * DEMAND TCLS = (DEMAND - ADEMAND) * PVALUE * CLS PMFGV = 5.545678 * (DEMAND * (l/UNCERT)) ** -.252713 WMFGV = 5.545678 * ((ADEMAND/B) * (l/UNCERT)) ** -.252713 WMFGF = 341.772155 + .430380 * ADEMAND FGCS = PMFGV * DEMAND MFGCP = (WMFGV * ADEMAND) + WMFGF PLTL = -.025 + 4.1666 * UNCERT CTL = .214286 + .035714 * PVALUE CLTL = CTL * 2 TRCUS = PLTL * CLTL + (l-PLTL) * CTL TRCUBM = .05 * WUBIQM TRCNUBM = (TRCUS/ (1 + WUBIQM)) * (1-WUBIQM) TRCUP = TRCUBM + TRCNUBM TRCS = TRCUS * DEMAND TRCP = TRCUP * ADEMAND BSTOCKS = DEMAND / 11 BSTOCKP 8 ADEMAND / 11 STDVUS - UNCERT * DEMAND STDVUP UNCERT * ADEMAND 140 TABLE 3.24. Continued Variable Equation SSTOCKS = STDVUS * DESPRO SSTOCKP = STDVUP * DESPRO ICCS = PVALUE * ICCI ICCP = PVALUE * (1 - VUBIQM) * ICCI INVS = (BSTOCKS + SSTOCKS) * ICCS INVP = (BSTOCKP + SSTOCKP) * ICCP TCS = MFGCS + TRCS + INVS TCP = TCLS + MFGCP + TRCP + INVP 141 becomes available when ubiquitous materials are not transported from plant to warehouse in the alternative of postponement. The plant variable manufacturing cost (PMFGV) is a function of DEMAND and UNCERT. The relationship between PMFGV and DEMAND is a negatively sloped exponential curve, whereby a higher level of demand corresponds to a lower PMFGV. The relationship of PMFGV with UNCERT is positive and linear, where a lower level of uncertainty will allow the firm to operate the manufacturing function with a higher proportion of optimum batch sizes and, thus, at a lower cost. The variable DEMAND is exponential, while UNCERT is linear. Because the inverse of a linear function is exponential, UNCERT is input in the equation for PMFGV in its inverse form (1/UNCERT). In this format, the two variables fit the same equation without distorting the relationships. Variable PMFGV varies between 15 and 90 cents per unit Of product, while variable WMFGV, the fixed warehouse manufacturing cost, varies between $600 and $21000 per product per period. A distinctive feature of the variable SSTOCKP in this application of the simulator is that the number of units of product in safety stock remains almost the same. It is affected only by the adjusted demand. What varies is the 142 average weight of the inventory, since only negligible amounts of ubiquitous materials are inventoried. It does not significantly affect its value, because the value of ubiquitous materials is assumed to be very low. The Objective of the application of the simulator to Model E, the time postponement-simulation model, is to decide whether products should be moved to the warehouse in anticipation of a customer order (speculation), or after that order has been received (postponement). The application has three subroutines: customer service, inventory, and transportation. The cost trade-off in the decision to postpone the shipment of goods to the warehouse is an increase in the cost of lost sales due to an increase in delivery time, an increase in transportation costs due to a greater proportion of LTL shipments to the warehouses, and a decrease in inventory carrying costs due to consolidation of inventories at the plant level. Application Assumptions Although the assumptions for_this application are not different from the application of the simulator to other models, two assumptions are reiterated here for greater 143 clarity. First, the time postponement-speculation model assumes form speculation: that is, products are not processed at the warehouse level. Second, the increase in delivery time does not affect delivery time consistency. Figures 3.16 and 3.16A show the block diagram for the computer program. Tables 3.25 to 3.27 present the variable list and the unit of analysis for each variable. Table 3.28 shows the range and the value levels for the inputs. Table 3.29 lists the constant values used as inputs to the simulator. Table 3.30 presents the application relationships in this application. The rest of this part addresses the criteria used to arrive at the relationships in Table 3.30. Application Relationships Two of the relationships in the alternative of postponement are examined further: the transportaion cost and the level of safety stock. The cost of transportation in the alternative of postponement is calculated with the same equation used for the alternative of speculation. The difference is that an increase in the proportion of LTL shipments is assumed. The proportion of LTL shipments in the alternative of postponement is fixed at 75 %. The level of safety stock in the alternative of postponement is a function of the level of safety stock 144 under speculation and of the number of warehouses in the system. The greater the number of warehouses, the greater the reduction in the level of safety stock made possible by postponing the shipment of goods to the warehouse. The number of warehouses in the system is a constant value of 3. Therefore, the level of inventory in the alternative of postponement will be equal to 1.8 times less the inventory in the alternative of speculation. Validation 9: Inputs In this part, literature and empirical support for the inputs to the simulator are discussed. The discussion is arranged by subroutines. In the subroutine customer service, the demand is adjusted downwards by 5 percent to compensate for an expected increase in delivery time if the firm decides to postpone the distribution of a product. The figure of 5 percent is a reasonable number, based on an empirical relationship between order cycle times and demand levels, whereas an increase of 2 days in order cycle time will cause the expected demand level to decrease by an average of 6.7 percent (LaLonde and Zinszer, 1976, p. 23,24). The cost of lost sales is set at 35 percent of the product's value. It is the contribution not made to profits because a sale was not completed. In the simulator, the 145 W MODEL E 4 BLOCK DIAGRAM 146 W MODEL E - SUBROUTINES IMflDnWUT NEDDWUI DUI: Dflfi: DWAND DEMAND IDCBU' UNORT PWQDE PWUUE GET GET ADBWUWI NNWMND l TM3 TRCP 147 TABLE 3.25. VARIABLE LIST--CUSTOMER SERVICE SUBROUTINE Variable name Definition Unit PVALUE Product value, manufacturer's Dollars per unit sales price of product DECDEM Percent decline in demand Index DEMAND Demand level for a product Units per period ADEMAND Adjusted demand Units per period CLS Cost of lost sales Proportion of product value TCLS Total cost of lost sales Total dollars 148 TABLE 3.26. VARIABLE LIST--INVENTORY SUBROUTINE Variable name Definition Unit BSTOCKS Base inventory if speculation Units of product BSTOCKP Base inventory if postponement Units of product UNCERT Uncertainty of demand Index variability STDVUS One standard deviation of Units of product demand if speculation STDVUP One standard deviation of Units of product demand if postponement DESPRO Level of inventory protection Number of standard devia- tions of demand NWHSES Number of warehouses supplying the market ICCI Inventory carrying cost Index-proportion of product value ICC Inventory carrying cost Dollars per unit SSTOCKS Safety stock if speculation Units of product SSTOCKP Safety stock if postponement Units of product INVS Inventory cost if speculation Total dollars INVP Inventory cost if postponement Total dollars TABLE 3. 149 27. TRANSPORTATION SUBROUTINE AND TOTAL COST Variable name Definition Unit PLTL Proportion of units of product Percentage CTL CLTL TRCS TRCP TCS TCP shipped at LTL rates Cost of TL transportation Cost of LTL transportation Transportation cost if speculate Transportation cost if postpone Total cost if speculation Total cost if postponement Dollars per unit Dollars per unit Total dollars Total dollars Total dollars Total dollars 150 TABLE 3.28. VARIABLE RANGE AND VALUE LEVELS Variable PVALUE DEMAND UNCERT Range 1.00-15.00 600-48000 .03-.15 Value Levels 1.00 600 .030 2.75 6600 .045 4.50 12500 .060 6.25 18500 .075 8.00 24000 .090 9.75 30000 .105 11.50 36000 .120 13.25 42000 .135 15.00 48000 .150 TABLE 3.29. CONSTANT VALUES Constant Value DECDEM 5 CLS .35 NWHSES 3 DESPRO 2.0 ICCI .25 151 TABLE 3.30. APPLICATION RELATIONSHIPS Variable Equation ADEMAND = ((100 - DECDEM)/ 100) * DEMAND TCLS = (DEMAND - ADEMAND) * PVALUE * CLS BSTOCKS = DEMAND /11 BSTOCKP = ADEMAND /11 STDVUS = UNCERT * DEMAND STDVUP = UNCERT * ADEMAND ICC = PVALUE * ICCI SSTOCKS = STDVUS * DESPRO SSTOCKP = STDVUP * DESPRO /(.6 + .4 * NWHSES) INVS = (BSTOCKS + SSTOCKS) * ICC INVP = (BSTOCKS + SSTOCKP) * ICC PLTL = -.025 + 4.1666 * UNCERT CTL = .214286 + .035714 * PVALUE CLTL = CTL * 2 TRCS = (( PLTL * CLTL) + (l-PLTL) * CTL) * DEMAND TRCP = ((.75 * CLTL) + (.25 * CTL)) * ADEMAND TCS = INVS + TRCS TCP = TCLS + INVP + TRCP 152 contribution margin is determined as an approximation of the average between high and low margin products. Margins are obtained from the accounting literature. One product, smoking pipes, has a contribution margin of 45 percent, while a second product, food retail items, has a contribution margin of 19 percent. (Horngreen, 1974, p.263,351). Several inputs are discussed in the inventory subroutine. The range for uncertainty of demand variability is based on the fact that this input is a substitute for the standard deviation of demand, which cannot be generated because the simulation is static. Statistically, the value of the standard deviation can be estimated at one fourth of the range for the variable demand, assuming that the demand is normally distributed. To estimate a range for the demand, it is assumed that the error of a poor forecast is +/- 30 percent, while the error of an accurate forecast is assumed to be +/- 5 percent (Cox and Rao, 1975, p. 75). The poor forecast is used to estimate the upper limit of the input UNCERTAINTY, whereas the accurate forecast is used to estimate the lower limit of the input. The base stock is estimated to be equal to half of the safety stock. This relationship is approximately the average between a high relationship of base to safety stock, where base and safety stock are equal (Heskett, Ivie, Glaskowsky, 1973, p. 292), and a low relationship between base and 153 safety stock, where the base stock is equal to one-fifth of the safety stock (Lambert and Stock, 1982, p. 292). In the simulator, the equation for safety stock is a function of three variables: uncertainty, demand, and the level of protection for uncertainty. The level of protection is a constant. By using an average value within the range for uncertainty, the value for the base stock is derived as 1/11th. of the demand. The values for the constants in the inventory subroutine are obtained as follows: the level of protection for demand uncertainty (DESPRO) is set at 2 standard deviations of demand (Bowersox, 1978, p. 185). The number of warehouses in the system is an assumption in the normative cost models. Finally, the cost of carrying inventories (ICCI) is set at 25 percent of the product value (Lambert and Stock, 1982, p. 262). In the transportation subroutine, the cost of LTL transportation is equal to twice the cost of TL transportation (Coyle, Bardi,and Cavinato, 1982, p.251). The cost savings from the transportation of products in bulk is estimated at between 19 and 53% of the original expense (Heskett, Ivie, Glaskowsky, 1973, p. 598). Since the average value between these two numbers is nearly 35 percent, the cost of bulk transportation is assumed equal to 65 percent of the TL rate for the same product. 154 The remaining inputs in the simulator were validated on the basis of personal interviews with practitioners. Two interviews were conducted: Mr. Jim Countryman, Vice- President for Distribution, Del Monte USA; and Mr. David Friedson, President, Windmere Corporation. The two respondents were asked to evaluate the range for inputs not validated within the business literature. As a result of their helpful comments, the range for a number of inputs was reviewed. The last section in this chapter presents the research hypotheses and the methodology adopted to test them. BE§EABQH_HXEQIHE§I§_AND_MEIEQDQLQ§X This section is divided into two parts: research hypotheses and methodology. The first part contains the research hypotheses, which are drawn from the research objective of learning the importance of a number of product physical and demand characteristics on the decision to postpone or speculate on the distribution of a product. There are between three and five hypothesis for each of the five models, for a total of twenty hypotheses in the study. The second part contains the methodology. It is divided in three major segments. The tests selected to validate the simulator are in the first segment. To provide a statistical background for the test of the hypothesis, a review of the 155 most important features of discriminant analysis is presented in the second segment. The statistical procedure adopted to test the hypotheses is in the third segment. Research H o heses The research hypotheses are presented below. Model A A1. The GREATER the level of demand (DEMAND), the GREATER the incentive to postpone labeling to the warehouse level. A2. The GREATER the level of uncertainty of demand (UNCERT), the GREATER the incentive to postpone labeling to the warehouse level. A3. The GREATER the number of brands that a product is offered to the market (NBRANDS), the GREATER the incentive to postpone labeling to the warehouse level. A4. The GREATER the product value (PVALUE), the GREATER the incentive to postpone labeling to the warehouse level. Model B B1. The GREATER the total level of demand for a product (DEMANDT), the GREATER the incentive to postone packaging to the warehouse level. B2. The GREATER the level of uncertainty of demand (UNCERT), the GREATER the incentive to postpone packaging to the warehouse level. BB. The GREATER the number of package sizes that the product is offered to the market (NSPACK), the GREATER the incentive to postpone packaging to the warehouse level. B4. The GREATER the value of the product (PVALUE), the greater ther incentive to postpone packaging to the warehouse level. 156 Model C C1. The GREATER the level of demand (DEMAND), the GREATER the incentive to postpone assembly to the warehouse level. C2. The GREATER the level of uncertainty of demand (UNCERT), the GREATER the incentive to postpone assembly to the warehouse level. C3. The GREATER the number of versions in which a product is offered to the market (NVER), the GREATER the incentive to postpone assembly to the warehouse level. C4. The GREATER the reduction in product cube (CUBER) made possible by shipping unassembled products to the warehouse level, the GREATER the incentive to postpone assembly to the warehouse level. C5. The GREATER the value of the product (PVALUE), the GREATER the incentive to postpone assembly to the warehouse level. Model D D1. The GREATER the level of demand (DEMAND), the GREATER the incentive to postpone manufacturing to the warehouse level. D2. The GREATER the level of uncertainty of demand (UNCERT), the GREATER the incentive to postpone manufacturing to the warehouse level. D3. The GREATER the weight of ubiquitous materials (WUBIQM) relative to the total weight of the product, the GREATER the incentive to postpone manufacturing to the warehouse level. D4. The GREATER the value of the product (PVALUE), the GREATER the incentive to postpone manufacturing to the warehouse level. Model E E1. The GREATER the level of demand (DEMAND), the GREATER the incentive to postpone shipment to the warehouse level. E2. The GREATER the level of uncertainty of demand (UNCERT), the GREATER the incentive to postpone shipment to the warehouse level. E3. The GREATER the product value (PVALUE), the GREATER the incentive to postpone shipment to the warehouse level. 157 Methodglogy An overview of the methodology for this research must include four basic steps. The first step is to generate the input for the simulator. For each of the models, the inputs are assigned a number of value levels, which are reported in Tables 3.2, 3.8, 3.15, 3.22, and 3.28. The number of value levels assigned to all input variables in a given model is a function of the number of variables in that model, to assure an adequate run size. The input for each of the application of the simulator is given by all possible combinations of the value levels for all input variables. The next three steps, simulator, validation tests, and hypothesis testing procedure, are explained below. Simulator A Lotus 1-2-3 spreadsheet is utilized as the simulator in this research. The objective of the simulator is to generate one output per product, postpone or speculate. The input to the simulator is the matrix defined in the paragraph above. Such matrix is placed at the beginning of the spreadsheet, with all products displayed in the first column. Thus, the spreadsheet has as many rows as there are products in the sample. The input variables occupy the next columns; there are as many columns as there are inputs in 158 one particular model. The subsequent columns contain the algorithm as defined in Tables 3.4, 3.10, 3.17, 3.24, and 3.30. The computation of the output is the next step, and it is repeated for each product in the sample. The last column in the spreadsheet contains the output. Postponement is represented by the number one, while speculation is represented by the number zero. Validation Tests Each of the applications to the simulator is validated according to the following three steps. One, the simulation output is compared to an output calculated by hand in a sub- sample of ten products. The goal of this test is to check for any programming mistakes in the application of the simulator. The objective of step two is to find out if the simulator is performing according to the theory used to build it. A group of ten products that should be clearly postponed, and a group of ten products that should be cleared speculated on are selected, and run on the simulator. Expected and observed outputs are then compared. Step three is a face validity test. One expert in the fields of computer simulation and business logistics was 159 asked to answer the following two questions for each of the applications of the simulator: - Are there any logic errors in the simulator? — Is the range for the inputs reasonable? Discriminant Analysis Discriminant analysis is a multivariate statistical procedure with a large number of applications in business research. It involves deriving the linear combination of a number of independent variables that discriminate best between a priori defined groups (Hair, Tatham, Anderson, Grablowsky, 1979, p. 85). The procedure is most useful for three major purposes in research: to classify units (subjects, products, etc.) into groups, to 'profile' characteristics of groups, and to identify major dimensions which differentiate among groups (Crask and Perreault, 1977, p. 60). Discriminant analysis assumes two conditions fOr Optimal application. Independent variables are metric and normally distributed, and the covariance matrices are equal. However, discriminant analysis is considered very robust to violations of these assumptions. (Hair, Tatham, Anderson, Grablowsky, 1979, p. 86). A number of concepts are important to understand the technique. The discriminant function is a linear equation where the independent variables are related to the z-score, 160 which is a number generated by the sum of all independent variables, multiplied by their respective unstandardized discriminant weights. The 2 score is compared to the cutting score to determine the classification of a particular product or subject: if the product/subject is on one side of the cutting score, it is classified in one group; otherwise, it is classified in a second group. The cutting score is determined with a formula based on the mean (centroid) and on the size of the two groups. The discriminant weight is determined by the variance structure of the independent variable. Unstandardized weights are used in the discriminant function, while standardized weights are partial correlation coefficients between the dependent and one of the independent variables. Thus, standardized discriminant weights are useful to determine the relative importance of independent variables. Discriminant loadings are also useful to estimate the relative importance of independent variables. Discriminant loadings are the simple correlation coefficient between an independent variable and the discriminant function. Finally, the hit-ratio is the percentage number of cases classified correctly with the discriminant function, relative to the actual membership of a subject/product. The last issue in discriminant analysis is interpretation. Morrison (1969, p. 162) provides an eight point general framework for that purpose, which is 161 reproduced below: 1. A linear discriminant function is appropriate only when the groups covariance matrices are equal (or nearly equal). 