v. - DEVELOPMENT OF A DYNAMIC SIMULATION MODEL FOR PLANNING PHYSICAL DISTRIBUTION m FORMULATION OF THE MATHEMATICAL MODEL ‘ Thesis for the Degree of D. B. A I MICHIGAN STATE UNIVERSITY OMAR KEITH HELFERICH 3.970 IIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII I“ I IBRARY (I ”Tlxt‘lofill ”$2“: . :i' Lug; Mailman)? E 23 10405 1820 f This is to certify that the thesis entitled . ., DEVELOPMENT OF A DYNAMIC SIMULATION MODEL FOR PLANNING PHYSICAL DISTRIBUTION SYSTEMS: FORMULATION OF THE MATHEMATICAL MODEL presented by OMAR KEITH HE LFER I CH has been accepted towards fulfillment of the requirements for D . B . A . degree in PRODUCT I ON Mg 'I I’LQf/Laflg/ Y, {At/t" 44¢ Major rofessor S Date November IOQ 970 0-169 m 21*?- 23 7&7 ABSTRACT DEVELOPMENT OF A DYNAMIC SIMULATION MODEL FOR PLANNING PHYSICAL DISTRIBUTION SYSTEMS: FORMULATION OF THE MATHEMATICAL MODEL BY Omar Keith Helferich In the past decade the recognition of the importance of cost and service implications has increased the interest in the development and application of management science tech— niques to decision making associated with the design and administration of systems to control raw materials and finished goods flow. In general, however, the majority of the problems considered in the past have been defined such that the basic components or subsystems of the total physical distribution system have been modeled independently rather than considering the interaction and tradeoffs within the total system. In this context the PD system includes the facility component, the communications component, the inven— tory component, the transportation component, and the ware- housing (unitization) component. The problems have also been stated in terms of a short term or tactical planning horizon while neglecting the strategic planning horizon. Finally, the problem definitions have in general not included the sequential or staged decision problem which Omar Keith Helferich assumes that current decisions have an effect on the problem- solution decision process in future time periods or stages. The overall objective of an ongoing research project at the Graduate School of Business at Michigan State Univer- sity has been to develop a viable long-range planning model for physical distribution systems design. The goal has been to develop a model, referred to as the Long Range Environ- mental Planning Simulator (LREPS), that includes (1) all of the basic components of the physical distribution system, (2) a strategic planning horizon, and (3) the sequential decision problem. Two additional general research criteria established were that the model be modular in construction and universal in application for a broad class of manufactur- ing firms. In formulating the mathematical model an overall sys- tems approach was required. This approach is discussed in the Literature Review, Chapter II and the Approach to Mathe- matical Design, Chapter III. The general design approach consisted of performing activity analyses for each subsystem of the model using the following procedure: (1) State the objective of the activity, (2) Develop the conceptual approach using several alternatives for each activity, (3) Select the best alternative(s) for each activity, (4) Develop the speci- fications, input, output, and transformations for the selected alternative(s) , (5) Collect, perform analysis and prepare data for the selected alternative(s) , and finally (6) Program the selected alternative(s). The above procedure although listed as a sequence was in fact an iterative process. Omar Keith Helferich Several special design concepts were used in the devel- fico mumum ammflxpflz .sonmmmmm mo cowmfi>wo .Amcfleoonunom ”cmmfi£OHz .mcfimcmq ummmv snowmocoz .mEOumNm coflusnfluumflo HMOHwhnm mo coflpwasefim OHEmcwo ..Hm um .xOmum3om .h .o H ummocou Hopoz mEmumwm mmmeIIm.H Guzman H Emkw>w mo >mHH4Hmem4m muH>mmm mm4m m0hmmm mm4w mm ¥u2“ 0 w z dwzz_ zzou um ozmkm the period of time usually 5 to 10 years over the period ofguoblem consideration. For this variable the problem is classified as either a short term (operational) planning model‘with considerations for l-2 years or a long—range (strategic) planning horizon where consideration is fre- Quently 5-10 years.2 The dichotomy non-sequential versus sequential is used to Classify a physical distribution planning model relative u>the influence of current decisions on future decisions "mdelhl the model. Hadley describes a sequential decision a Problem which involves making two or more decisions at different points in time, and which has 53 property that the later decision(s) may be in- fluenced not only by the previous decisions, but a SC) by some stochastic parameters whose values will act-‘~1ally have been observed before later decisions are made. 28 The key difference between sequential and non-sequential decision problems is that future decisions in sequential problems may be based partially on information known in the future but unknown at present. One of the frequent ap- proaches to solution Of sequential decision problems uses the functional equation technique of dynamic programming.4 The dependent variable, type of solution technique, refers to the general technique, either analytical or heuristic that is the primary solution technique for the planning model. In this thesis analytical includes any one of the mathematical techniques