2 2. The D statistic (which may be transformed to an F statistic) only tests the statistical significance of the difference between groups. Recall the effect of the sample size on statistical significance. 3. Beware of the upward bias that results from classifying the same individuals used to calculate the discriminant function. 4. Beware of the different chance models that can result when groups have different sizes. Remember that greatly unequal-sized groups make interpretation of the classification table difficult. 5. The effective sample size is governed by the smaller group. 6. Have the discriminant coefficients been normalized by the standard deviations of the independent variables? 7. In forming the classification decision, be sure that prior probabilities and opportunity costs of misclassification have been considered. 8. Will the independent variables used for discrimination be operational? The items of this framework that are relevant for this research are used as the basis for the data analysis in Chapter IV. Hypothesis Testing Procedure The hypotheses are tested with a three step procedure. First, once the output of the simulation is generated, it is attached to the input data, hence creating an input/output matrix. Such a matrix contains the values for all input 162 variables and the output (postpone or speculate) for all products. The input/output matrices for each of the applications of the simulator appear in Appendix A. Second, the input output matrix is split into two equivalent halves of approximately the same size. The first half is named the analysis sample, and the second is the hold-out sample. A discriminant analysis is performed in the analysis sample, using the input variables as the independent variables and the output as dependent variables. The discriminat function is then tested in the hold-out sample, and the hit-ratio is computed for validation purposes. In order for the discriminant function to be considered for further analysis, the hit ratio has to be larger than the chance of correctly classifying products without the discriminant function. In addition, a t-test of significance is performed on the hit-ratio at an alpha level of five percent. Third, hypotheses are tested with the discriminant weights. If the discriminant weight is significant at an alpha level of five percent, and if the algebraic sign of the discriminant weight is as hypothesized, the hypothesis is accepted. QHAEIEB_I! DAIA_ANALX§I§ The purpose of this chapter is to present the data analysis. It is structured in five separate sections, one for each application of the simulator. Each of these sections is subdivided into four parts. The first part demonstrates the validation procedure for the application of the simulator. The second part presents the application input/output, where the procedure for generating the input is explained, and the application output reported. The third part, findings, contains the discriminant analysis used to test the hypotheses pertinent to the application of the simulator at hand. Finally, the fourth part analyzes results in the context of business logistics theory. MODEL A This first section discusses the application of the simulator to Model A, the labeling model. 163 164 yalidatien The procedure to validate the application of the simulator to Model A is threefold. The first procedure is a test to determine whether any computational mistakes exist in the computer algorithm. To that end, hand and computer calculations are compared in a subsample of ten products. In this application of the simulator, no differences were found up to two decimal points in the total cost for any of the two subroutines: labeling and inventory. The objective of the second test is to determine whether this application of the simulator responds to the inputs according to the theory used to build it. To that end, ten extreme products where the labeling process should be clearly postponed to the warehouse level, and ten extreme products where the labeling process should be clearly speculated at the plant level are chosen, and the expected output is compared to the observed output. The criterion to select the products for the comparison is to choose products within the highest or lowest two levels of each variable. In this particular application, products to be postponed should have a high level of demand, a high product value, a high level of demand uncertainty, and a large number of brands. Products to be speculated on should have opposite characteristics. The result of the comparison is demonstrated in Table 4.1. Clearly, all products conform to 165 the expected outcome. In this table, as in the last two chapters in this dissertation, the variable postponement is represented by the number 1, while the variable speculation is represented by the number 0. IAELE_&11 R T U S O E EME PRODUCTS PRODUCT DEMAND UNCERTAINTY N.BRANDS VALUE EXP. OBS. 1 600 0.03 1 1.00 0 0 2 600 0.03 1 4.50 0 0 3 600 0.03 2 1.00 0 0 4 600 0.03 2 4.50 0 0 5 600 0.06 1 1.00 0 0 6 600 0.06 1 4.50 0 0 7 600 0.06 2 1.00 0 0 8 600 0.06 2 4.50 0 0 9 12000 0.03 1 1.00 0 0 10 12000 0.03 1 4.50 0 0 11 36000 0.12 6 15.00 1 1 12 36000 0.12 6 11.50 1 1 13 36000 0.15 6 15.00 1 1 14 36000 0.15 6 11.50 1 1 15 48000 0.12 6 15.00 1 1 16 48000 0.12 6 11.50 1 1 17 48000 0.15 6 15.00 1 1 18 48000 0.15 6 11.50 1 1 19 48000 0.15 5 15.00 1 1 20 48000 0.15 5 11.50 1 1 The third step in the validation procedure is the face validity test. Its objective is to Obtain from an expert in computer simulation and in business logistics answers to two questions: Are there any errors of logic in the application of the simulator? Is the range for the application inputs reasonable? Dr. David J. Closs, Associate Professor at Michigan State University agreed to comment on the 166 questions. Professor Closs' review was invaluable to this application of the simulator. 1' t'o t O The inputs to the application are generated from Table 3.2 in the previous chapter. Each of these input variables is assigned five levels within the range established for it. The input table consists of all possible combinations of the four input variables. Consequently, the total number of products in the input table is equal to 625. The output of the application is obtained by running the input table through the application relationships, as defined on Table 3.1 in Chapter III. This application is programmed to run on a Lotus 123 spreadsheet. Once the output is generated for every one of the 625 products, it is incorporated as the last column in the input/output table. The output for Model A produced 201 cases of postponement and 424 cases of speculation. Pingings The hypotheses pertinent to this application of the simulator are tested with the use of discriminant analysis. A review of the relevant aspects of the technique can be found in the methodology section of Chapter III. In this 167 part, the analysis focuses initially on the discriminant analysis itself, followed by the formal test of hypotheses using the discriminant weights and a test of significance. Discriminant Analysis The discriminant analysis is performed on an analysis sample and validated on a hold-out sample. These samples are extracted from the original list of products in the input/output matrix. Odd numbered products are in the analysis sample, and even numbered products in the hold-out sample. The only exception is product number 625, which is in the hold-out sample. The analysis presented in the tables below is based on the analysis sample, while the hit-ratio presented in Table 4.8 is based on the hold-out sample. Table 4.2 introduces the mean values for the independent variables, as well as the centroids for the two groups. Table 4.3 shows the correlation matrix for the independent variables. The next four tables present a test of significance and the correlation coefficient for the discriminant function, the significance tests for the independent variables, the discriminant weights and loadings, and the test for equality of group covariance matrices, respectively. 168 PS DEMAND UNCERTAINTY N.BRANDS P.VALUE CENTROIDS 0 23957 .07766 2.911 6.397 -.75344 1 24232 .11633 4.438 11.428 1.64527 TOTAL 24044 .08981 3.391 7.977 ----- TABLE_111 QQBEELATIQE_EATBIX DEMAND UNCERT NBRANDS PVALUE DEMAND 1.000 UNCERT -.010 1.000 NBRANDS -.010 -.200 1.000 PVALUE -.011 -.257 -.229 1.000 TABLE_111 DIEQBIMIHANI_EQEQTIQN_QQBEELAIIQN CORR. COEFFICIENT CHI-SQUARED D.F. SIGNIFICANCE .74503 2249.44 4 .0000 169 W S C - E T V VARIABLE F SIGNIFICANCE DEMAND .0178 .8938 ** UNCERT 67.55 .0000 NBRANDS 53.11 .0000 PVALUE 88.77 .0000 ** - Not significant. W . C 1.. 1’ x- . . . 9 x- A. x . VARIABLE DISCR. WEIGHT RANK DISCR. LOADING RANK DEMAND .0320 4 .0068 4 UNCERT .7815 2 .4179 2 NBRANDS .7220 3 .3705 3 PVALUE .8465 1 .4790 1 W O 'S S ROUP V C TR C S BOX'S M APPROXIMATE F DEGREES OF FREEDOM SIGNIFICANCE 33.818 3.3245 174569.4 170 ACTUAL NUMBER OF CORRECTLY HIT-RATIO VARIABLE CASES OBSERVED CLASSIFIED ERROR (CORR./ACTUAL) POSTPONEMENT 103 79 24 .76 SPECULATION 210 203 7 .96 TOTAL 313 282 31 .90 * * - significant at an alpha level of 5 percent. Hypothesis Testing The hypotheses for Model A are stated in Chapter III. However, for greater clarity, they are reproduced below. A1. The GREATER the level of DEMAND, the GREATER the incentive to postpone labeling to the warehouse level. A2. The GREATER the level of UNCERTAINTY of demand, the GREATER the incentive to postpone labeling to the warehouse level. A3. The GREATER the NBRANDS, the GREATER the incentive to postpone labeling to the warehouse level. A4. The GREATER the PVALUE, the GREATER the incentive to postpone labeling to the warehouse level. There are two alternative approaches one can adopt to test the hypotheses. The first involves the use of discriminant weights, while the second is based on the use of discriminant loadings. The major advantage of using loadings is that they are considered more stable than the weights (Hair, Anderson, Tatham, Grablowsky, 1979, p. 108). 171 To understand the advantage of the first approach, it is important to note that the loadings are simple correlations between the estimate of the dependent variable and the independent variable. On the other hand, weights are partial correlation coefficients that measure the strength of the relationship between an independent and the dependent variable when other independent variables are held constant. However, as can be noted from observing Table 4.3, the level of correlation among the independent variables is very low. In these cases, the discriminant weights and the discriminant loadings will provide a similar ranking of the relative importance of the independent variables. Table 4.6 provides the discriminant weights needed to determine the directionality of the relationships in the hypotheses above, while Table 4.5 provides the significance tests. A hypothesis is accepted if the directionality is as predicted and if the independent variable is significant at an alpha level of five percent. An examination of Table 4.5 shows that the variable DEMAND is not significant at an alpha level of five percent and, thus, Hypothesis A1 is rejected. The remaining variables are significant. It can be observed in Table 4.2 that the centroid for the postponement group is larger than the one for the speculation group. It follows, then, that a positive sign in the discriminant weights indicates a direct relationship between an increase in the value of an 172 independent variable and the incentive to postpone labeling to the warehouse level. As a consequence, Hypotheses A2 to A4 are accepted, since the sign of the discriminant weight follows the criteria outlined above. The relationship between the independent variables and the incentive to postpone is further illustrated in Figures 4.1 to 4.4. Dissueeieu The discussion of the findings consists of two segments. The objective of the first segment is to demonstrate that the discriminant analysis is valid and that the results can be used with reasonable certainty of its correctness. In the second segment, results are explained within the context of business logistics theory. Validation of the Discriminant Analysis Morrison (1969) presents a series of eight points to be considered when interpreting a discriminant analysis. Of these, four appear relevant in the context of this research. First, the covariance matrices for the two groups must be equal. The test for equality of covariance matrices is in Table 4.7 and shows that these actually are not equal. Two N OF P’JSTPONEME "1'5 80 70" 60‘ 550-1 20‘ 173 FIGURE—4.3.1 MODEL A - RELATIONSHIP BETWEEN DEMAND AND THE INCENTIVE TO POSTPONE a! O 20 4O (Thousands) DEMND U O..4O N. OF POSTPONEMENTS 174 W MODEL A - RELATIONSHIP BETWEEN UNCERTAINTY AND THE INCENTIVE TO POSTPONE so 76 - (so - 50‘ 40 ~ ,» ~30 " /" 2.. / / 0 0.02 0.04 0.06 0.0! 0.1 0.12 0.14 UNCERTAINTY U 0. .45 N. OF POSTPONEME HTS 30 70" 60‘ ‘ ///////B—f_d——fl 50-4 / 40- //// 175 W MODEL A - RELATIONSHIP BETWEEN NUMBER OF BRANDS AND THE INCENTIVE TO POSTPONE 3f) - a NUHKR 0F BRANDS-i N, OF POSTPONEMENT; 176 W MODEL A - RELATIONSHIP BETWEEN PRODUCT VALUE AND THE INCENTIVE TO POSTPONE so 70 - / 60 4 so 4 40" / 30q / 20'1 / 10‘ ff PRODUCT VALUE 16 177 factors must be considered in interpreting the results of the equality of covariance test. One, the discriminant analysis is considered a robust technique to violations of the assumption of equal covariance matrices (Klecka, 1975). Two, the test itself is considered very sensitive to nonnormality of the independent variables, and may therefore be invalid to determine the equality of covariance matrices when the independent variables are uniformly distributed, as in this analysis (Morrison, 1976). Second, the two groups must be statistically different. The chi-square test for the difference between groups is presented in Table 4.4, and shows that the two groups are in fact statistically different. Third, the discriminant function must not be validated with the same data applied to extract the function or an upward bias may result. To prevent such bias in this analysis, the data set was split into an analysis and a hold-out sample. The classification table with the hit-ratio is presented in Table 4.8. The hit-ratio of 90 percent is adequately high. Fourth, the hit-ratio should be compared with prior classification criterion, which is the probability that a product will be correctly classified without the discriminant function. The criterion utilized to calculate that probability is the proportional chance criterion (Morrison, 1969), and the value is 57 percent. 178 Explaining Results Four hypotheses are tested, and each is examined in greater detail. Hypothesis Al is rejected because the discriminant weight is not significant. This is explained by the fact that the variable DEMAND has two opposite effects on the decision to postpone or to speculate on the labeling of a product. The first effect is on the cost of labeling. The higher the level of demand, the higher the economies of scale enjoyed from labeling products at the plant level and, therefore, the higher the incentive to speculate. The second effect is on inventory carrying costs. The higher the level of demand, the higher the costs of maintaining inventories. As a result, the incentive to postpone labeling to the warehouse is greater, since the cost differential between the alternatives of postponement and speculation in the inventory subroutine is enhanced. Results suggest that the two effects are equally strong and that variable DEMAND has no significant impact on the decision to postpone or to speculate labeling to the warehouse level. The explanation for the results obtained in Hypothesis A2 is that the effect of UNCERTAINTY on the cost of carrying inventories outweighs the effect on the labeling cost. The effect of demand UNCERTAINTY on inventory carrying cost is related to its impact on the level of safety stocks, which 179 is well documented in the literature (Bowersox, 1978, p. 151-2). The higher the level of UNCERTAINTY, the higher the level of safety stock, and the higher the cost of speculation relative to the cost of postponement. The effect of UNCERTAINTY on the cost of labeling derives from the fact that a high level of demand variability will increase the number of non-optimum size labeling runs and thus increase the cost of postponement relative to the cost of speculation. Variable UNCERTAINTY appears to have a strong effect on the decision to postpone or to speculate on the labeling of a product. In Hypothesis A3, variable NBRANDS also has two opposing effects on this application of the simulator. First, the number of brands affects the cost of labeling because the higher the number of brands, the shorter the size of each labeling run and, hence, the higher the cost of postponement relative to the cost of speculation. Second, the higher the number of brands, the lower the opportunity to consolidate safety stocks, and the higher the cost of speculation relative to the cost of postponement. Results indicate that the second effect is stronger than the first, and that a higher number of brands increases the cost advantage of postponing labeling to the warehouse level. Variable NBRANDS appears to have a moderately strong effect on the decision to postpone or to speculate on the labeling of a product. 180 In Hypothesis A4, the effect of PVALUE on the simulator is unidimensional. PVALUE is directly related to the cost of carrying inventories. Therefore, the higher the value of a product, the higher the incentive to postpone labeling to the warehouse level. In conclusion, three variables appear to influence the decision to postpone or to speculate on the labeling of a product: the value of the product, the uncertainty of demand, and the number of brands in which the product is Offered in the marketplace. The level of demand appears to have a weak impact in that decision. MQDEL_B The second section in this chapter discusses the application of the simulator to Model B, the packaging model. Like the discussion of Model A, it is subdivided into four parts: simulator validation, application input/output, findings, and explanation of results. Va ' t'on Validating the application of the simulator to Model B is a threefold procedure. The first test determines whether there are any computational mistakes in the computer algorithm. To that end, hand and computer calculations are compared in a subsample of ten products. In this application 181 of the simulator, no differences were found up to two decimal points in the total cost for any of the three subroutines; packaging, transportation, and inventory. The second test determines whether this application of the simulator responds to the inputs according to the theory used to build it. To that end, ten extreme products where the packaging process should be clearly postponed to the warehouse level, and ten extreme products where the packaging process should be clearly speculated at the plant level are chosen, and the expected output is compared to the observed output. The criterion to select the products for the comparison is to choose products within the highest or lowest three levels of each variable. In this particular application, products to be postponed should have a high level of demand, a high product value, a high level of demand uncertainty, and a large number of package sizes. Products to be speculated on should have opposite characteristics. The result of the comparison is demonstrated in Table 4.9, where, clearly, all products conform to the expected outcome. In this application of the simulator, as in the previous one, variable postponement is represented by the number 1, while the variable speculation is represented by the number 0. 182 TAELE_112 OBS R D L_I XP- D 0 T' OR _XT’ "0l PRODUCT DEMAND UNCERTAINTY NSPACK PVALUE EXP. OBS. 1 600 0.03 1 1.00 0 0 2 600 0.03 1 4.50 0 0 3 1440 0.03 2 1.00 0 0 4 1440 0.03 2 4.50 0 0 5 600 0.06 1 1.00 0 0 6 600 0.06 1 4.50 0 0 7 1440 0.06 2 1.00 0 0 8 1440 0.06 2 4.50 0 0 9 2500 0.03 1 1.00 0 0 10 2500 0.03 1 4.50 0 0 11 37200 0.15 5 15.00 1 1 12 37200 0.15 5 11.50 1 1 13 44000 0.12 4 15.00 1 1 14 44000 0.12 4 11.50 1 1 15 48000 0.12 5 15.00 1 1 16 48000 0.12 5 11.50 1 1 17 44000 0.15 4 15.00 1 1 18 44000 0.15 4 11.50 1 1 19 48000 0.15 5 15.00 1 1 20 48000 0.15 5 11.50 1 1 The face validity test forms the third step in the validation procedure. The objective of this test is to request input from an expert in computer simulation and in business logistics to answer two questions: Are there any errors of logic in the application of the simulator? Is the range for the application inputs reasonable? Dr. David J. Closs, Associate Professor at Michigan State University agreed to comment on the questions. Professor Closs' review was invaluable to this application of the simulator. 183 Application lnputzgutpup The inputs to the application are generated from Table 3.8 of the previous chapter, where the input variables were assigned five levels within the range established for them. That table consists of all possible combinations of the four input variables. Hence, the total number of products in the input table is equal to 625. The output of the application is obtained by running the input table through the application relationships, as defined in Table 3.10 in Chapter III. The application is programmed to run on a Lotus 123 spreadsheet. Once the output is generated for every one of the 625 products, it is incorporated as the last column in the input/output table. The output for Model B produced 419 cases of postponement and 206 cases of speculation. The hypotheses pertinent to this application of the simulator are tested by using discriminant analysis. A review of the relevant aspects of the technique is found in the methodology section of Chapter III. In this part, the analysis focuses initially on the discriminant analysis itself, followed by the formal test of hypotheses using the discriminant weights and a test of significance. 184 Discriminant Analysis The discriminant analysis is performed on an analysis sample and validated on a hold-out sample. These samples are extracted from the original list of products in the input/output matrix. Even numbered products are in the analysis sample, while Odd numbered products are in the hold-out sample. The analysis shown in the tables below is based on the analysis sample, whereas the hit-ratio in Table 4.16 is based on the hold-out sample. Table 4.10 introduces the mean values for the independent variables, as well as the centroids for the two groups. Table 4.11 shows the correlation matrix for the independent variables. The next four tables present a test of significance and the correlation coefficient for the discriminant function, the significance tests for the independent variables, the discriminant weights and loadings, and the test for equality of group covariance matrices, respectively. 185 PS DEMANDT UNCERT. NSPACK PVALUE CENTROIDS 0 11616 .07029 2.476 3.800 -1.57140 1 18599 .10000 3.265 10.130 .79709 TOTAL 16249 .09000 3.000 8.000 ------ TABLE flgll WK DEMANDT UNCERT NSPACK PVALUE DEMANDT 1.000 UNCERT -.087 1.000 NSPACK .558 -.096 1.000 PVALUE -.189 -.267 -.208 1.000 CORR. COEFFICIENT CHI-SQUARED D.F. SIGNIFICANCE .74675 251.22 4 .0000 186 W ES N - D EN V S VARIABLE F SIGNIFICANCE DEMANDT 19.30 .0000 UNCERT 38.27 .0000 NSPACK 179.3 .0000 PVALUE 24.54 .0000 W ' iv. 2 4" in. 'NG VARIABLE DISCR. WEIGHT RANK DISCR. LOADING RANK DEMANDT .2594 4 .2222 4 UNCERT .6296 2 .3129 2 NSPACK .3618 3 .2440 3 PVALUE .9701 1 .6772 1 W "1'4 F OxUL 0 G'O P C\70;_’. C L. RIC BOX'S M APPROXIMATE F DEGREES OF FREEDOM SIGNIFICANCE 15.313 1.5065 10, 210127.6 .1297 187 IEEEJLAEIQ. C SS C N T OR 0 -OUT S ACTUAL NUMBER OF CORRECTLY HIT-RATIO VARIABLE CASES OBSERVED CLASSIFIED ERROR (CORR./ACTUAL) POSTPONEMENT 212 202 10 .95 SPECULATION 101 87 ' 14 .86 TOTAL 313 290 23 .92 * * - significant at an alpha level of 5 percent. Hypothesis Testing The hypotheses for Model B are stated in Chapter 3. However, for the purpose Of greater clarity, they are reproduced below. Bl. The GREATER the level of DEMANDT, the GREATER the incentive to postpone packaging to the warehouse level. B2. The GREATER the level of UNCERTAINTY of demand, the GREATER the incentive to postpone packaging to the warehouse level. B3. The GREATER the NSPACK, the GREATER the incentive to postpone packaging to the warehouse level. B4. The GREATER the PVALUE, the GREATER the incentive to postpone packaging to the warehouse level. One can adopt two alternative approaches test these hypotheses. The first involves the use of discriminant weights, while the second is based on the use of discriminant loadings. The major advantage of loadings is 188 that they are considered more stable than the weights (Hair, Anderson, Tatham, Grablowsky, 1979). To understand the advantage of the first approach, it is important to note that the loadings are simple correlations between the estimate of the dependent variable and the independent variable. On the other hand, weights are partial correlation coefficients that measure the strength of the relationship between an independent and the dependent variable when other independent variables are held constant. As noted in Table 4.11, there is a degree of colinearity among some of the independent variables. Consequently, adopting the first approach in this analysis is advised. Table 4.14 provides the discriminant weights needed to determine the directionality of the relationships in the hypotheses above, while Table 4.13 provides the significance tests. A hypothesis is accepted if the directionality is as predicted and if the independent variable is significant at an alpha level of five percent. An examination of Table 4.13 shows that all variables are significant at an alpha level of five percent. It can be Observed in Table 4.10 that the centroid for the postponement group is larger than the centroid for the speculation group. It follows that a positive sign in the discriminant weights indicates a direct relationship between an increase in the value of an independent variable and the incentive to postpone packaging to the warehouse level. 189 As a consequence, all hypotheses are accepted, since the sign of the discriminant weight follows the criteria outlined above. The relationship between the independent variables and the incentive to postpone is further illustrated in Figures 4.5 to 4.9. 215.621.15.123 The discussion of the findings consists of two segments. In the first segment, the objective is to demonstrate that the discriminant analysis is valid and that the results can be used with reasonable certainty of its correctness. In the second segment, the objective is to explain results within the context of business logistics theory. Validation of the Discriminant Analysis Morrison (1969) presents a series of eight points to be considered when interpreting a discriminant analysis. Of these, four appear relevant to this research. First, the covariance matrices for the two groups must be equal. The test for equality of the covariance matrices 190 W MODEL B - RELATIONSHIP BETWEEN DEMAND AND THE INCENTIVE TO POSTPONE llOfi 100" -a 90— // 80: B/ 704 / N OF PO STPONENE NTS JO‘T 0 T T T I I 84 40 '20 CHwMomwm) DEMANDT OF P'CISTP‘DNEMENTS N. 191 W MODEL B - RELATIONSHIP BETWEEN.UNCERTAINTY AND THE INCENTIVE TO POSTPONE 120 110 ‘t 100 " so 4 80‘ 7O -‘ 60m 50 r 40‘ 0.02 0.04 0 .06 0.08 UNCERTAINTY 0.l 0.12 f H— 0.14 0.16 N OF POSTPONEMENTS 192 W MODEL B - RELATIONSHIP BETWEEN NUMBER OF PACKAGE SIZES AND THE INCENTIVE TO POSTPONE 110 m 100 4 90.. W 801 / 7o-« 60‘ 50- 40- .30-I 20-I 10 ‘ NSPACK N. OF POSTPONEME NTS 193 EME—L}. MODEL B - RELATIONSHIP BETWEEN PRODUCT VALUE AND THE INCENTIVE TO POSTPONE 120 110 " mt) -* 90 '1 Em -' 70" f 60" / 40-1 30-4 PRODUCT VALUE 16 194 is in Table 4.15. It shows that the covariance matrices actually are not equal. Two factors must be considered in interpreting the results of the equality of covariance test. One, the discriminant analysis is considered a robust technique to violations of the assumption of equal covariance matrices (Klecka, 1975). Two, the test itself is considered very sensitive to nonnormality of the independent variables, and thus may not be valid to determine the equality of the covariance matrices when the independent variables are uniformly distributed, as in this analysis (Morrison, 1976). Second, the two groups must be statistically different. The chi-square test for the difference between groups is presented in Table 4.12, and shows that the two groups are in fact statistically different. Third, the discriminant function must not be validated with the same data applied to extract the function. If that happens, an upward bias in the hit-ratio may result. To prevent such bias, the data set is split into an analysis sample and a hold-out sample to prevent such bias. The classification table with the hit-ratio is presented in Table 4.16. The hit-ratio of 92 percent is adequately high. Fourth, the hit—ratio should be compared with a prior classification criterion, which is the probability that a product will be correctly classified without the discriminant function. The criterion utilized to calculate 195 that probability is the proportional chance criterion (Morrison, 1969), and the value is 55 percent. Explaining Results Four hypotheses are tested, and each is examined in greater detail. Hypothesis B1 is accepted. Variable DEMANDT affects the the three subroutines of this application of the simulator. In the first effect, it is directly related to the cost of packaging. A high value of DEMANDT increases both the cost of packaging and the difference between the cost of packaging at the warehouse compared to the cost of packaging at the plant. As a result, in this first effect, a high value of DEMANDT is an incentive to speculate on the packaging of a product. This effect, however, is opposed by the effects on the two other subroutines. A high level of DEMANDT increases the overall level of inventories in the system by increasing the number of units in stock. Similarly, a higher level of DEMANDT increases the overall cost of transportation in the system. In these last two effects, a high level of DEMANDT increases the cost advantage of postponement as opposed to speculation at the plant level. A positive algebraic sign in the discriminant weight shows that the second and third effects outweigh the first. Variable DEMANDT appears to have a weak effect on the decision to postpone packaging to the warehouse level. 196 The results obtained in Hypothesis B2 can be explained by the two effects of variable UNCERTAINTY on this application of the simulator. Both effects follow the same direction, where a high level of UNCERTAINTY is an incentive to postpone packaging to the warehouse level. In the first effect, a high level of UNCERTAINTY increases the level of safety stocks. This effect is well documented in the literature (Bowersox, 1978, p. 151-2). In the second effect, UNCERTAINTY of demand is important in determining the difference in transportation costs in the alternatives of postponement and speculation, because the level of uncertainty determines the proportion of shipments that are truckload, as opposed to less-than-truckload. Variable UNCERTAINTY appears to have a moderately strong effect on the decision to postpone packaging to the warehouse level. In Hypothesis B3, variable NSPACK also has two opposing effects in this application of the simulator. First, the number of package sizes affects the cost of packaging because the higher the number of package sizes, the shorter the size of each packaging run and the higher the unit cost of packaging. Therefore, a higher number of package sizes increases the cost of postponement relative to the cost of speculation. Second, the higher the number of package sizes, the higher the opportunity to consolidate safety stocks with postponement. Results suggest that the second effect is stronger than the first, and that a higher number of package 197 sizes increases the cost advantage of postponing packaging to the warehouse level relative to the cost of speculating at the plant level. Variable NSPACK appears to have a weak effect on the decision to postpone or to speculate on the packaging of a product. In Hypothesis B4, the effect of PVALUE on this application of the simulator is threefold. One, PVALUE is a component of the cost of carrying inventories. The higher the value of the product, the higher the inventory carrying cost differential between the alternatives of postponement and speculation, and the higher the incentive to postpone. Two, PVALUE has an effect on the cost of packaging, because it is assumed that higher value products carry more elaborate packages that are costlier to handle. Three, higher transportation value rates or higher insurance costs are assumed in the relationship between PVALUE and transportation costs. Hence, PVALUE has an effect on the overall level of transportation cost. Results suggest that the first and the last effects are stronger than the second. Therefore, the higher the value of a product, the higher the incentive to postpone packaging to the warehouse level. Variable PVALUE appears to have a strong effect on the decision to postpone or to speculate on the packaging of a product. In conclusion, two variables appear to contribute most to the decision to postpone or to speculate on the packaging 198 of a product: the value of the product and the uncertainty of demand. The level of demand and the number of packages in which a product is offered in the marketplace appear to have weaker impacts on that decision. MODEL Q The third section in this chapter discusses the application of the simulator to Model C, the assembly model. As in previous sections, it is subdivided into four parts: application validation, application input/output, findings, and explanation of results. human The procedure to validate the application of the simulator to Model C is threefold. The first procedure is a test is to determine whether there are any computational mistakes in the computer algorithm. To that end, hand and computer calculations are compared in a subsample of ten products. In this application of the simulator, no differences were found up to two decimal points in the total cost for any of the four subroutines; assembly, customer service, transportation, and inventory. The objective of the second test is to determine whether this application of the simulator responds to the 199 inputs according to the theory used to build it. To that end, ten extreme products where the assembly process should be clearly postponed to the warehouse level, and ten extreme products where the assembly process should be clearly speculated at the plant level are chosen, and the expected output compared to the observed output. The criterion to select the products for the comparison is to choose products within the highest or lowest two levels of each variable. In this particular application, products to be postponed should have a high level of demand, a high product value, a high level of demand uncertainty, a high level of cube reduction, and a large number of versions. Products to be speculated on should have the opposite characteristics. The result of the comparison is demonstrated in Table 4.17. It is clear that all products conform to the expected outcome. In this table, as well as in the last two chapters in this dissertation, the variable postponement is represented by the number 1, while the variable speculation is represented by the number 0. The third step in the validation procedure is the face validity test. The objective of the test is to request the input from an expert in computer simulation and in business logistics to answer two questions: Are there