such as linear prOgramming, least squares, dynamic programming, and inventory theory. Heuristic techniques are non-optimizing including such modeling techniques as simulation, which may or may not incorporate analytical (Optimization) techniques for solu- tion of subsets of activites or components within the total model. The unifying dimension refers to the orientation of the model in develOping measures of cost and/or service. The unifying dimension of a model is classified as spatial if the cost and/or service are developed based on location or transit time. If the model uses order—cycle time as the measure of physical distribution system performance, the model is classified as temporal or time oriented.5 The behavior of the model refers to classification of static versus dynamic. A dynamic model is defined as one 29 where information feedback control lOOps provide time- varying interactions within the model.6 The environmental inputs are one of the operating forces that influence physical distribution policy and are external to the firm. The environmental forces are sum- . 7 marized by Bowersox as: Industry Competitive Structure Market Differentials Network of Service Industries Legal Structure . Economic Forces U'lthI-J O 0. It is not the purpose of this thesis to establish and/or attempt to prove the hypothesis that "A given physi- cal distribution planning problem defined in terms of the independent variables component structure, planning hori- zon, and influence by previous decisions would dictate a 'suggested best' solution approach in terms of the depen- dent variables type Of solution technique, unifying dimen- sion, behavior of system model, and environmental inputs." There is, however, evidence in the literature that lends support to the relationship of physical distribution prob- lem to solution approach as defined above. Literature Support Solution Approach.--In terms of the solution approach there is support in the literature that suggests that complex problems frequently encountered in business must be solved with heuristic models, such as simulation, since mathematical analysis has not been capable of yielding 30 general analytical solutions. The alternative, an experi- mental approach with the real system is frequently too costly in time and money.8’9'lo The paper by Geisler and Steger considers alternative techniques in logistics systems analysis.11 The authors, after classifying logistics systems by a set of character- istics, present a classification of systems analysis tech- niques and their attributes as illustrated in Table 2.1. The objectives of systems analysis as stated by Geisler and Steger are to: 1. Determine their Operating characteristics 2. Study their completeness, and consistency 3. Evaluate new policies and procedures 4. Do sensitivity testing. The object of selection from among these systems-analysis techniques, according to the authors, is to find the one technique that best deals with system characteristics in achieving the purpose Of the analysis. The authors further state: . . . simulation plays a very important and cen- tral role in the Spectrum of techniques used, par- ticularly in dealing with those facets of a system that are not now or may never be subject to a high enough degree of abstraction to lend themselves to analytical treatment.12 The conditions affecting choice between heuristic and 13 optimizing models are discussed by Kuehn. The value of optimizing models according to Kuehn is that the computa- tional method leads to the best possible solution or set of 31 mmzqflccome coummmmm O>Humcumuad mo :Oflumcfinfioo one: xfimmmch.ocH .GM3HH .Q pumsowm auaaoa sauna onu aoauoouac a“ unannouaa uuuauum auaaauuu< “use; "mmocMHHH .OOO3OEomV cuss .m .O can mmouo .M .0 an OODHOO .mmcflcmwm Omuooamm ucmEmmwcmz chaumuOmo =rmflmmamc¢ mEmummm moaumflmoq ca .Hmmmum .4 .3 can HOHmHOO .< .2 H T . . .aowuauaoawuoaxm iv :0 a «unusuaoa an «o onmm ' . . . £32.33, comm ' o o o O O o o o “”00 v o o o o o o cam-“Ham A o o o o 0%UHHHDfix0Hm ‘i O o o o o “UHU“HQEHW T cowuoauumbn mo oouwuo couuaazawm mcuaacufi maovoz coauuaaaam «ecu vanes Hoax uwuhaac< coauaasaam nouaaaoo mumoa osu Scum vanes wGHEflU 6H 0am mflOHufl>H0mDO Hag “coauaaaawm Ousnuuuu< Oscacnooa a .mmusnauuua Mamas can mmsvflcnoma mflmhamcd mEmumhm mo cOAUOOAmammmHU make the model suitable for testing the effect of any assumptions for a given future year. In summary, the Shycon and Maffei planning model does not consider the inventory or communications component, is non-sequential, and is primarily a short range planning model. It cannot, therefore, provide the answer to the Problem statement of this thesis. The model, however, does include the essential parts which influence warehouse loca- tion. It thus provides background information for develOp- ment Of the location algorithm for the LREPS mathematical Inodel. Ballou.-—Ballou considers the question of what combi- Ilation of multiple optimal warehouse location alternatives SINDuld be chosen to maximize cumulative profits from loca- tion for a given planning period.50 In this model the math- ennatical technique dynamic programming is used to find the optimal solution to the multi-period location problem. Ballou states that: 49 A physical distribution system can be conceptualized as several inventory storage points (nodal points) interconnected by a transportation network (links). Location of inventories or location of warehouse facilities, transportation service choices, and inventory-level alternatives are the three major decision areas that concern the physical distribu- tion manager about the design of a distribution system. 