any errors of logic in the application of the simulator? Is the range for the application inputs reasOnable? Dr. David J. Closs, Associate Professor at Michigan State University agreed to 200 comment on the questions. Professor Closs' review was invaluable to this application of the simulator. TABLE_1111 SER D S O U S PRODUCT DEMAND UNCERTAINTY NVER CUBER PVALUE EXP. OBS. 1 600 0.03 1 .10 1.00 0 0 2 600 0.03 1 .10 6.00 0 0 3 600 0.03 1 .23 1.00 0 0 4 600 0.03 1 .23 6.00 0 0 S 600 0.03 3 .10 1.00 0 0 6 600 0.03 3 .10 6.00 O 0 7 600 0.03 3 .23 1.00 0 0 8 600 0.03 3 .23 6.00 0 0 9 16500 0.03 1 .10 1.00 0 0 10 16500 0.03 1 .10 6.00 0 0 11 48000 0.15 6 .50 15.00 1 1 12 48000 0.15 6 .50 11.00 1 1 13 48000 0.15 6 .36 15.00 1 1 14 48000 0.15 6 .36 11.00 1 1 15 48000 0.15 4 .50 15.00 1 1 16 48000 0.15 4 .50 11.00 1 1 17 48000 0.15 4 .36 15.00 1 1 18 48000 0.15 4 .36 11.00 1 1 19 32000 0.15 6 .50 15.00 1 1 20 32000 0.15 6 .50 11.00 1 1 A ’ ut The inputs to the application were generated from Table 3.15 in the previous chapter. Each of the input variables is assigned four levels within the range established for each. The input table consists of all possible combinations of the 201 five input variables. Thus, the total number of products in the input table is equal to 1024. The output of the application is obtained by running the input table through the application relationships, as defined in Table 3.17 in Chapter III. The application is programmed to run on a Lotus 123 spreadsheet. Once the output is generated for every one of the 1024 products, it is incorporated as the last column in the input/output table. The output for Model C produced 269 cases of postponement and 755 cases of speculation. findings The hypotheses pertinent to this application of the simulator are tested with the use of discriminant analysis. A review of the relevant aspects of the technique can be found in the methodology section of Chapter III. In this part, the analysis focuses initially on the discriminant analysis itself, and is followed by the formal test of hypotheses using the discriminant weights and a test of significance. Discriminant Analysis The discriminant analysis is performed on an analysis sample and validated on a hold-out sample. These samples are extracted from the original list of products in the 202 input/output matrix. The data is broken down in groups of four products which are assigned to the analysis and the hold-out samples in an alternated sequence. The analysis presented in the tables below is based on the analysis sample, while the hit-ratio presented in Table 4.24 is based on the hold-out sample. Table 4.18 introduces the mean values for the independent variables, as well as the centroids for the two groups. Table 4.19 shows the correlation matrix for the independent variables. The next ,four tables present a test of significance and the correlation coefficient for the discriminant function, the significance tests for the independent variables, the discriminant weights and loadings, and the test for equality of group covariance matrices, respectively. PS DEMAND UNCERT. NVER CUBER PVALUE CENTROIDS 0 23576 .0869 3.241 .2860 7.661 -.26223 1 26306 .0990 4.251 .3306 9.961 .76267 TOT 24275 .0900 3.500 .2975 8.250 ----- IABLE_1;12 QQBBELAIIQH_MAIBIK DEMAND UNCERT NVER CUBER PVALUE DEMAND 1.000 UNCERT “.008 1.000 CUBER “.008 “.015 “.033 1.000 PVALUE “.013 “.023 “.049 “.446 1.000 IA§L§_5129 DI§QBIHINAHI_EQHQIIQN_QQBBELAIIQH CORR. COEFFICIENT CHI“SQUARED D.F. SIGNIFICANCE .40891 92.85 5 .0000 IAELE_1121 E ' “ 9 'E DEN V ’ A. VARIABLE F SIGNIFICANCE DEMAND 2.338 .1269 ** UNCERT 7.215 .0075 NVER 32.45 .0000 CUBER 8.884 .0030 PVALUE 19.25 .0000 ** - Not significant. 204 VARIABLE DISCR. WEIGHT RANK DISCR. LOADING RANK DEMAND .1806 5 .1510 5 UNCERT .3142 4 .2654 4 NVER .6354 3 .5629 1 CUBER .6672 2 .2945 3 PVALUE .7725 1 .4336 2 IA§L§_iLZl -..'S y ' .Ux ., 1. ' . 2' g- y. ' CS BOX'S M APPROXIMATE F DEGREES OF FREEDOM SIGNIFICANCE 123.40 8.1037 15, 244744.0 .0000 TABLE_&IZA S A N O O D-OUT ACTUAL NUMBER OF CORRECTLY HIT-RATIO VARIABLE CASES OBSERVED CLASSIFIED ERROR (CORR./ACTUAL) POSTPONEMENT 138 83 55 .60 SPECULATION 374 295 79 .78 TOTAL 512 378 134 .73 * * - significant at an alpha level of 5 percent. 205 Hypothesis Testing The hypotheses for Model C are stated in Chapter III. However, for the purpose of greater clarity, they are reproduced below. C1. The GREATER the level of DEMAND, the GREATER the incentive to postpone assembly to the warehouse level. C2. The GREATER the level of UNCERTAINTY of demand, the GREATER the incentive to postpone assembly to the warehouse level. C3. The GREATER the NVER, the GREATER the incentive to postpone assembly to the warehouse level. C4. The GREATER the CUBER, the GREATER the incentive to postpone assembly to the warehouse level. C5. The GREATER the PVALUE, the GREATER the incentive to postpone assembly to the warehouse level. One can adopt alternative approaches to test the hypotheses. The first involves the use of discriminant weights, and the second the use of discriminant loadings. Using loadings has a major advantage; they are considered more stable than the weights (Hair, Anderson, Tatham, Grablowsky, 1979, p. 104). To understand the advantage of the first approach, it is important to note that the loadings are simple correlations between the estimate of the dependent variable and the independent variable. On the other hand, weights are partial correlation coefficients that measure the strength of the relationship between an independent and the dependent variable when other independent variables are held constant. As can be noted 206 from observing Table 4.19, there is some degree of colinearity among two of the independent variables. As a result, it is advisable to adopt the first approach in this analysis. Table 4.22 provides the discriminant weights needed to determine the directionality of the relationships in the hypotheses above, while Table 4.21 provides the significance tests. A hypothesis is accepted if the directionality is as predicted and if the independent variable is significant at an alpha level of five percent. An examination of Table 4.21 shows that the variable DEMAND is not significant at an alpha level of five percent and, therefore, Hypothesis C1 is rejected. The remaining variables are significant. It can be observed in Table 4.18 that the centroid for the postponement group is larger that the centroid for the speculation group. It follows that a positive sign in the discriminant weights indicates a direct relationship between an increase in the value of an. independent variable and the incentive to postpone assembly to the warehouse level. As a consequence, Hypotheses C2 to C5 are accepted, since the sign of the discriminant weight follows the criteria outlined above. The relationship between the independent variables and the incentive to postpone is further illustrated in Figures 4.10 to 4.14. .JSTP‘DNEMENTS OF H. MODEL C - RELATIONSHIP BETWEEN DEMAND AND 207 W THE INCENTIVE TO POSTPONE 150 Mo 1301 120 .. 110 .1 100 "‘ 90 4 so - 7o 4 so -+ 50 1 4o - :50 - 2O “ 10 - Umwmwn) DBMND OF P'CDSTP‘ONENENTS N. 208 W MODEL C - RELATIONSHIP BETWEEN UNCERTAINTY AND THE INCENTIVE TO POSTPONE 150 140 A 1.30 d 1201 no 1 100 -1 90 - no - 7o - so - 50 1 40‘ :50 a 20* 10-4 0.02 I I 0.04 I I f I I I I I I I I 0.06 0.08 0.1 0.12 0.14 UNCERTAINT‘I' 0.16 N OF POSTPONEMENTS 209 W MODEL C - RELATIONSHIP BETWEEN NUMBER OF PRODUCT VERSIONS AND THE INCENTIVE TO POSTPONE 150 140 1 130 ‘4 1201 110 - 100‘ 90 '- 80 -' 7O " 60 - / 50 - 40 - -/ 30-4 / zo~ G/ 10“ NVER N. OF PCISTPONDJENTS 210 EME—44.1.2 MODEL C - RELATIONSHIP BETWEEN CUBE REDUCTION AND THE INCENTIVE TO POSTPONE 150 140 - 130 "' 120 “ no u 100 "‘ so - so -4 70 “I 60 .. oo - 4o - :«3 a 20“ 10"1 0.2 0.4 CU ER 0.6 N. OF POSTPONENE NTS MODEL C - RELATIONSHIP BETWEEN PRODUCT VALUE 211 W13. AND THE INCENTIVE TO POSTPONE 150 140 '- 130 “ 120““ 110 - 100“ 90- IOfi 70" 601 60d 40% JO-I 20" 10+ PRODUCT VALUE 16 212 Discuss'on Two segments form the discussion of the findings. The objective of the first segment is to demonstrate the validity of the discriminant analysis and to show that the results can be used with reasonable certainty of its correctness. In the second segment, results are explained within the context of business logistics theory. Validation of the Discriminant Analysis Morrison (1969) presents a series of eight points to be considered when interpreting a discriminant analysis. In the context of this research, four appear to be relevant. First, the covariance matrices for the two groups must be equal. The test for equality of the covariance matrices is on Table 4.23. It shows that the covariance matrices actually are not equal. Two factors must be considered in interpreting the results of the equality of covariance test. One, the discriminant analysis is considered a robust technique to violations of the assumption of equal covariance matrices (Klecka, 1975). Two, inasmuch as the test itself is considered very sensitive to nonnormality of the independent variables, it may not be valid to determine the equality of the covariance matrices when the independent variables are uniformly distributed, as in the case here (Morrison, 1976). 213 Second, the two groups must be statistically different. In Table 4.20, the chi-square test for the difference between groups shows that the two groups are in fact statistically different. Third, the discriminant function must not be validated with the same data applied to extract the function. If that happens, an upward bias in the hit-ratio may result. In this analysis, the data set is split into an analysis sample and a hold-out sample to prevent such bias. The classification table with the hit-ratio is presented in Table 4.24. The hit-ratio of 73 percent is reasonably high. Fourth, the hit-ratio should be compared with a prior classification criterion, which is the probability that a product will be correctly classified without the discriminant function. The criterion utilized to calculate that probability is the proportional chance criterion (Morrison, 1969), and the value is 61 percent. Explaining Results Five hypotheses are tested, and each is examined in greater detail. Hypothesis C1 is rejected because the discriminant weight is not significant. Variable DEMAND has two opposite effects on the decision to postpone or to speculate on the assembly of a product. In the first effect, a high value for DEMAND increases the cost of lost sales 214 because the simulator assumes that sales decline by five percent in the alternative of postponement. Demand also increases the cost of assembly by increasing the total cost differential between the alternatives of postponement and speculation. The second effect is on inventory carrying costs. The higher the level of DEMAND, the higher the costs of maintaining inventories. The incentive to postpone assembly to the warehouse is greater, therefore, since a high level of DEMAND magnifies the inventory carrying cost differential between the alternatives of postponement and speculation. Results suggest that variable DEMAND has no significant impact on the decision to postpone assembly to the warehouse level. The explanation for the results obtained in Hypothesis C2 is that the effect of UNCERTAINTY on the cost of carrying inventories and on the transportation cost outweighs the effect on the assembly cost. The effect of UNCERTAINTY on the inventory carrying cost is related to its impact on the level of safety stocks, a subject well documented in the literature (Bowersox, 1978, p. 151-2). A high level of UNCERTAINTY increases the inventory carrying cost in the alternative of speculation relative to the cost of postponement. The effect of UNCERTAINTY on the cost of transportation is related to the assumption that a higher level of UNCERTAINTY implies a higher proportion of less- than-truckload shipments and, therefore, to a higher 215 transportation cost. The higher the level of UNCERTAINTY, the higher the transportation cost advantage to postpone the assembly of products to the warehouse level. The effect of UNCERTAINTY on the cost of assembly is explained because demand variability increases the number of non-optimum size assembly runs and, therefore, increases the unit cost of assembly in the alternative of postponement. Variable UNCERTAINTY appears to have a weak impact on the decision to postpone or to speculate on the assembly of products. In Hypothesis C3, variable NVER has a unidimensional effect in this application of the simulator. The higher the number of product versions offered in the marketplace, the higher the opportunity to consolidate safety stocks in the alternative of postponement, and the higher the cost of advantage of postponing assembly to the warehouse level. The results indicate that the effect of variable NVER on the decision to postpone or to speculate on the distribution of a product is moderately strong. In Hypothesis C4, variable CUBER also has a moderately strong and positive impact on the decision to postpone or to speculate on the assembly of a product. The effect of variable CUBER on this application of the simulator is on transportation costs. The higher the reduction in cube achieved by shipping products unassembled, the higher the incentive to postpone assembly to the warehouse level. 216 In Hypothesis C5, the effect of PVALUE on this application of the simulator is threefold. One, PVALUE is a component of the cost of carrying inventories. The higher the value of the product, the higher the inventory carrying cost differential between the alternatives of postponement and speculation, and the higher the incentive to postpone. Two, PVALUE has a small effect on the overall level of transportation cost, because it is assumed that higher valued products have higher value rates in transportation or higher insurance costs. Three, PVALUE affects the total cost of lost sales. The higher the PVALUE, the higher the opportunity cost of a decline in demand. Results suggest that PVALUE is a strong variable in the decision to postpone or to speculate on the assembly of a product. The higher the value of a product, the greater the incentive to postpone assembly to the warehouse level. In conclusion, three variables appear to contribute the most to the decision to postpone or to speculate on the assembly of a product: the value of the product, the reduction in cube made possible by shipping unassembled goods to the warehouse, and the number of versions of a product offered in the marketplace. The level of demand and the uncertainty of demand variation seem to have a weaker impact. 217 MODEL Q The fourth section in this chapter discusses the application of the simulator to Model D, the manufacturing model. As in the discussion in the previous sections, it is subdivided into four parts: application validation, application input/output, findings, and explanation of results. Validation A threefold procedure to validate the application of the simulator is used. A test to detect any computational mistakes in the computer algorithm is the first procedure. To that end, hand and computer calculations are compared in a subsample of ten products. In this application of the simulator, no differences were found up to two decimal points in the total cost for any of the four subroutines; manufacturing, customer service, transportation, and inventory. The objective of the second test is to determine whether this application of the simulator is responding to the inputs according to the theory used to build it. To that effect, ten extreme products where the manufacturing process should be clearly postponed to the warehouse level, and ten extreme products where the manufacturing process should be 218 clearly speculated at the plant level are chosen, and the expected output is compared to the observed output. The criterion to select the products for the comparison is to choose products within the highest or lowest two levels of each variable. In this particular application, products to be postponed should have a high level of demand, product value, demand uncertainty, and proportion of ubiquitous materials as a function of product weight. Products to be speculated on should have opposite characteristics. The result of the comparison is demonstrated in Table 4.25. It is clear that all products conform to the expected outcome. In this table, as well as in the last two chapters in this dissertation, the variable postponement is represented by the number 1, and the variable speculation is represented by the number 0. The third step in the validation procedure is the face validity test. Its objective is to request the input from an expert in computer simulation and in business logistics to answer two questions: Are there any errors of logic in the application of the simulator? Is the range for the application inputs reasonable? Dr. David J. Closs, Associate Professor at Michigan State University agreed to comment on the questions. Professor Closs' review was invaluable to this application of the simulator. 219 TAELE_112§ 0- ' I AND .’ 9110 O ' O; i a "OPUCTS PRODUCT DEMAND UNCERTAINTY WUBIQM PVALUE EXP. OBS. 1 600 0.03 .30 1.00 0 O 2 600 0.03 .30 4.50 0 O 3 600 0.03 .42 1.00 0 0 4 600 0.03 .42 4.50 0 0 5 600 0.06 .30 1.00 0 0 6 600 0.06 .30 4.50 0 O 7 600 0.06 .42 1.00 0 0 8 600 0.06 .42 4.50 0 O 9 12000 0.03 .30 1.00 0 0 10 12000 0.03 .30 4.50 0 0 11 36000 0.15 .80 15.00 1 1 12 36000 0.15 .80 11.50 1 l 13 48000 0.12 .68 15.00 1 1 14 48000 0.12 .68 11.50 1 l 15 48000 0.12 .80 15.00 1 1 16 48000 0.12 .80 11.50 1 1 17 48000 0.15 .68 15.00 1 l 18 48000 0.15 .68 11.50 1 1 19 48000 0.15 .80 15.00 1 l 20 48000 0.15 .80 11.50 1 1 Application Inputzgutpgt The inputs to the application are generated from Table 3.22 in the previous chapter. Each of the input variables is assigned five levels within the range established for each of these variables. The input table consists of all possible combinations of the four input variables. The total number of products in the input table is, therefore, equal to 625. The output of the application is obtained by running the input table through the application relationships, as 220 defined in Table 3.24 in Chapter III. The application is programmed to run on a Lotus 123 spreadsheet. Once the output is generated for every one of the 625 products, it is incorporated as the last column in the input/output table. The output for Model D produced 138 cases of postponement and 487 cases of speculation. Findings The hypotheses pertinent to this application of the simulator are tested with the use of discriminant analysis. A review of the relevant aspects of the technique can be found in the methodology section of Chapter III. In this part, the analysis will focus initially on the discriminant analysis itself, and will be followed by the formal test of hypotheses using the discriminant weights and a test of significance. Discriminant Analysis The discriminant analysis is performed on an analysis sample and validated on a hold-out sample. These samples are extracted from the original list of products in the input/output matrix. In this application, odd numbered products are in the analysis sample, while even numbered products are in the holdout sample. 