5 In treating only the location problem independently of other alternatives, Ballou states that an upper limit is established on the profits that the distribution system can generate, due to the fact that one degree of freedom in overall system design is lost. The concern in this model is to determine the location plan that describes when and where relocation should take place throughout the planning period. This plan is estab- lished at present time (time zero) for the entire planning horizon and is the Optimum plan based on the problem state- ment and the forecasted revenue and cost levels. The model provides an example of a multi-component model that con- siders the sequential decision problem. Ballou states in this regard that: . . . existing models, although sophisticated lack a certain amount of scope, eSpecially for providing solutions Ehft indicate the Optimum location pattern over time. The basic elements of transportation and location are considered in the model developed by Ballou. Inventory, *warehouse Operation, and communications are not, however, incfluded in the problem definition. The planning horizon is pmimarily short—range for the model as presented in the 50 literature. As in the two previous models, however, the inputs could be modified to reflect long-range estimates of environmental factors. The problem is defined by Ballou states that future decisions are to be influenced by pre- vious decisions. Thus the problem does investigate the multi-period or sequential decision problem. The solution technique found to be apprOpriate by Ballou was dynamic programming: . . . the best location plan is found by recasting the problem into a sequence of single—decision events. Then, according to Bellman's Principle of Optimality: in a sequence Of decisions, whatever the initial decision, the remaining decisions must Eifiitifi‘étinii‘iiité‘i‘é’i‘s‘iii?“’5’3.39? the State resulting The dynamic programming technique is an analytical tech- nique for finding a warehouse location-relocation plan that will yield maximum cumulative profits for a given planning horizon. The unifying dimension for this dynamic programming model is spatial even though delivery time is used as a basis for measuring service. As indicated previously by Heskett, transit time alone does not make a model time- oriented. The model must also develOp a measure of the total cycle time, and a measure of service dependability. In summary, the model developed by Ballou is basi- callyaalocation model with transportation costs and transit time used as the basis for measuring system performance. A key component, inventory control, however, is not con- sidered. The model considers the sequential decision 51 problem and thus provides a useful framework for develOping this aspect of the LREPS mathematical model. The model is dynamic in the sense that it uses a completely recursive system of equations to solve the multi-period problem. It solves the multi-stage decision problem. Forrester.--The model of the industrial system devel- Oped by Forrester attempts to match production rate to rate of final consumer sales.55 The process of production and distribution according to Forrester is the central core of many industrial companies. A recurring problem is to match the production rate to the rate of final consumer sales. Forrester states that: It has often been Observed that a distribution sys- tem of cascaded inventories and ordering procedures seems to amplify small disturbances that occur at the retail level.56 The model develOped by Forrester as shown in Figure 2.5, deals with the structure and policies within a multi-stage distribution system. Flows of information, order, and materials are required to define the model. Three types of information are required according to Forrester: (l) the organizational structure, (2) delays in decisions and actions, and (3) the policies governing purchases and in- ventories. The organizational structure includes the nodes or stages at which inventory exists; the factory, distribu- tor, and retailer. Delays in flow of orders (information) and flow of goods are necessary to determine the dynamic 52 FACTORY DL 1 FACTORY ‘ INVENTORY WAREHOUSE NODE DL ’ \ i DL DL \ DISTRIBUTORS INVENTORY DL NODE / o 1» RETAILERS \ INVENTORY NODE DL / / ORDERS FROM CUSTOMERS DELIVERY OF GOODS (ASSUMED RATE) TO CUSTOMERS DLI-Iklmy11me Figure 2.5--Organization of Production-Distribution System1 1J. W. Forrester, Industrial Dynamics (Cambridge, Massachusetts: The M.I.T. Press, Massachusetts Institute of Technology, 1961), p. 22. 53 characteristics of the system. Three principal components are defined by Forrester: (1) orders to replace goods sold, (2) orders to adjust inventories upward or downward as the level of business activity changes, and (3) orders to fill the supply pipelines with in-process order and shipments. The physical distribution components included in the industrial dynamics production-distribution simulator are: (l) transportation, (2) inventory, (3) communications de- lays, (4) a fixed set of locations, and (5) warehouse or unitization. The organization structure is a single factory, and single factory warehouse, multi-distributors and multi- retailers. The distributors and retailers are each repre- sented by single location in the model. Aggregate increases and decreases in sales are assumed. Therefore, this model should be considered a single product type model. The problem as stated is thus one of total physical distribu- tion system components for a single channel, single supply source, with multi-stage inventory nodes. The model as developed is a "closed" system. Inputs are initialized as rate equations. Since the model is not presented as a decision making tool there is no reference to a planning period horizon for decision making. The re- sponse of simulation runs to various changes in inputs is measured for dynamic effects on system variables in terms of 1-3 years. The period of influence could therefore be 54 considered short-range or long—range. The problem as stated is sequential since the objective is to examine possible fluctuating or unstable behavior arising from the principal structural relationships and policies over time. The general solution approach used by Forrester is heuristic. He makes the point that mathematical analysis is not powerful enough to yield general analytical solutions to situations as complex as the total physical distribu- tion system. Forrester constructs a mathematical model of the industrial system that tells how the conditions at one point in time lead to subsequent conditions at future points in time. The behavior of the model is observed and experi- ments are conducted to answer Specific questions about the system that is represented by the mathematical model. The name "simulation" is often applied to this process of con- ducting experiments on a model rather than attempting the experiments with the real system. Forrester states that simulation consists of: . . . tracing through, step by step, the actual flows of orders, goods, and information, and ob- serving the series Of new decisions that take place.57 The unifying dimension in the model is "time" as pre- viously stated by Forrester: . . . to be able to determine the dynamic charac- teristics of this system, we must know the delays in the flows of orders and goods. 55 The behavior of the model is dynamic in the sense that it consists of information-control loops and deals with time- varying interaction. The model develOped by Forrester presents Observa- tions and results of experimentations related to the dynam- ics of the total physical distribution system. It, thus, provided valuable insight in develOping the dynamic aspects of the LREPS mathematical model. Carrier Air Conditioning Company.--The model develOped by Carrier Air Conditioning Company uses a combination of simulation and linear prOgramming for a physical distribu- tion system}59 The problem as defined includes elements of tranSportation, inventory, warehousing, communications, and location and thus is a total physical distribution model as defined in this thesis. The planning horizon is not stated, but it appears thatzthe model is run using activity levels for one Oper- atirmgyear. It could be considered short-range or long- ran9e, since the model inputs could and apparently have beeni modified to simulate different markets, customer de- maIKi, production schedules, freight rates, shipping modes, delifiVery times, inventory costs, warehouse rates and hand- ling rates. The problem as discussed in the article and illus- trated in the input/output forms appears to be non- SequSantial. The decision maker requests the proposed 56 physical distribution system he wishes to measure. The combination simulation and linear programming model then is used to develop the costs and a customer service level for the requested inputs. The general solution approach as previously stated is heuristic with the optimization technique, linear pro- gramming incorporated in the model. The unifying dimen- sion appears to be spatial rather than time oriented. The model incorporates a measure of the time Of order proces- sing and transit time, and the percentage of market within a number of days. However, as defined in this thesis the time dimension refers to the use of unit inventory control, transit time, order processing times, delays due to stock- outs, etc. tO develOp the only true "temporal" measure-- the total order cycle. Merely reporting a transit time and/pr order processing time does not make the model time- oriented . The model could be dynamic within the simulation of agiven year. However, it does not appear to be dynamic inthe sense of the definition stated in this thesis, which :HTIUires information-feedback lOOps or recursive equations. The Inodel is short-range in the sense that it simulates one year: at a time. The effect of changes in environmental in- puts; could, however, be tested for any given future year whicfli would provide long-range capabilities. 57 In summary the Carrier Air Conditioning Company model includes elements of all of the components of the physical distribution system. The problem, however, does not con- sider the sequential decision problem, the unifying dimen- sion is spatial rather than temporal, and the model is pri- marily oriented toward short-range planning. The model does present an illustration of the integration Of a heu- ristic technique for general overall solution with analyti- cal techniques incorporated for analysis of individual components. In this case, linear programming is used to solve the location problem within the constraints of the general solution provided by the simulation model. Packer.