221 The analysis presented in the tables below is based on the analysis sample, while the hit-ratio presented in Table 4.32 is based on the hold-out sample. Table 4.26 introduces the mean values for the independent variables, as well as the centroids for the two groups. Table 4.27 shows the correlation matrix for the independent variables. The next four tables present a test of significance and the correlation coefficient for the discriminant function, the significance tests for the independent variables, the discriminant weights and loadings, and the test for equality of group covariance matrices, respectively. PS DEMAND UNCERT. WUBIQM PVALUE CENTROIDS 0 21999 .0835 .5211 6.728 -.48697 1 31522 .1128 .6516 12.544 1.78072 TOT 24044 .0898 .5492 7.977 ----- 222 DEMAND UNCERT WUBIQM PVALUE DEMAND 1.000 UNCERT -.077 1.000 WUBIQM -.082 -.100 1.000 PVALUE —.139 -.170 -.181 1.000 TABLE_412§ DIEQBInINANT_EHN£IIQN_QQEEELATIQN CORR. COEFFICIENT CHI-SQUARED D.F. SIGNIFICANCE .68266 193.24 4 .0000 TABLE_1122 s - v VARIABLE F SIGNIFICANCE DEMAND 17.76 .0000 UNCERT 27.16 .0000 WUBIQM 30.80 .0000 PVALUE 94.09 .0000 VARIABLE DISCR. WEIGHT RANK DISCR. LOADING RANK DEMAND .4674 4 .2562 4 UNCERT .5583 3 .3168 3 WUBIQM .5872 2 .3374 2 PVALUE .8566 1 .5897 1 TABLE_1111 '0 'S I . . x . ;. . .V1- 1 213; BOX'S M APPROXIMATE F DEGREES OF FREEDOM SIGNIFICANCE 57.339 5.6014 10, 66535.0 .0000 ACTUAL NUMBER OF CORRECTLY HIT-RATIO VARIABLE CASES OBSERVED CLASSIFIED ERROR (CORR./ACTUAL) POSTPONEMENT 71 53 18 .74 SPECULATION 242 236 6 .97 TOTAL 313 289 24 .92 * * - significant at an alpha level of 5 percent. 224 Hypothesis Testing The hypotheses for Model D are stated in Chapter III. However, for the purpose of greater clarity, they are reproduced below. D1. The GREATER the level of DEMAND, the GREATER the incentive to postpone manufacturing to the warehouse level. D2. The GREATER the level of UNCERTAINTY of demand, the GREATER the incentive to postpone manufacturing to the warehouse level. DB. The GREATER the relative weight of ubiquitous materials (WUBIQM), the GREATER the incentive to postpone manufacturing to the warehouse level. D4. The GREATER the PVALUE, the GREATER the incentive to postpone manufacturing to the warehouse level. There are two alternative approaches to adopt in testing the hypotheses. In the first, the use of discriminant weights is involved, and in the second, discriminant loadings are adopted. use of discriminant loadings. The major advantage of using loadings is that they are considered more stable than the weights (Hair, Anderson, Tatham, Grablowsky, 1979, p. 104). To understand the advantage of the first approach, it is important to note that the loadings are simple correlations between the estimate of the dependent variable and the independent variable. On the other hand, weights are partial correlation coefficients that measure the strength of the relationship between an independent and the dependent variable when other independent variables are held constant. As can be noted 225 from Table 4.27, there is a low level of colinearity among the independent variables. Consequently, either the use of the discriminant weights or the loadings should produce the same results. However, in order to remain consistent with the other models, the discriminant weights are utilized. Table 4.30 provides the discriminant weights needed to determine the directionality of the relationships in the hypotheses above, while Table 4.29 provides the significance tests. A hypothesis is accepted if the directionality is as predicted and if the independent variable is significant at an alpha level of five percent. An examination of Table 4.29 shows that all variables are significant at an alpha level of five percent. Table 4.26 reveals that the centroid for the postponement group is larger than the centroid for the speculation group. Thus, a positive sign in the discriminant weights indicates a direct relationship between an increase in the value of an independent variable and the incentive to postpone manufacturing to the warehouse level. As a consequence, Hypotheses D1 to D4 are accepted, since the sign of the discriminant weight follows the criteria outlined above. The relationship between the independent variables and the incentive to postpone is further illustrated in Figures 4.15 to 4.18. N OF POSTPONEME N15 226 W MODEL D - RELATIONSHIP BETWEEN DEMAND AND THE INCENTIVE TO POSTPONE 70 ‘50"I sol 40“ 20 - x" 10-d / Ghouunwb) DEMAND N . OF POSTPONEME NTS MODEL D - RELATIONSHIP BETWEEN UNCERTAINTY AND THE INCENTIVE TO POSTPONE 227 W 70 60“ 30‘ 20d 10“ / 0.02 0.04 0 .06 0 .08 UNCERTAINTY 0.1 0.12 0.14 0.16 N, OF POST P'DNEME NTS 228 W MODEL D - RELATIONSHIP BETWEEN THE WEIGHT PROPORTION OF UBIQUITOUS MATERIALS AND THE INCENTIVE TO POSTPONE 70 60 "I 504 30‘ / 40+ / ,/ / /’ 10 ‘1 / ../ '3 I r I I I I T 0 0.2 0.4 0 6 0.3 N. OF POSTPONEMENTS MODEL D - RELATIONSHIP BETWEEN PRODUCT VALUE AND THE INCENTIVE TO POSTPONE 229 [191.131.43.11 70 60" 40d 30— 204 1f) “ / r I I I 6 8 PRODUCT VALUE 10 12 14 16 230 Discussion The findings are discussed in two segments. The objective of the first segment is to demonstrate that the discriminant analysis is valid and that the results can be used within a reasonable level of certainty of its correctness. In the second segment, results are explained within the context of business logistics theory. Validation of the Discriminant Analysis Morrison (1969) presents a series of eight points to consider when interpreting a discriminant analysis. Among these, four seem to be relevant in the context of this research. First, the covariance matrices for the two groups must be equal. The test for equality of the covariance matrices on Table 4.31 shows that the covariance matrices actually are not equal. Two factors must be considered in interpreting the results of the equality of the covariance test. One, the discriminant analysis is considered a robust technique to violations of the assumption of equal covariance matrices (Klecka, 1975). Two, the test itself is considered very sensitive to nonnormality of the independent variables, and therefore may not be valid to determine the equality of the covariance matrices when the independent 231 variables are uniformly distributed, as in this analysis (Morrison, 1976). Second, the two groups must be statistically different. The chi-square test for the difference between groups is presented in Table 4.28, and shows that the two groups are in fact statistically different. Third, the discriminant function must not be validated with the same data applied to extract the function. If that happens, an upward bias in the hit-ratio may result. In this analysis, the data set is split into an analysis sample and a hold-out sample to prevent such bias. The classification table with the hit-ratio is in table 4.32. The hit-ratio of 92 percent is adequately high. Fourth, the hit-ratio should be compared with a prior classification criterion, which is the probability that a product will be correctly classified without the discriminant function. The criterion utilized to calculate that probability is the proportional chance criterion (Morrison, 1969), and the value is 65 percent. Explaining Results Four hypotheses are tested and each is examined in greater detail. In Hypothesis D1, variable DEMAND has two opposite effects on the decision to postpone or to speculate on the manufacturing of a product. In the first effect, a 232 high value for DEMAND increases the cost of lost sales because the simulator assumes that sales decline by five percent in the alternative of postponement. It also increases the differential between the cost of manufacturing at the warehouse relative to the cost of manufacturing at the plant. The second effect is on inventory carrying costs. The higher the level of DEMAND, the higher the costs of maintaining inventories. Therefore, the incentive to postpone manufacturing to the warehouse is greater. Results suggest that the second effect is slightly stronger than the first one, and that variable DEMAND has a weak impact on the decision to postpone or to speculate on the manufacturing of a product. The explanation for the results obtained in Hypothesis D2 is that the effect of UNCERTAINTY on the cost of carrying inventories and on the transportation cost outweighs the effect on the manufacturing cost. The effect of UNCERTAINTY on the inventory carrying cost is related to its impact on the level of safety stocks, which is well documented in the literature (Bowersox, 1978, p. 151-2). The effect of UNCERTAINTY on the cost of transportation is related to the assumption that a higher level of UNCERTAINTY implies in a higher proportion of less-than-truckload shipments and, therefore, to a higher transportation cost differential between the alternatives of postponement and speculation. The higher the level of UNCERTAINTY, the higher the 233 transportation cost incentive to postpone manufacturing to the warehouse level. The effect of UNCERTAINTY on the cost of manufacturing derives from the fact that demand variability increases the number of non-optimum size manufacturing runs and, therefore, increase the unit cost of manufacturing in the alternative of postponement. Results suggest that the effect of variable UNCERTAINTY on the decision to postpone or to speculate on the manufacturing of a product is of moderate strength. In Hypothesis D3, variable WUBIQM also has a moderately strong and positive impact on the decision to postpone or to speculate on the manufacturing of a product. The effect of variable WUBIQM on this application of the simulator is on transportation costs. The higher the proportion of ubiquitous materials on the product's weight, the higher the incentive to postpone manufacturing to the warehouse level. In Hypothesis D4, PVALUE's effect on this application of the simulator is threefold. One, PVALUE is a component of the cost of carrying inventories. The higher the value of a product, the higher the inventory carrying cost differential in the alternatives of postponement and speculation, and the higher the incentive to postpone manufacturing to the warehouse level. Two, PVALUE's effect on the overall level of transportation cost is small, because it is assumed that higher value products have higher transportation value rates or insurance costs. Three, PVALUE affects the total cost of 234 lost sales. The higher the value of the product, the higher the opportunity cost of a decline in demand. Results suggest that PVALUE is a strong variable in deciding whether to postpone or to speculate on the manufacturing of a product. The higher the value of a product, the greater the incentive to postpone manufacturing to the warehouse level. In conclusion, three variables appear to moderately influence the decision to postpone or to speculate on the manufacturing of a product: the level of demand, the proportion of ubiquitous materials on the weight of products, and the uncertainty of demand. Variable PVALUE seems to have a Strong impact in the same decision. M92EL.E The fifth section in this chapter discusses the application of the simulator to Model E, the time postponement-speculation model. As discussed in previous sections, it is subdivided into four parts: application validation, application input/output, findings, and explanation of results. 1611513115211 The procedure to validate the application of the simulator to Model E is threefold. The first procedure is a 235 test to determine whether there are any computational mistakes in the computer algorithm. To that end, hand and computer calculations are compared in a subsample of ten products. In this application of the simulator, no differences were found up to two decimal points in the total cost for any of the three subroutines: customer service, transportation, and inventory. To determine whether this application of the simulator is responding to the inputs in accordance with the theory used to build it, is the second test's objective. To that end, ten extreme products where products should be clearly postponed in time at the plant level, and ten extreme products where the products should be clearly speculated at the warehouse level are chosen, and the expected output is compared to the observed output. The criterion to select the products for the comparison is to choose products within the highest or lowest three levels of each variable. In this particular application, products to be postponed should have a high level of demand, a high product value, and a high level of demand uncertainty. Products to be speculated on should have the opposite characteristics. The result of the comparison is demonstrated in Table 4.33, where all products clearly conform to the expected outcome. In this table, as well as in the last two chapters in this dissertation, the variable postponement is represented by the number 1, while the variable speculation is represented by the number 0. 236 The third step in the validation procedure is the face validity test. The objective of the test is to request the input of an expert in computer simulation and in business logistics to answer two questions: Are there any errors of logic in the application of the simulator? Is the range for the application inputs reasonable? Dr. David J. Closs, Associate Professor at Michigan State University has agreed to comment on the questions. Professor Closs' review was invaluable to this application of the simulator. IAELE_5132 0. 'VI 1 I ,- I 0 U o; - 1! ”on 5 PRODUCT DEMAND UNCERTAINTY PVALUE EXP. CBS. 1 600 0.03 1.00 O O 2 600 0.03 2.75 0 O 3 600 0.03 4.50 0 O 4 6600 0.03 1.00 O O 5 6600 0.03 2.75 O 0 6 6600 0.03 4.50 0 O 7 600 0.06 1.00 O 0 8 600 0.06 2.75 0 O 9 600 0.06 4.50 O 0 10 6600 0.06 1.00 O 0 11 48000 0.15 15.00 1 1 12 48000 0.15 13.25 1 1 13 48000 0.15 11.50 1 1 14 42000 0.15 15.00 1 l 15 42000 0.15 13.25 1 1 16 42000 0.15 11.50 1 1 17 48000 0.135 15.00 1 1 18 48000 0.135 13.25 1 l 19 48000 0.135 11.50 1 l 20 42000 0.135 15.00 1 l 237 Appiication Inputhutpgt The inputs to the application are generated from Table 3.28 in the previous chapter. Each of the input variables is assigned nine levels within the range established for each of these variables. The input table consists of all possible combinations of the three input variables. Therefore, the total number of products in the input table is equal to 729. The output of the application is obtained by running the input table through the application relationships, as defined on Table 3.30 in Chapter III. The application is programmed to run on a Lotus 123 spreadsheet. Once the output is generated for every one of the 729 products, it is incorporated as the last column in the input/output table. The output for Model E produced 319 cases of postponement and 410 cases of speculation. Findings The hypotheses pertinent to this application of the simulator are tested with the use of discriminant analysis. Relevant aspects of the technique are reviewed in the methodology section of Chapter III. In this part, the analysis focuses initially on the discriminant analysis itself, and is followed by the formal test of hypotheses using the discriminant weights and a test of significance. 238 Discriminant Analysis The discriminant analysis is performed on an analysis sample and validated on a hold-out sample. These samples are extracted from the original list of products in the input/output matrix. In this application, even numbered products are in the analysis sample, while odd numbered products are in the holdout sample. The analysis presented in the tables below is based on the analysis sample, while the hit-ratio presented in Table 4.40 is based on the hold-out sample. Table 4.34 introduces the mean values for the independent variables, as well as the centroids for the two groups. Table 4.35 shows the correlation matrix for the independent variables. The next four tables present a test of significance and the correlation coefficient for the discriminant function, the significance tests for the independent variables, the discriminant weights and loadings, and the test for equality of group covariance matrices, respectively. IAELE_4114 U S N 0 PS DEMAND UNCERT. PVALUE CENTROIDS 0 23094 .0640 7.453 -1.09337 1 25727 .1234 8.704 1.40968 TOT 24044 .0900 8.000 ------ 239 DEMAND UNCERT PVALUE DEMAND 1.000 UNCERT “.101 1.000 PVALUE “.011 “.163 1.000 TABLE—111é DI§QBIMINANT—EHNQIIQNLQQBBELBIIQN CORR. COEFFICIENT CHI“SQUARED D.F. SIGNIFICANCE .77962 337.42 3 .0000 IABLE.1111 . I - . . N. T 2 ”LS VARIABLE F SIGNIFICANCE DEMAND 2.683 .1023 ** UNCERT 503.1 .0000 PVALUE 6.974 .0086 ** - Not significant. 240 IAELE_113§ S I N I HTS ISCRI INANT N S VARIABLE DISCR. WEIGHT RANK DISCR. LOADING RANK DEMAND .1750 3 .0691 3 UNCERT 1.0103 1 .9469 1 PVALUE .2789 2 .1114 2 TAELE_1112 =O ' g _ , OF i0 ' I Y Q :0 ' COVI’ AN tiT' C S BOX'S M APPROXIMATE F DEGREES OF FREEDOM SIGNIFICANCE 20.806 3.4358 6, 806112.5 .0021 TABLE_£1£Q N -O ACTUAL NUMBER OF CORRECTLY HIT-RATIO VARIABLE CASES OBSERVED CLASSIFIED ERROR (CORR./ACTUAL) POSTPONEMENT 160 128 32 .80 SPECULATION 205 184 21 .89 TOTAL 365 312 53 .85 * * - significant at an alpha level of 5 percent. 241 Hypothesis Testing The hypotheses for Model E are stated in Chapter III. However, in the interest of greater clarity, they are restated below. E1. The GREATER the level of DEMAND, the GREATER the incentive to postpone shipment to the warehouse level. E2. The GREATER the level of UNCERTAINTY of demand, the GREATER the incentive to postpone shipment to the warehouse level. E3. The GREATER the PVALUE, the GREATER the incentive to postpone shipment to the warehouse level. There are two alternative approaches one can adopt to test the hypotheses. The first approach involves the use of discriminant weights, while the second approach is based on the use of discriminant loadings. The major advantage of using loadings is that they are considered more stable than the weights (Hair, Anderson, Tatham, Grablowsky, 1979, p. 104). To understand the advantage of the first approach, it is important to note that the loadings are simple correlations between the estimate of the dependent variable and the independent variable. Conversely, weights are partial correlation coefficients that measure the strength of the relationship between an independent and the dependent variable when other independent variables are held constant. As can be noted from observing Table 4.35, there is a low level of colinearity among the independent variables. 242 Consequently, either the use of the discriminant weights or the loadings should produce the same results. However, in 'order to remain consistent with the other models, the discriminant weights are utilized. Table 4.38 provides the discriminant weights needed to determine the directionality of the relationships in the hypotheses above, while Table 4.37 provides the significance tests. A hypothesis is accepted if the directionality is as predicted and if the independent variable is significant at an alpha level of five percent. An examination of Table 4.37 shows that variables UNCERTAINTY and PVALUE are significant at an alpha level of five percent, while variable DEMAND is not. It can be observed in Table 4.34 that the centroid for the postponement group is larger that the centroid for the speculation group. It follows that a positive sign in the discriminant weights indicates a direct relationship between an increase in the value of an independent variable and the incentive to postpone shipment to the warehouse level. As a consequence, Hypothesis E1 is rejected, and Hypotheses E2 and E3 are accepted, since the sign of the discriminant weight follows the criteria outlined above. The relationship between the independent variables and the incentive to postpone is further illustrated in Figures 4.19 tO 4.21. N. OF POSTPONEMENTS 243 W MODEL E - RELATIONSHIP BETWEEN DEMAND AND THE INCENTIVE TO POSTPONE 90 80 “ 7U“ 60“ 50“ 40“ 30“ 20“ 101 40 (Thousands) DEMAND N. OF POSTPONEMENTS 244 W MODEL E - RELATIONSHIP BETWEEN UNCERTAINTY AND THE INCENTIVE TO POSTPONE 90 80“ 70“ 60“ 50“ 40“ .30-I 20" 0.02 I if 0 .04 I T 1 0.06 0.08 UNCERTAINTY 0.1 T FT 0.12 0.14 0.16 N. OF POSTPONEMENTS 245 W MODEL E - RELATIONSHIP BETWEEN PRODUCT VALUE AND THE INCENTIVE TO POSTPONE 90 80“ 70" . +~————0 40 -I f / G“ 20 “ 10 “‘ 0 I I I I I I I I I I I I I 0 2 4 6 8 10 12 PRODUCT VALUE 246 Discussion The discussion of the findings consists of two segments. The objective of the first segment is to demonstrate that the discriminant analysis is valid and that the results can be used within a reasonable level of certainty of its correctness. In the second segment, results are explained within the context of business logistics theory. Validation of the discriminant analysis Morrison (1969) presents a series of eight points to consider when interpreting a discriminant analysis. Of these, four appear relevant in the context of this research. First, the covariance matrices for the two groups must be equal. The test for equality of the covariance matrices is in Table 4.31. It shows that the covariance matrices actually are not equal. Two factors must be considered in interpreting the results of the equality of covariance test. One, the discriminant analysis is considered a robust technique to violations of the assumption of equal covariance matrices (Klecka, 1975). Two, the test itself is considered very sensitive to nonnormality of the independent variables, and therefore may not be valid to determine the equality of the covariance matrices when the independent 247 variables are uniformly distributed, as in this analysis (Morrison, 1976). Second, the two groups must be statistically different. The chi-square test for the difference between groups is presented in Table 4.28, and shows that the two groups are in fact statistically different. Third, the discriminant function must not be validated with the same data applied to extract the function. If that happens, an upward bias in the hit-ratio may result. In this analysis, the data set is split into an analysis sample and a hold-out sample to prevent such bias. The classification table with the hit-ratio is presented in Table 4.32. The hit-ratio of 85 percent is adequately high. Fourth, the hit-ratio should be compared with a prior classification criterion, which is the probability that a product will be correctly classified without the discriminant function. The criterion utilized to calculate that probability is the proportional chance criterion (Morrison, 1969), and the value is 51 percent. Explaining Results Three hypotheses are tested and each is examined in greater detail. In Hypothesis E1, variable DEMAND has two opposite effects on the decision to postpone or to speculate on the shipment of a product to the warehouse level. In the 248 first effect, a high value for DEMAND increases the cost of lost sales because the simulator assumes that sales decline by five percent in the alternative of postponement. It also increases the total transportation cost differential between the alternatives of postponement and speculation. Transportation is costlier under the alternative of postponement, and the higher the level of demand, the greater the difference in total dollars. The second effect is on inventory carrying costs. The higher the level of DEMAND, the higher the costs of maintaining inventories. Results indicate that the two effects are of equal strength and, therefore, variable DEMAND appears to have no significant impact on the decision to postpone or to speculate on the shipment of products to the warehouse level. The explanation for the results obtained in Hypothesis E2 is that the effect of UNCERTAINTY on the transportation cost is outweighed by the effect on inventory carrying cost. The effect of UNCERTAINTY on the inventory carrying cost is related to its impact on the level of safety stocks, which is well documented in the literature (Bowersox, 1978, p. 151-2). The effect of UNCERTAINTY on the cost of transportation is related to the assumption that a higher level of UNCERTAINTY implies in a higher proportion of less- than-truckload shipments and, therefore, to a higher transportation cost differential between the alternatives of 249 postponement and speculation. The higher the level of uncertainty, the greater the incentive to postpone shipment to the warehouse level. Results suggest that the effect of variable UNCERTAINTY on the decision to postpone or to speculate on the shipment of a product is strong. In Hypothesis E3, the effect of PVALUE on this application of the simulator is threefold. One, PVALUE is a major determinant of the cost of carrying inventories. Two, PVALUE has a small effect on the overall level of transportation cost, although no direct effect on the transportation cost difference in the alternatives of postponement or speculation. Three, PVALUE affects the total cost of lost sales. The higher the value of the product, the higher the opportunity cost_of a decline in demand. Results suggest that PVALUE has a weak effect on the decision to postpone or to speculate on the shipment of a product to the warehouse level. The higher the value of a product, the greater the incentive to postpone shipment to the warehouse level. In conclusion, of the three variables studied in this application of the simulation, UNCERTAINTY seems to have a strong effect on the decision to postpone or to speculate on the shipment of a product to the warehouse level, whereas variable PVALUE appears to have a weak effect, and variable DEMAND no significant effect. The concluding chapter has three goals. The first is to present a summary of the research and review the conclusions. The second is to provide an overview of the managerial implications of the research. The final goal is to suggest areas for further research in postponement- speculation within distribution and logistics channels. The chapter is structured into four sections: a summary of the research, presentation of the conclusions, a discussion of managerial implications and, finally, suggestions for further research. BE§EAE§H_§HMMABX The principle of postponement-speculation proposes that changes in location and/or in the form of a product be made at the time and place where it minimizes the total cost of distribution. The focus of the research was to study this principle as it affects the total cost of distributing a particular product. More specifically, the objectives of the research were to provide a systematic approach to postponement- 250 251 speculation decisions, and insight into the most important product physical and demand characteristics that influence whether the distribution of a product should be postponed or speculated. In order to fulfill these objectives, three research questions were addressed. The first two questions were concerned with the objective of developing a systematic approach to postponement-speculation decisions: What are the specific logistical costs involved in the decision to postpone or to speculate, in time or form, on the distribution of a given product? How should these costs be measured and integrated in a managerial decision framework? The third question was concerned with the objective of understanding the impact of product physical and demand characteristics on postponement-speculation decisions: What is the relative importance of different physical and demand characteristics on the decision to postpone or to speculate the distribution of a particular product? Each of these questions covered one aspect of the research. The three questions were interconnected to achieve the overall purpose of this study -- to enable researchers and managers to use the principle of postponement- speculation in the design of logistical systems. The first research question concerns the need to identify logistics costs relevant to the principle. The 252 second question integrated relevant costs in a framework suitable for managers and researchers in the design of logistical systems. The third question examined the importance of demand related variables such as the sales volume or demand variability, and product characteristics such as weight or cube upon the decision to postpone or to speculate. To quantify the principle of postponement-speculation for decision making, a research design was developed. It comprised three basic steps: first, the general principle was partitioned into five distinct types. Second, normative cost models were developed for each type. Third, the normative cost models were replicated in a computer simulation analysis of selected variables. Each step is explained further, and is followed by the presentation of the research results and limitations. Five types of postponement-speculation were defined. The first four types refer to changes in the form of products, which occurs at the plant level (speculation), or at the warehouse level (postponement). Four types of change in the form of products were considered: labeling, packaging, assembly, and manufacturing. The term "processing” encompasses all four types of form change. The 253 last type was time postponement-speculation, in which goods are moved from plant to warehouse in anticipation of the receipt of a customer order (speculation), or after the customer order is received (postponement). No a 'v s The five types of postponement-speculation were analyzed in terms of total cost by the use of five normative cost models. These models contain all logistics costs relevant to postponement-speculation decisions. Each model is a step-by-step procedure enabling managers to collect and organize data for a decision in postponement-speculation. The segment of the distribution network modeled was the plant-warehouse. One plant and three warehouses were assumed. Finally, models were designed to be static. Costs were computed for a single time period. Although not all costs are relevant to every model, the cost categories included in the analysis were the following: customer service level (cost of lost sales), processing, inventory, warehousing, and transportation. Costs must be computed at the plant and warehouse levels. For speculation, the status quo alternative, costs can be directly measured. For postponement, costs are estimated. The objective is to determine which alternative, postponement or speculation, offers the lowest cost distribution for a specific product. 254 The outcome of a normative cost model is at the product level and can not be generalized for the total firm. : u! 5. 1 !' In order to test hypotheses relating to postponement or speculation for a range of product physical and demand variables, the five cost models were replicated by a unique computer simulation for each type. The simulator treated the product physical and demand characteristics as input variables. The logistics cost structure was the algorithm. The output to the simulation provided data to determine if distribution should be postponed or speculated. A number of value levels was defined for each of the product physical and demand characteristics. The array of value levels tested varied for each product physical and demand characteristic. A total input table in each application was generated to reflect all possible value level combinations for aIl product physical and demand characteristics. To isolate significant product physical and demand input variables, a discriminant analysis was completed. In the analysis, postponement-speculation was the dependent variable and product physical and demand characteristics were the independent variables. The level of significance was determined on the basis of the absolute magnitude of the discriminant weights, whereby a larger weight indicates 255 greater importance. se 5 Table 5.1 summarizes the results of the research. Product physical and demand characteristics are presented in the first column. Results for each model are in the subsequent columns. The most important variable in labeling postponement- speculation (Model A), appeared to be product value. The absolute magnitude of the discriminant weight suggests that, among the variables studied, the value of a product is the most important predictor of whether the distribution of that product should be postponed or speculated. The uncertainty of the demand and the number of brands seemed also important. However, results show that the level of demand appeared to be irrelevant. The distribution of thirty-two percent of products studied in this type should be postponed, while the remaining sixty-eight percent should be speculated. In packaging postponement-speculation (Model B), the product value appeared to be the most important predictor of postponement-speculation. Uncertainty of demand also seemed important, while the number of package sizes and the level of demand appeared less relevant in predicting whether the 256 MODEL A MODEL B MODEL C MODEL D MODEL E DEMAND N.S .25 N.S .46 N.S UNCERTAINTY .78 .62 .31 .55 1.01 PRODUCT VALUE .84 .97 .77 .85 .27 NUMBER OF BRANDS .72 --- --- —-— --- NUMBER OF PACKAGE SIZES --- .36 --— --- --- NUMBER OF PRODUCT VERSIONS --- --- .53 -—— --- CUBE REDUCTION --- --- .66 —-- --- WEIGHT OF UBIQUI- TOUS MATERIALS --- --- --- .53 --- PRODUCTS POSTPONED (%) 32 67 26 22 43 N.S - Not significant distribution of a product should be postponed or speculated. Of the products studied in this type, sixty-seven percent should have their distribution postponed. In assembly postponement-speculation (Model C), three variables appeared to contribute most to the decision to postpone or speculate on the distribution of a product: the value of the product, the reduction in cube made possible by shipping unassembled goods to the warehouse, and the number of product versions offered in the marketplace. The level of demand and the uncertainty of demand seemed to have a weaker 257 impact. Twenty-six percent of the products studied in this type should have their distribution postponed. In manufacturing postponement-speculation (Model D), three variables appeared to have a moderate influence on the decision to postpone or speculate on the distribution of a product: the level of demand, the proportion of ubiquitous materials contained in the product weight, and the uncertainty of demand. The value of the product apparently had a strong impact in the same decision. Of products studied in this type, twenty-two percent should have their distribution postponed. Of the three variables studied in time postponement- speculation (Model E), uncertainty of demand seemed to affect most strongly the decision to postpone or to speculate on product shipment to the warehouse. The value of the product had a weak effect. The level of demand had no significant effect. Forty-three percent of the products studied in this type should have their distribution postponed. 'mit As in any investigation, this research had a number of limitations. To maintain the problem within manageable proportions, models are kept at the firm level. No consideration is given to other channel institutions 258 involved in the distribution process. The findings are valid only for the environment assumed in this research. This limitation includes ranges determined for input variables as well as the numbers chosen for constant values. The research was limited by the focus on the product level, because it ignores the possibility that a firm level decision for several products Could require the sub-optimization of the decision for an individual product. In addition, the research was limited by the simulator and application assumptions which are defined in the third chapter. Application assumptions are specific to each model, but the more general simulator assumptions were the following: -- The research was conducted from the point of view of a manufacturer which has a sufficient level of channel power to decide whether to postpone or to speculate on product distribution. -- The status quo was assumed to be speculation. Therefore, time speculation was assumed whenever one of the form postponement-speculation models was considered, and vice- versa . QQNQLHSIQNE A further examination of Table 5.1 provides the basis for a number of conclusions concerning research results. As 259 stated in the discussion of each individual hypothesis in chapter IV, 17 of the 20 hypotheses were accepted based on significant discriminant weights. Three of the hypotheses were rejected because the discriminant weights were not significant. Despite the fact that applications of the simulator were independent, some patterns were observed across results. The following conclusions were generalized. Conciusion n,1 - Product value is the most important variable in form postponement-speculation. gongigsign_niz - Uncertainty of demand is the most important variable in time postponement-speculation. Conclusion 3,; - Uncertainty of demand is the second most important variable for form postponement-speculation types having a low level of processing (labeling and packaging). Q93g1u§1g3_nig - For form postponement-speculation types with a high level of processing (assembly and manufacturing), the second most important variable is related to the transportation savings made possible from postponement: the reduction in cube made possible by the shipment of unassembled products, and the proportion of ubiquitous materials contained in the product weight, respectively. gongiusign_nifi - The level of demand is the least important variable in all types of postponement-speculation studied. angiugign_n‘§ - With the exception of labeling postponement-speculation, where no transportation savings from postponement are possible, as the level of processing increases in the form postponement-speculation types, the proportional number of postponements in each model decreases. s - The most promising types, defined as the likelihood that postponement will generate savings in the distribution of a product, are packaging and time postponement-speculation. 