--The next two models which are reviewed in this section emphasize the inventory component. The first by Packer is basically a single component model since it annsiders basically only the inventory component.60 The Prohflem as Packer defines it concerns a company that manu- f«Statutes two classes of inventory. One is subject to deter- mill’listic demand, and the second includes overhead inven- tDries such as components which are probablistic demand. in"? objectives are to determine the most effective para- metric values for use in exponential smoothing formulas and to SUJantify the benefits resulting from the application of proExbsed inventory decision rules. The general program is outlined in Figure 2.6. 58 The program generally functions as follows: 1. The values, switches, etc., are initialized. 2. The demand for the month is read. 3. A new forecast is made. 4. If any previous orders are due (lead time has expired since last order), incoming stock is added to the quantity on hand. 5. Any back orders unfilled from last month are filled. 6. The stock available is compared with a newly calcula- ted order point. 7. If the order point equals or exceeds the stock avail- able, an order quantity is calculated and the order is placed. 8. Sufficient stock is 'issued' to meet current demand; a back order is established if current demand exceeds the stock available. 9. Under one option, detail relative to each month's activity is written. Under the second option, only summary totals are produced. For either Option, pro- gram returns, reads the next month's demand, and repeats the loop from Step 2. 10. When the end of the simulated period (2 years) is reach- ed, summary totals are written listing: (a) the average inventory in units and dollars; (b) the number of stock- outs, demands, and orders; (c) the service percentage (in terms Oflxnflldemands made/demands filled and quan— tity demanded/quantity filled); (d) safety and alpha factors; and (c) the average forecast error. 11. When all the items in the sample have gone through the above program, a summary report is run listing the following for each inventory class for the simulated period: (a) average inventory investment, (b) total and average orders placed per item, (c) total and average stockouts per item, (d) the number of sample items in the group. 12. If any more 'knob' cards are present, the parameters are changed according to those cards and the entire process begins again. Flgure 2.6--Simulation and Adapted Forecasting Applied to Inventory Control1 as 1A. H. Packer, "Simulation and Adaptive Forecasting VOlADplied to Inventory Control," Operations Research, ‘ 15 (August, 1967), p. 670. 59 The problem as defined is a multi-item, single stage stochastic demand inventory problem. It is thus a single component problem. As implied by Packer the planning hori- zon of the problem could be considered either long-range or short-range. The emphasis as written is, however, short- range. The problem is sequential in that future decisions Of when to order and the amount to order are a function of previous decisions. The solution approach selected by Packer was that of adaptive forecasting and statistical determination Of safety stock. This is a technique suggested by Brownfn' These techniques consist of using the exponential smoothing method for estimating demand, and establishing the level Of safety stock based on the past success in estimating demand. A heuristic-simulation solution technique is used to seek runnerical solution to the two problems defined. Packer States that: . . considering the large number of items involved it appeared unrealistic to attempt to achieve an Optimal policy for any of the individual items. Packem4s decision to some extent was based on a statement bY Hannssmann: From the Operations research vieWpoint, the theory has been carried to a degree of mathematical SOphis- tication in some areas which is not fruitful in light of the fact that the inventory problem is only one aSpect of a complex system.63 In essence there is no unifying dimension in this model in terms of time or space. It is a single stage, 60 single location model and order cycle effects or delays are not considered. Stockouts are considered, but in terms of cost, not order cycle considerations. Packer states that his model is a static model. The model is dynamic, however, according to the definition in this thesis. The current deficiency (surpluses) of the inventory effect future decisions via information feedback—control loOps. The environmental inputs are established to implement the nmdel for short-range by assuming that cost parameters are constant. For longer range Packer develOps a set of curves relating cost parameters between items and over time. The model can therefore be classified as both short-range and long-range. Packer's model includes only the inventory component, thus it cannot be considered as the basis for the general Soltmdon approach to the LREPS mathematical model. However, it pmovided the basis for develOpment of the inventory com- Exnuent which is presented in the Operations Subsystem acti- Vities of Chapters IV and V. Ballou.