260 HANAQEBIAL_IHELIQAIIQN§ Quantifying the principle of postponement-speculation has a number of implications for management. The implications are grouped into two broad categories: implications related to the utilization of the principle, and implications related to the determination of what products are best suited for postponement. The utilization of the principle of postponement- speculation is an opportunity for management to improve the productivity of logistics systems in several areas. First, transportation costs can be reduced by postponing the final processing of products to the warehouse, therefore allowing goods to be shipped in bulk, unassembled, or shipped only over short distances, as in the case of ubiquitous materials. Second, by delaying final processing and/or the shipment of goods to the warehouse until a customer order is received, the manager can reduce dependence on sales forecasting to allocate products to warehouses. Finally, form postponement adds flexibility to inventories, since final processing is made to order. Such flexibility may be perceived by customers as an increase in service and, hence, may be a source of competitive advantage. 261 In order to determine whether to postpone or to speculate in the distribution of a product, managers have to compute costs using a procedure similar to the normative cost models developed in this research. A number of managerial guidelines result from this research. These guidelines help to identify situations under which savings from postponement in the distribution of a product are most likely to occur. 1. The uncertainty of demand was the first or the second most important variable in time postponement- speculation model and in the two low processing form postponement-speculation types. A postponement opportunity exists for products with a high degree of uncertainty in the sales volume. At this level, sales forecasting becomes both difficult and inaccurate, and, hence, postponement of the distribution may become a feasible alternative. The range for the uncertainty of sales in this research was between +/- 5% (low uncertainty) and +/- 30% (high uncertainty). 2. The level of the demand was the least important variable in all situations studied. Two managerial implications evolve from this conclusion. First, postponement opportunities may exist regardless of the level of the demand. Second, the existence of predictable variations on the level of sales, such as any form of seasonality, does not impede these opportunities. 262 3. Postponement opportunities may exist for higher value products, especially in form postponement-speculation. In this research, the range of product values was from 1.00 to 15.00 dollars per unit. 4. A postponement opportunity may exist for products where the cube is greatly reduced when the product is shipped unassembled to the warehouse, and for products where ubiquitous materials account for a large share of the total weight. The range for cube reduction in this research was between 10 to 50 percent of the original cube. The range for the weight of ubiquitous materials was from 30 to 80 percent of the total weight. 5. The variables tested in this research were found to be reasonably independent. Consequently, the combination of two or more favorable factors could enhance the probability that postponement will generate greater savings in the distribution of a product. 6. Packaging and time postponement-speculation are situations where savings from postponement are more likely to occur. No generalization concerning the magnitude of the savings can be supported by using the product physical and demand characteristics as predictors. 263 QQESTIQN§_EQB_EHBIHEB_BE§EAEQH The questions for further research are based on the findings and limitations of the research. Five areas for further research are identified. First, important variables such as customer service level, inventory carrying cost, and the number of warehouses in the distribution system were assumed constant in this research, to keep the problem within manageable proportions. Research investigating the importance of these variables for postponement-speculation decisions would be a significant contribution. Second, the value of the product and the uncertainty of demand were shown to be important variables in all models studied. However, the value range of the variables is limited. Therefore, a study of the importance of these variables outside the range established in this research will be important. The same is true for other variables of significance in this research. Third, this dissertation is restricted to the plant - warehouse segment. A research that replicates these findings at different segments in the distribution system, such as the warehouse - customer segment, is also a contribution. 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APPENDIX W IOQQO‘Ul-thI-i 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 UNUUUUNNNNNHHHHHO)GOIOIOUIUIUIUIUIUWWUUNNNNNHHHHH 270 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 OHOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 271 U'Iu“quNNNNNI-‘HHHHO‘GOIGOIUIUIWUIUIUUUUUNNNNNHHHPHO‘O‘O‘O‘O‘UIUIUIUI DS LUE 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 OHHHOOHHOOOOOOOOHHHOOHHHOOHPOOOHOOOOOOOOOHHOOOl-‘I-‘OO R U 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 01010waQNNNNNHHHHHOIOI01G01UIUIUIUIUIUUwUUNNNNNHHHHI-‘O‘OIOIGGUIUIUIUI 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 OOOOOOOOOOOOOOOOOHHHHOHHHHOHHHOOHHOOOOOOOOHHHOOHHPO O U 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 '162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 273 UIUIUIUUUUUNNNNNHHHHHOOIOIOIOUIUIUIUlUIUUUNUNNNNNI—‘HHHHO‘O‘M0101010101 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 HOOHHOOOHOOOOOOOOOHPOOOHHOOOPOOOOOOOOOOOOOOOOOOOOOO S PRO UCT 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 T. 274 UIUUIUMUUUNNNNNHHHHHOIOQOIOIUIUIUIUIUIMUUUUNNNNNHHHHHO‘O‘GO‘OIUIUI D UE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00' 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 HPOHHHOOHHHOOOOOOOHHHHOHHHOOHHPOOHHOOOOOOOOHHHOOHH PRO UCT 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 ND 12000 12000 12000 12000 12000 12000 12000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 ‘24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 C T. 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 275 B U'IUIWUUIJUOONNNNNHHHHHOIOO‘OIOIUIUIUIUIUIUUUUUNNNNNHHHHHO‘OIGOIOIUIU DS LUE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 P OOOHOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOHHPHOHP U) 276 Wig—MW 294 24000 0.06 5 11.50 1 295 24000 0.06 5 15.00 1 296 24000 0.06 6 1.00 0 297 24000 0.06 6 4.50 0 298 24000 0.06 6 8.00 0 299 24000 0.06 6 11.50 1 300 24000 0.06 6 15.00 1 301 24000 0.09 1 1.00 0 302 24000 0.09 1 4.50 0 303 24000 0.09 1 8.00 0 304 24000 0.09 1 11.50 0 305 24000 0.09 1 15.00 0 306 24000 0.09 2 1.00 0 307 24000 0.09 2 4.50 0 308 24000 0.09 2 8.00 0 309 24000 0.09 2 11.50 0 310 24000 0.09 2 15.00 1 311 24000 0.09 3 1.00 0 312 24000 0.09 3 4.50 0 ' 313 24000 0.09 3 8.00 0 314 24000 0.09 3 11.50 1 315 .24000 0.09 3 15.00 1 316 24000 0.09 5 1.00 0 317 24000 0.09 5 4.50 0 318 24000 0.09 5 8.00 1 319 24000 0.09 5 11.50 1 320 24000 0.09 5 15.00 1 321 24000 0.09 6 1.00 0 322 24000 0.09 6 4.50 0 323 24000 0.09 6 8.00 1 324 24000 0.09 6 11.50 1 325 24000 0.09 6 15.00 1 326 24000 0.12 1 1.00 0 327 24000 0.12 1 4.50 0 328 24000 0.12 1 8.00 0 329 24000 0.12 1 11.50 0 330 24000 0.12 1 15.00 0 331 24000 0.12 2 1.00 0 332 24000 0.12 2 4.50 0 333 24000 0.12 2 8.00 0 334 24000 0.12 2 11.50 1 335 24000 0.12 2 15.00 1 336 24000 0.12 3 1.00 0 337 24000 0.12 3 4.50 0 338 24000 0.12 3 8.00 1 339 24000 0.12 3 11.50 1 340 24000 0.12 3 .15.00 1 341 24000 0.12 5 1.00 0 342 24000 0.12 5 4.50 1 343 24000 0.12 5 8.00 1 0 UC 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 C 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 277 UIU'IUIUUUh)UNNNNNI-‘I-‘HHHGO‘O‘O‘GWUIUIMUUUUDJUNNNNNPRHHHGO‘O‘O‘O‘MU‘I US 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 OOOOOOOOOOOOOOOOOOHHHHOHHHHOHHHOOHHHOOOOOOOHHHHOPH W 394 36000 0.03 5 11.50 395 36000 0.03 5 15.00 396 36000 0.03 6 1.00 397 36000 0.03 6 4.50 398 36000 0.03 6 8.00 399 36000 0.03 6 11.50 400 36000 0.03 6 15.00 401 36000 0.06 1 1.00 402 36000 0.06 1 4.50 403 36000 0.06 1 8.00 404 36000 0.06 1 11.50 405 36000 0.06 1 15.00 406 36000 0.06 2 1.00 407 36000 0.06 2 4.50 408 36000 0.06 2 8.00 409 36000 0.06 2 11.50 410 36000 0.06 2 15.00 411 36000 0.06 3 1.00 412 36000 0.06 3 4.50 413 36000 0.06 3 8.00 414 36000 0.06 3 11.50 415 36000 0.06 3 15.00 416 36000 0.06 5 1.00 417 36000 0.06 5 4.50 418 36000 0.06 5 8.00 419 36000 0.06 5 11.50 420 36000 0.06 5 15.00 421 36000 0.06 6 1.00 422 36000 0.06 6 4.50 423 36000 0.06 6 8.00 424 36000 0.06 6 11.50 425 36000 0.06 6 15.00 426 36000 0.09 1 1.00 427 36000 0.09 1 4.50 428 36000 0.09 1 8.00 429 36000 0.09 1 11.50 430 36000 0.09 1 15.00 431 36000 0.09 2 1.00 432 36000 0.09 2 4.50 433 36000 0.09 2 8.00 434 36000 0.09 2 11.50 435 36000 0.09 2 15.00 436 36000 0.09 3 1.00 437 36000 0.09 3 4.50 438 36000 0.09 3 8.00 439 36000 0.09 3 11.50 440 36000 0.09 3 15.00 441 36000 0.09 5 1.00 442 36000 0.09 5 4.50 443 36000 0.09 5 8.00 278 "U HOOHHOOOHOOOOOOOOOHPOOOHHOOOHOOOOOOOOOOOOOOOOOOOOOB UC 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 279 UIUIU'INuUUUNNNNNHHHHHGGUIOIGUIUIUIUIUIUUUUUNNNNNHHPHHG01001010101 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 PHOHHHOOHHHOOOOOOOHHHHOHHHHOHHHOOHHOOOOOOOOHHHOOPP PRODUCT 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 36000 36000 36000 36000 36000 36000 36000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 280 UIUIWUUUUUNNNNNHHHHHGOOIOIGUIU'IU'IUIUIUUWUUNNNNNHHHHHGGGGOUIU 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00‘ 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 OOOHOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOHHPHOPP P 0 UC 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 .48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48080 48000 48000 48000 48000 48000 48000 48000 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 281 mmmuuUUUNNNNNI-‘HPPHOGOO‘OIUIUIUIUIUIUUUUUNNNNNHHHHHOIGGOGUIUI DS UE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 ' 4.50 8.00 PHOHHHOOI—‘HOOOOOOOOHHHOOHHHOOHHOOOHOOOOOOOOOHPOOOHH 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 '48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 282 GOIOIOIOIUIUIUIUIUIUUUUUNMNNNPHHHPO‘O‘GO‘O‘UIUI 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 HHHHOHHHHOHHHOOHHHOOOOOOOHHHHOPP U) \ONQO‘U‘IhUNI—I UCT 600 600 600 600 600 1440 1440 1440 1440 1440 2340 2340 2340 2340 2340 3300 3300 3300 3300 3300 3600 3600 3600 3600 3600 600 600 600 600 600 1440 1440 1440 1440 1440 2340 2340 2340 2340 2340 3300 A ND C 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 - O L B - IN U 0 SPACK a-u44tauIoaaneon:NI-han-homtnunmtnpusaspush:wtnuoueoNINIDAJHI-hawr- 283 UE 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 MAT OHHHOOHHOOOOOOOOHHOOOHHOOOPOOOOOOOOOOOOOO (I) 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 3300 3300 3300 3300 3600 3600 3600 3600 3600 600 600 600 600 600 1440 1440 1440 1440 1440 2340 2340 2340 2340 2340 3300 3300 3300 3300 3300 3600 3600 3600 3600 3600 600 600 600 600 600 1440 1440 1440 1440 1440 2340 2340 2340 2340 2340 3300 3300 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 284 abbUUUUUNIONMNHHI—‘HHUIUIUIUIUI-b-bthbUUUUUNNNNNI-JHHHHUIUIUIUIUI-buhuhh 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 I-I'OHHHHOHHHOOPOOOOHHHPOPHI—‘HOHHHOOHHPOOOOOOOI—‘HHOOPHHO R UCT 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 3300 3300 3300 3600 3600 3600 3600 3600 600 600 600 600 600 .1440 1440 1440 1440 1440 2340 2340 2340 2340 2340 3300 3300 3300 3300 3300 3600 3600 3600 3600 3600 2500 2500 2500 2500 2500 6000 6000 6000 6000 6000 9750 9750 9750 9750 9750 13750 13750 13750 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 uhbbUQUUUNNNNNI-‘HHHHUIUIUIUIUIIbIb##bUUUUUNNNNNI-‘PHHHUIUIUIUIUIIFIbh UE 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 HOOHHOOOHHOOOOOOOOHHPHOHHPHOHHHHOHHHHOHOOOOPHHHOHHH P O C 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 13750 13750 15000 15000 15000 15000 15000 2500 ' 2500 2500 2500 2500 6000 6000 -6000 6000 6000 9750 9750 9750 9750 9750 13750 13750 13750 13750 13750 15000 15000 15000 15000 15000 2500 2500 2500 2500 2500 6000 6000 6000 6000 6000 9750 9750 9750 9750 9750 13750 13750 13750 D 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 286 fibbUUUUUNNNNNHHHHHUIUIUIUIUIhIhbthUUUI-DNNNNMHHHHHUIWUIUIUIbh UE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 HHOHHHHOHHHHOHHOOOHHHHOHHHHOHHHOOPHHOOHOOOOHHHOOHH O UCT 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 13750 13750 15000 15000 15000 15000 15000 2500 2500 2500 2500 2500 6000 6000 6000 6000 6000 9750 9750 9750 9750 9750 13750 13750 13750 13750 13750 15000 15000 15000 15000 15000 2500 2500 2500 2500 2500 6000 6000 6000 6000 6000 9750 9750 9750 9750 9750 13750 13750 13750 C 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 287 bbubUwUUUNNNNNI-‘PPHI-JUIUIUIUIUIIhhhhhuuUUUNNNNNHHHHHUIUIUIUIUIhIF UE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 h-HI-hoHI-haor-hiwrac>wrahewcarapt-haorah-HI-C>Hr-howcahaHrah:or-haH<3c>HI-baH<:hIH PRO UCT 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 '263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 13750 13750 15000 15000 15000 15000 15000 4300 4300 4300 4300 4300 10320 10320 10320 10320 10320 16770 16770 16770 .16770 16770 23650 23650 23650 23650 23650 25800 25800 25800 25800 25800 4300 4300 4300 4300 4300 10320 10320 10320 10320 10320 16770 16770 16770 16770 16770 23650 23650 23650 R 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 288 S CK hub-bwwaUNNNNNHHI-‘HHUIUIUIUIUI-bbbubéuuquNNNNNI-‘HHHHUIUIUIUIUIIFIA UE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 .15.00 1.00 4.50 8.00 HHOHPHHOHHHOOHHOOOHHHOOHHHOOHPOOOHHOOOHOOOOHHHHHHH 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 UCT 23650 23650 25800 25800 25800 25800 25800 4300 4300 4300 4300 4300 10320 10320 10320 10320 10320 16770 16770 16770 16770 16770 23650 23650 23650 23650 23650 25800 25800 25800 25800 25800 4300 4300 4300 4300 4300 10320 10320 10320 10320 10320 16770 16770 16770 16770 16770 23650 23650 23650 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 289 bub#00quNNNNNNHHHHHUIUIUIUIUIb-hhbubUUUWUNNNNNHHHHHUUU‘IU‘IUI‘I-b LUE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 HHOHHPHOPHPHOHHHOOHHHHOHHHHOHHHHOHHHHOHHHOOHHHHOHH 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 UCT 23650 23650 25800 25800 25800 25800 25800 4300 4300 4300 4300 4300 10320 10320 10320 10320 10320 16770 16770 16770 16770 16770 23650 23650 23650 23650 23650 25800 25800 25800 25800 25800 6200 6200 6200 6200 6200 14880 14880 14880 14880 14880 24180 24180 24180 24180 24180 34100 34100 34100 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 290 S CK naauuuuuwwwMNHHHHHmmmmmbAAbbuuuuuuuuwwpppwHmmmmmhs U 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 HOOHHHOOHHOOOHOOOOHHHHHHHHHHHHHPHHHHHOHHHHOHHHHOHH UC 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 34100 34100 37200 37200 37200 37200 37200 6200 6200 6200 6200 6200 14880 14880 14880 14880 14880 24180 24180 24180 24180 24180 34100 34100 34100 34100 34100 37200 37200 37200 37200 37200 6200 6200 6200 6200 6200 14880 14880 14880 14880 14880 24180 24180 24180 24180 24180 34100 34100 34100 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 291 S C ##4-Uh)UNuNNNNNHHHHHUIUIUIUIUIIA-b##éwquUNNNNNHHHHPUIUIUIUIUIhIh UE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 HHOHHHHOHHHHOHHHOOHHHHOHHHHOHHHHOHHHOOHHOOOHHHOOHH PRODUC 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 34100 34100 37200 37200 37200 37200 37200 6200 6200 6200 6200 6200 14880 14880 14880 14880 14880 24180 24180 24180 24180 24180 34100 34100 34100 34100 34100 37200 37200 37200 37200 37200 6200 6200 6200 6200 6200 14880 14880 14880 14880 14880 24180 24180 24180 24180 24180 34100 34100 34100 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 292 ub‘bétdh’UtthNIOhiNBOF‘Hr‘F‘HlflUNmtflUthbhanbUtdhiutdhiw10A)NI‘F‘HI‘F‘UINUNUlflth UE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 HHHHHHHHHHPHOHHHHOHPHPOHHHHOHHHPOHHHHOHPHHOHHHHOHH PR DUCT 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 34100 34100 37200 37200 37200 37200 37200 8000 8000 8000 8000 8000 19200 19200 19200 19200 19200 31200 31200 31200 31200 .31200 44000 44000 44000 44000 44000 48000 48000 48000 48000 48000 8000 8000 8000 8000 8000 19200 19200 19200 19200 19200 31200 31200 31200 31200 31200 44000 44000 44000 D C RT. 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 293 S 459-humUUMNNNNNHHHHPUIUIUIUIUIIFIAhub-bUUUUUNNNNNHHHHPUIUIUIUIUIIFIF K DUE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00, 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 HHOHHHHOHPHOOHHOOOHHHOOHHHOOPHHOOHHOOOHOOOOHHHHHHH PRO UCT 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 44000 44000 48000 48000 48000 48000 48000 8000 8000 8000 8000 8000 19200 19200 19200 19200 19200 31200 31200 31200 31200 31200 .44000 44000 44000 44000 44000 48000 48000 48000 48000 48000 8000 8000 8000 8000 8000 19200 19200 19200 19200 19200 31200 31200 31200 31200 31200 44000 44000 44000 D UNC T. 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 294 uhbubUUUUUNNNNNHI-‘HI-‘I-‘UIUIUIUIU'IIF#hfiubuuUUUNNNNNHHI-‘HHUIUIUIUIUIhfi C ALUE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 .4.50 8.00 HHOHHHHOHHHHOHHHHOHHHHOHHHHOHHHHOHHHHOHHHOOHHHHOPH 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 UCT 44000 44000 48000 48000 48000 48000 48000 8000 8000 8000 8000 8000 19200 19200 19200 19200 19200 31200 31200 31200 31200 31200 44000 44000 44000 44000 44000 48000 48000 48000 48000 48000 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 T. 295 UIUIUIUIUI-bbubthUUUUNNNNNI-‘HHHHUIUIUIUIUIfib 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 HIHP'HI‘P‘HF‘F‘HIJPAPIdhiHFJHHHF‘HFJPAHO<3F‘HF‘F‘HIJPJHIJP‘HFHF‘HIJF‘HIJF‘HI‘F‘HI‘P‘HI‘F‘HI‘F‘OI‘P’HF‘P‘HIJPJH S 0 UC 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 304 0101010101010101010mlhbubbfihbbubhbbhhfihuuwuuuuuuuwwawUHHI-‘HHHH 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23' 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 UE 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 P HOOHHOOHOOOHHHOHHOOHOOOOOOOHHOOHHOOI—‘OOOOOOOOOOOOOO RO UC 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 ‘16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 0.11 0.11 0.11 0.11 0.11 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 hdbbnbibbuhlbblbhnbibuwnhiwtdhbw4003UIdhiwtdh’ufidh‘HrdF‘HIJP‘HIJF‘HIJF‘HIJO\GCRO\Q 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 A UE 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 U) or-haHcahaH<3c>Hrac>orarawcoraH<3c>Hrac>orac>o<3c>o<3c>oc:c>o<3c>oo<3c>wrahaora P UCT 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 16500 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.0.3 306 uuuuuuuuuuuwuuupppppppwHHHHHHHHmmmmmmmmmmmmmmmmoap 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36' 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 V E 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 .11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 0000000OOOOOOOOOOOOOOOOOOOOOOOOHHHOHPHOHHOOHHOOHHP 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 ‘566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 UCT 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 '32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 D RT. 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 307 R. UHHHHHPPHHHHHHHHHOImammamammmmGGmmfibéhbbééfibbhbfibufiuu 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO PRO UCT 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 D RT. 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.11 0.11 0.11 308 HHHmmammmmmmmmmmmmmbbbbhphpbpbshaaouuuuuuuuuuuuuuu 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 "0 (I) OOOHHOOHHOOOOOOOOOOHHOOHOOOOOOOOOOOI—‘I—‘OOOOOOOOOOOOO PRO UCT 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 D 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 309 mmmmmbhbhhbphhbhbpbun-hut.)uuuuuuuuuuuuuuppppppppppppp 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 OHOOOHHHOHHOOHHOOOOOOHHOOHHOOHOOOOOOOO000000000000 WE 694 32000 0.11 6 0.23 6.00 695 32000 0.11 6 0.23 11.00 696 32000 0.11 6 0.23 15.00 697 32000 0.11 6 0.36 1.00 698 32000 0.11 6 0.36 6.00 699 32000 0.11 6 0.36 11.00 700 32000 0.11 6 0.36 15.00 701 32000 0.11 6 0.50 1.00 702 32000 0.11 6 0.50 6.00 703 32000 0.11 6 0.50 11.00 704 32000 0.11 6 0.50 15.00 705 32000 0.15 1 0.10 1.00 706 32000 0.15 1 0.10 6.00 707 32000 0.15 1 0.10- 11.00 708 32000 0.15 1 0.10 15.00 709 32000 0.15 1 0.23 1.00 710 32000 0.15 1 0.23 6.00 711 32000 0.15 1 0.23 11.00 712 32000 0.15 1 0.23 15.00 713 32000 0.15 1 0.36 1.00 714 32000 0.15 1 0.36 6.00 715 32000 0.15 1 0.36 11.00 716 32000 0.15 1 0.36 15.00 717 32000 0.15 1 0.50 1.00 718 32000 0.15 1 0.50 6.00 719 32000 0.15 1 0.50 11.00 720 32000 0.15 1 0.50 15.00 721 32000 0.15 3 0.10 1.00 722 32000 0.15 3 0.10 6.00 723 32000 0.15 3 0.10 11.00 724 32000 0.15 3 0.10 15.00 725 32000 0.15 3 0.23 1.00 726 32000 0.15 3 0.23 6.00 727 32000 0.15 3 0.23 11.00 728 32000 0.15 3 0.23 15.00 729 32000 0.15 3 0.36 1.00 730 32000 0.15 3 0.36 6.00 731 32000 0.15 3 0.36 '11.00 732 32000 0.15 3 0.36 15.00 733 32000 0.15 3 0.50 1.00 734 32000 0.15 3 0.50 6.00 735 32000 0.15 3 0.50 11.00 736 32000 0.15 3 0.50 15.00 737 32000 0.15 4 0.10 1.00 738 32000 0.15 4 0.10 6.00 739 32000 0.15 4 0.10 11.00 740 32000 0.15 4 0.10 15.00 741 32000 0.15 4 0.23 1.00 742 32000 0.15 4 0.23 6.00 743 32000 0.15 4 0.23 11.00 310 U! '0 POOHPOOPPHOHHOOHHOOHOOOI—‘OOOOOOOOOOOOOOOHHHOHHOOHHO\ 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 UCT 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 32000 .32000 32000 32000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 T. 311 :0 uuuuuuuuuHHHHHHHHHHHHHHHHmammmmammammammmpbaapnoho 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 UE 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 OOOOOOOOOOOOOOOOOOOOOOOOOHHHOHHHOHHHOHHOOHHHOPHHOH PR UCT 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 D 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 T. 312 HHHHHHHHHHHOIOIOIOImmammmmasmmmmpbh4.45.6.5»AAAAhbbhuuuuuuu 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23. 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 UE 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 P (I) OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO000000000 'RODU 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 .WvL 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 -48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 J D 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 313 OGGOGO‘GGQU‘QO‘Gfié-fiufibfifiubbahhhfifibbuuuuUUUWUUUUUUUUHHHHHE 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 OHHOOOOOOOOOOHHOOHOOOOOOOOOOOHHOOOOOOOOOOOOOOOOOOO PRODUCT 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 {LED 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 .;T. 0.07 0.07 0.07 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 314 all-bubbub-b#bbbhbbthUUUUUUUUUMUD-DUNUHPHHHHHHHHHHHHHHO‘O‘O‘ a:' 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 HHOI—‘HOOHHOOOOOOHHHOHHOOHOOOOOOOOOOOOOOOOOOOOOOOHHO PRODUCT 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 D 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 T. 315 uhUUh’UUUUUUwuuUUUUHHHHHHPPHHHHHPHHOIGOIGOIGOIOIOIGOIOIO‘OIOIGh ER 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 0.10 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 E "U (n OHHHOHHOOHHOOHOOOHOOOOOOOOOOOOOOOHHHOHHOOHHOOHOOOP\ 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 316 mmGGmmmfimGGO‘GmOmbhbbfifibubbbubhuhhh 3’ 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50' 0.50 0.10 0.10 0.10 0.10 0.23 0.23 0.23 0.23 0.36 0.36 0.36 0.36 0.50 0.50 0.50 0.50 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 1.00 6.00 11.00 15.00 HHHOHHHOHHHOHHOOHHHOHHHOHHOOHHO U) PP N MAT EBODUCT DEMAND DNCEBT. EDDIQM EEADUE 1 600 0.03 0.30 1.00 2 600 0.03 0.30 4.50 3 600 0.03 0.30 8.00 4 600 0.03 0.30 11.50 5 600 0.03 0.30 15.00 6 600 0.03 0.42 1.00 7 600 0.03 0.42 4.50 8 600 0.03 0.42 8.00 9 600 0.03 0.42 11.50 10 600 0.03 0.42 15.00 11 600 0.03 0.55 1.00 12 600 0.03 0.55 4.50 13 600 0.03 0.55 8.00 14 600 0.03 0.55 11.50 15 600 0.03 0.55 15.00 16 600 0.03 0.68 1.00 17 600 0.03 0.68 4.50 18 600 0.03 0.68 8.00 19 600 0.03 0.68 11.50 20 600 0.03 0.68 15.00 21 600 0.03 0.80 1.00 22 600 0.03 0.80 4.50 23 600 0.03 0.80 8.00 24 600 0.03 0.80 11.50 25 600 0.03 0.80 15.00 26 600 0.06 0.30 1.00 27 600 0.06 0.30 4.50 28 600 0.06 0.30 8.00 29 600 0.06 0.30 11.50 30 600 0.06 0.30 15.00 31 600 0.06 0.42 1.00 32 600 0.06 0.42 4.50 33 600 0.06 0.42 8.00 34 600 0.06 0.42 11.50 35 600 0.06 0.42 15.00 36 600 0.06 0.55 1.00 37 600 0.06 0.55 4.50 38 600 0.06 0.55 8.00 39 600 0.06 0.55 11.50 40 600 0.06 0.55 15.00 41 600 0.06 0.68 317 1.00 OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOE 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 UCT 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 318 0.68 0.68 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 ,0.55 0.68 0.68 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO U) PRO UCT 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 319 0.68 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 _ 1.00 4.50 8.00 OOOOOOOOOOOOOOOOOOOOOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOO S PR DUCT 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 T. 320 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 OOOHOOOOOOOOOOOOOOPHOOOHOOOOOOOOOOOOOOOOOOOHOOOOOO PRO UCT 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 T. 321 M 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 UE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 HOOHHHOOHHOOOOOOOOHHHOOHHHOOHHOOOHOOOOOOOOOHHOOOHH PRODUCT 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 12000 12000 12000 12000 12000 12000 12000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 D 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 T. 322 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 '0.68 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 OOOHOOOOOOOOOOOOOOHOOOOOOOOOOOOOOOOOOOOOOOOPHHOOHH 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 CT 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 '24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 323 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 - 4.50 8.00 POOHHOOOHOOOOOOOOOHHHOOPHOOOHHOOOOOOOOOOOOOHHOOOHP P O UCT 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 24000 24000 24000 24000 24000 24000 24000 24000 24000 ,24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 24000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 324 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 M UE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 OOOOOOOOOOOOOOOOOOPHHOOHHHOOPHHOOHHCOOPOOOOHHHOOHH PR DUCT 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 '36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 D T. 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 325 M 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 UE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 8.00 OOOHHOOOHOOOOOOOOOHHOOOHHOOOHOOOOOOOOOOOOOOHOOOOPO U) P 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 UCT 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 36000 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 326 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 M UE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 HOOHHHOOHHOOOHOOOOHHHOOHHHOOPPOOOHHOOOOOOOOHHHOOHH S RODUCT 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 36000 36000 36000 36000 36000 36000 36000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 327 . WU I M 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 PV UE 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 OOOPOOOOOOOOOOOOOOHOOOOPOOOOOOOOOOOOOOOOOOOHHHOOHH 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 UCT 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 C T. 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 328 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 -0.68 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50' 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 POOHHOOOHI—‘OOOOOOOOHHHOOPPOOOHHOOOHOOOOOOOOOHPOOOHH PRO UCT 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 '48000 48000 48000 48000 48000 48000 48000 48000 48000 48000 D 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 T. 329 0.68 0.68 0.80 0.80 0.80 0.80 0.80 0.30 0.30 0.30 0.30 0.30 0.42 0.42 0.42 0.42 0.42 0.55 0.55 0.55 0.55 0.55 0.68 0.68 0.68 0.68 0.68 0.80 0.80 0.80 0.80 0.80 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 1.00 4.50 8.00 11.50 15.00 HHHHOHHHOOHHHOOHHoocHoooowvwoowwm APP DIX - - N U EBODUCT DEMAND UNQEBI, EYALDE 21$ 1 600 0.030 1.00 0 2 600 0.030 2.75 0 3 600 0.030 4.50 0 4 600 0.030 6.25 0 5 600 0.030 8.00 0 6 600 0.030 9.75 0 7 600 0.030 11.50 0 8 600 0.030 13.25 0- 9 600 0.030 15.00 0 10 6600 0.030 1.00 0 11 6600 0.030 2.75 0 12 6600 0.030 4.50 0 13 6600 0.030 6.25 0 14 6600 0.030 8.00 0 15 6600 0.030 9.75 0 16 6600 0.030 11.50 0 17 6600 0.030 13.25 0 18 6600 0.030 15.00 0 19 12500 0.030 1.00 0 20 12500 0.030 2.75 0 21 12500 0.030 4.50 0 22 12500 0.030 6.25 0 23 12500 0.030 8.00 0 24 12500 0.030 9.75 0 25 12500 0.030 11.50 0 26 12500 0.030 13.25 0 27 12500 0.030 15.00 0 28 18500 0.030 1.00 0 29 18500 0.030 2.75 0 30 18500 0.030 4.50 0 31 18500 0.030 6.25 0 32 18500 0.030 8.00 0 33 18500 0.030 9.75 0 34 18500 0.030 11.50 0 35 18500 0.030 13.25 0 36 18500 0.030 15.00 0 37 24000 0.030 1.00 0 38 24000 0.030 2.75 0 39 24000 0.030 4.50 0 40 24000 0.030 6.25 0 41 24000 0.030 8.00 0 330 24000 24000 24000 24000 30000 30000 30000 30000 30000 30000 30000 30000 30000 36000 36000 36000 36000 36000 36000 36000 36000 36000 42000 '42000 42000 42000 42000 42000 42000 42000 42000 48000 48000 48000 48000 48000 48000 48000 48000 48000 600 600 600 600 600 600 600 600 600 6600 6600 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 331 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO PRO UCT 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 6600 6600 6600 6600 6600 6600 6600 12500 12500 12500 12500 12500 12500 12500 12500 12500 18500 18500 18500 18500 18500 18500 18500 18500 18500 24000 24000 24000 24000 24000 24000 24000 24000 24000 30000 30000 30000 30000 30000 30000 30000 30000 30000 36000 36000 36000 36000 36000 36000 36000 36000 D 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 332 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 0) OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO PR DUCT 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 36000 42000 42000 42000 42000 42000 42000 42000 42000 42000 48000 48000 48000 48000 48000 48000 48000 48000 48000 600 600 600 600 600 600 600 600 600 6600 6600 6600 6600 6600 6600 6600 6600 6600 12500 12500 12500 12500 12500 12500 12500 12500 12500 18500 18500 18500 18500 D 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 333 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 U) OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO UC 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 18500 18500 18500 18500 18500 24000 24000 24000 24000 24000 24000 24000 24000 24000 30000 30000 30000 30000 30000 30000 30000 30000 30000 36000 36000 36000 36000 36000 36000 36000 36000 36000 42000 42000 42000 42000 42000 42000 42000 42000 42000 48000 48000 48000 48000 48000 48000 48000 48000 48000 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 334 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 E PU OOOOOOOOOOGOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO\ U) PRO UCT 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 600 600 600 600 600 600 600 600 600 6600 6600 6600 6600 6600 6600 '6600 6600 6600 12500 12500 12500 12500 .12500 12500 12500 12500 12500 18500 18500 18500 18500 18500 18500 18500 18500 18500 24000 24000 24000 24000 24000 24000 24000 24000 24000 30000 30000 30000 30000 30000 D C 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 335 E 1.00 12.00 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 ‘ 8.00 "U OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO\ U) PRO UCT 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 30000 30000 30000 30000 36000 36000 36000 36000 36000 36000 36000 36000 36000 42000 42000 42000 42000 42000 42000 42000 42000 42000 48000 48000 48000 48000 48000 48000 48000 48000 48000 600 600 600 600 600 600 600 600 600 6600 6600 6600 6600 6600 6600 6600 6600 6600 12500 D 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 336 UE 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 .1.00 P OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO0.00000000000000 PR U 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 '366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 12500 12500 12500 12500 12500 12500 12500 12500 18500 18500 18500 18500 18500 18500 18500 18500 18500 24000 24000 24000 24000 24000 24000 .24000 24000 24000 30000 30000 30000 30000 30000 30000 30000 30000 30000 36000 36000 36000 36000 36000 36000 36000 36000 36000 42000 42000 42000 42000 42000 42000 C 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 337 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 HHHHHHHHHHHHHHHHHHHHHHHHHPOOOOOOOOOOOOOOOOOOOOOOOO 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 UC 42000 42000 42000 48000 48000 48000 48000 48000 48000 48000 48000 48000 600 600 600 600 600 600 600 600 600 6600 6600 6600 6600 6600 6600 6600 6600 6600 12500 12500 12500 12500 12500 12500 12500 12500 12500 18500 18500 18500 18500 18500 18500 18500 18500 18500 24000 24000 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 338 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 HHHHHHHHPPHHHHHHHHHHHHHHHHHPHHHHHHHHHHHHHHHHHHPHHP P 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 UCT 24000 24000 24000 24000 24000 24000 24000 30000 30000 30000 30000 30000 30000 30000 30000 30000 36000 36000 36000 36000 36000 36000 36000 36000 36000 42000 42000 42000 42000 42000 42000 42000 42000 42000 48000 48000 48000 48000 48000 48000 48000 48000 48000 600 600 600 600 600 600 600 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.105 0.120 0.120 0.120 0.120 0.120 0.120 0.120 339 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 PHI-'0OPHHHHHPHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHPH PRO UCT 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 600 600 6600 6600 6600 6600 6600 6600 6600 6600 6600 12500 12500 12500 12500 12500 12500 12500 12500 12500 18500 18500 18500 18500 18500 18500 18500 18500 18500 24000 24000 24000 24000 24000 24000 24000 24000 24000 30000 30000 30000 30000 30000 30000 30000 30000 30000 36000 36000 36000 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 340 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 .4.50 OOOHHHHHOOOOHHHHPOOOOHHHHPOOOOHHHHHOQOOHHHHHOOOOHH P U 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 36000 36000 36000 36000 36000 36000 42000 42000 42000 42000 42000 42000 42000 42000 42000 48000 48000 48000 48000 48000 48000 48000 48000 '48000 600 600 600 600 600 600 600 600 600 6600 6600 6600 6600 6600 6600 6600 6600 6600 12500 12500 12500 12500 12500 12500 12500 12500 C 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 341 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 P‘HFHPAHIJFAOIHF‘HIJP'HIJP‘OIHF‘HIHFAHIJP‘OIJF'HIdP‘OCDCDOI‘F‘PI‘F’O¢DC>OIdFAPIJPAO UCT 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 -641 642 643 12500 18500 18500 18500 18500 18500 18500 18500 18500 18500 24000 24000 24000 24000 24000 24000 24000 24000 24000 30000 30000 30000 30000 30000 30000 30000 30000 30000 36000 36000 36000 36000 36000 36000 36000 36000 36000 42000 42000 42000 42000 42000 42000 42000 42000 42000 48000 48000 48000 48000 0.135 ”0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 342 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 '6.25 HHHOHHHHHHHHOPHHHHHHHOHHHHHHHHOPPHHHHHHOHHHHHHHHOH S 343 PRODUCT DEMAND DNQEBI, EEADDD £15 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 48000 48000 48000 48000 48000 600 600 600 600 600 600 600 600 600 6600 6600 6600 6600 6600 6600 6600 6600 6600 '12500 12500 12500 12500 12500 12500 12500 12500 12500 18500 18500 18500 18500 18500 18500 18500 18500 18500 24000 24000 24000 24000 24000 24000 24000 24000 24000 0.135 0.135 0.135 0.135 0.135 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 HHHHHHHHPHPHHHHHHHHHHHHHHPHHHHHHHHHHHPHHHHHHHHHHHH UC 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 30000 30000 30000 30000 30000 30000 30000 30000 30000 36000 36000 36000 36000 36000 36000 36000 36000 36000 42000 42000 42000 42000 42000 42000 42000 42000 42000 48000 48000 48000 48000 48000 48000 48000 48000 48000 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 344 E 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 1.00 2.75 4.50 6.25 8.00 9.75 11.50 13.25 15.00 "0 HHHHHHHHHHHHHHHHHHHPHHHHHHHHHHHHPHHHB MICHIGAN STATE UNIV. LIBRQRIES 1|!IIIHIIIIIIIIIUIHWIIIIIIIIHHHIIIHHIIIIIIIHHHI 31293007963725