--The second model, Ballou's dissertation, is a n“Jlti-component model with primary emphasis on the inven- tor)’ component.64 Ballou describes the problem as one of a nullti-stage inventory situation involving three firms. The (objective stated by Ballou is to test the effect of varj-<:>us inventory policies throughout a simulation period on Chost and profit levels. Transportation costs are also 61 altered to achieve sensitivity analysis. Decision rules are selected which yield the lowest total system cost under varying conditions. The problem as stated includes elements of the inven- tory, transportation, and communications components. It is a multi-stage inventory problem for a single, finished- goods inventory of several firms. The problem does not consider the location problem or distribution center Opera- tion. The planning horizon is primarily short term and the assmmption is that the facility network does not change. The problem is sequential in that current decisions in the model influence future decisions. For example, when demand is in excess of inventory level backorders are incurred. These backorders are eventually filled with reorders after a generated lead time. The general solution approach is simulation with ana- LYtical subroutines such as computation of the E00 incor- EMIrated as apprOpriate. The unifying dimension is time Witha measure of service, backorder level, being partially dependent on the expected lead time, itself is an element Ofthe total order cycle. The system behavior is dynamic inthe sense defined previously in this thesis. Information feedback-control lOOps are developed for such variables as jJuventory level. Finally, the environmental inputs such as; cost lead times, product price, etc. are modified via e)‘Eocjenous input to the model. 62 In summary, Ballou's inventory model does not consider all of the physical distribution components and thus cannot be used as a basis for the LREPS general solution approach. The model does, however, provide important insight rela- tive to the selection of the "best" inventory policy for stated assumptions and decision rules for managerial action. Mathematical Models Introduction Initially this section presents the definition and description of mathematical models, including the variables Of simulation models. This is followed by a review of literature concerning approaches suggested for model for- mulation. Qefinition and Description A mathematical model consists of four well defined elements: (1) components, (2) variables, (3) parameters, a1161(4) functional relationships?5 The primary components ill the LREPS model are related to the entities or objects ‘15 the three primary systems. A mathematical model can alfikD be defined as a set of equations whose solution ex- plains or predicts changes in the state of the system.66 Th'e‘variables are used to relate one component or entity to iinother and may be conveniently classified as exogenous, Status, and endogenous variables. 63 Exogenous variables are the independent or input vari- ables of the model and are assumed to have been pre- determined and given independently of the system being modeled. These variables may be regarded as acting upon the system but not being acted on by the system. Exo- genous variables can be classified as either controllable or non-controllable. Controllable (or instrumental) vari- ables are those variables or parameters that can be mani- pulated or controlled by the decision makers or policy makers of the system. Non-controllable variables are gener- ated by the environment of the system modeled and not by the system itself or its decision makers. Status variables or entities describe the state of the system or one of its components at any point in time. The attributes,or characteristics of the entity, may change in value through time. The set of attribute values at any leint in time define the "state of the system." Thus the Stattus variables are also referred to as state variables. Attributes are properties of entities and an entity is described by listing its attributes. 67 EndOgenous variables are the dependent or output ValTiables of the system and are generated from the inter- alction of the system's exogenous and status variables acc=<>rding to the system's Operating characteristics. The Sys"tem state, status, and endogenous variables can be used lnt1erchangeably to define variables whose value is gener- ated within the model. 64 The exogenous variables or parameters are classifed as "factors." A simulation experiment consists of a series Of computer runs in which tests are empirically made of the effects of alternative factor levels on the values of the endogenous levels. Parameters are considered to be those attribute values that do not change during simulation ex- periment(s). Functional relationships or transformations describe the interaction of the variables and components. The terms functional relationships, transformations, and algo- rithm are used interchangeably. Each refers to the mathe- matical function, logical Operation, or process Operation that relates predictively an activity's output to its input. An activity is a quantitative or logical relation of an input set of variables (or attributes) to an output set of variables (or attributes) by a mathematical function. Accomplishment of an activity usually results in a change of the system state. A general method of developing trans- formations is presented by Van Court Hare.68 approaches to Mathematical Modeling The general procedures for development of the LREPS mOdel were previously referred to in the Introduction, Figure 1.4. This chapter is concerned with the approach(es) suggested for the formulation of the mathematical model. Morris, in discussing the "art of modeling," states thatthe process of develOpment of a model by a management 65 69 The term scientist can best be described as intuitive. "intuitive" as used by Morris refers to ". . . thinking which the subject is unable or unwilling to verbalize." According to Morris, three basic hypotheses exist relative to model building. First, the process of model building can be viewed as a process Of "enrichment" or "elaboration." The model designer begins with a simple model and after obtaining a "tractable" model attempts to move in an evolutionary manner toward a more sophisticated model that more nearly reflects the complex management situation. "Analogy" or association with previously well devel- Oped logical structure is the second major requirement for develOpment of a successful model. Third and finally, the process of elaboration and enrichment involves several types of "looping" or "alter- ation" procedures. For example, as each version of the nmdel is tested a new version is develOped which leads in turn to subsequent tests. A second type of alteration is determining if a model version permits achievement of the designer's Objectives. If it does the designer may seek further enrichment or complication of assumptions. If, however, the model is not tractable (well-behaved) or can- not be solved the designer has to modify and/or simplify the assumptions. 66 Before a simulation model is designed, two important questions must be asked and answered: (1) What use will be made of the model (what questions will be asked)?; and (2) What are the requirements of accuracy and precision? An- swers to these questions determine the structure of a model. The model's structure, as stated by Kiviat is affected by such factors as: 1. The purpose of the model. 2. The accuracy and precision required of the output. 3 The detail required in the model to achieve the required precision. 4. The assumptions required at the system boundaries. 5. The assumptions required within the system boundaries for status representation decision parameters decision rules 70 6. The availability of necessary data. The model design is thus complicated by a combination of theoretical and practical factors. The theoretical factors determine such things as the system boundary interactions and decision rules, whereas the practical factors modify the theoretical decision, such as the level of detail in- corporated within the model. Kiviat states this as the reason for feedback lOOps in the modeling process itself. The model is thus an iterative process which must take into consideration the criteria of the model designer and the constraints of the environment. The final model reflects in both structure and implementation the influences of the real world system being studied, the questions that are of interest to the decision maker about the system, and the environment in which the model is to perform. 67 Modeling is therefore a continuous balancing of the costs of data collection and analysis against the costs (benefits) of precision, and program execution costs against the costs of model reprogramming. A five-stage iterative sequence describing the modeling process is pre- sented in Figure 2.7.71 Naylor states that: . . . the formulation of mathematical models consists of three steps: 1. Specification of components 2. Specification of variables and parameters 3. Specification of functional relationships72 He states further that although a complete knowledge of the system being modeled as well as proficiency in mathematics are necessary prerequisites for the formulation of a valid model, they are in no sense sufficient conditions. A successful mathematical model depends also on: 1. The eXperience of the model designer or analyst 2. Trial-and-error procedures 3. A considerable amount of luck. Naylor discusses a number of suggestions relative to the develOpment of mathematical models which can be sum- marized below. First, the question of how many variables to include in the model must be answered. Naylor indicates that the Selection of endOgenous or output variables is usually (Mytermined at the beginning of the study and thus do not Cause much difficulty. The choice of exogenous variables Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 68 ITERATIVE MODELING PROCESS Statement of a problem in general system terms. Definition of gross system boundaries. Statement of output(s) needed to solve the problem. Statement of (initial) assumptions. Definition of static and dynamic system Structure. Construction of minimal system model. Assessment of assumptions in light of Stage 1 goals. Determination of input data requirements and avail- ability. If input data required are not available, modify assumptions and model structure by returning to Stage 2. Determination of output possibilities. If output is insufficient, modify assumptions and model structure by returning to Stage 2. Prepare precise specifications for final model. Select a modeling and programming language. Reassess the implications of all assumptions for the future. Prepare a detailed plan for use of the model. . . . 1 Figure 2.7--A Five-Stage Iterative Modeling Process 1 P. J. Kiviat, Digital Computer Simulation Modeling (Rancepts (Santa Monica, California: The Rand Corporation, 19367). 69 is more difficult, since too few exogenous variables may lead to invalid models whereas too many may render computer simulation impractical due to the computer and programming requirements. The second major consideration is the complexity of the model. The number of variables in a model and its com- plexity are directly related to the programming time, com- putation time, and validity. A change in any one of these characteristics results in changes in all of the other characteristics. A third area of consideration is the computational efficiency of the model. In this model for example, the objective is to keep the total computer model processing time for a simulation run below a pre-determined elapsed time. This objective has a direct influence on the develOp— ment of the algorithms of the model. Computer programming time represents a fourth area of consideration. Thus the amount of SOphistication in the algorithms must be balanced against the increased pro- gramming efforts. The develOpment of requirements such that one of the existing simulation languages can be used must also be evaluated.73’74 The fifth area of interest is the validity of the HKXiel or the amount of realism incorporated in the model. 13KB model must adequately describe the real world system ariduse of the model should give reasonably good predic- tions of the behavior of the system for future time periods. 70 The final consideration that Naylor presents is the compatibility of the model with the type of experiments that are going to be conducted with the model. Thus the basic experimental design must be formalized prior to development of the mathematical model. At each level of model formulation Asimow recommends the use of an activity analysis approach similar to that illustrated in Figure 2.8 to specify the design problem. For each level the procedure suggested by Asimow would be as follows:75 1. 2. Derive the desired outputs of the system Determine the undesired outputs of the system Determine the inputs, which the system will transform into outputs Determine the constraints for input and output variables Consider the system constraints along with the design parameters Establish the appropriate measures of value for the output and input vari- ables and design parameters Use the appropriate relationships among the variable to develop the criteria for measuring the goodness of the proposed systems. A few of the potential difficulties encountered in Imathematical model building are also presented in the literature. 76’77 These can be summarized as follows: 71 Purposeful inputs Desired outputs ‘ DEVICE —-> OR Environmental ’Tléfl SYSTEM ~\\‘$ ‘Undesired outputs inputs Constraints Constraints Constraints on inputs on system on outputs Units of measure of inputs, outputs, and constraints (independent and dependent variables) and associated measures of value where needed Overall Objectives and the design criterion Figure 2.8--Format for Activity Analysis--General Planl lM. Asimow, Introduction to Design (Englewood Cliffs, NeMIJersey: PrentiCe-Hall, Inc., 1962i, p. 54. 72 1. Those variables which affect the behavior of the system but are in a practical sense impossible to quantify or measure 2. The number of required variables may exceed the capacity of the computer capabilities available 3. All of the exogenous variables that affect the output variables may not be known 4. Not all of the functional relation- ships between exogenous and endogenous variables may be known or possible to develop 5. In many cases the relationships between variables may be too complex to express in a set of mathematical equations. Summary The literature review suggests that a long-range planning model for total physical distribution operations should consist of the following attributes: l. A heuristic solution algorithm 2. Dynamic time varying interactions 3. Time as the unifying dimension 4. A procedure for changing environmental input factors. The review also indicates that such a model has not been developed or at least has not been reported in the literature. The models surveyed did consider various Conmdnations of the above attributes, but none of the HKKiels combined the two essential components, the location Tunablem and the selection of inventory policy into a dynamic 73 long-range planning model that uses total order cycle as the key measure of service. These models, however, did provide the basis for formulating the transformations for the activities of the LREPS mathematical model. The review related to model building procedures also provided background information that was essential for establishing the design procedures for formulating the LREPS model. The first step of the development of the LREPS mathetical model, the design approach, is presented in Chapter III. The steps of the design process and the LREPS mathematical model itself are presented in Chapters IV, V and VI. CHAPTER II--FOOTNOTE REFERENCES lBowersox, et al., Monograph. 2Steiner, pp. 22-24. 3Hadley, p. 159. 4Warren Hausman, ff., "Sequential Decision Problems: A Model to Exploit Existing Forecasters," Management Science, Vol. 16, No. 2 (October, 1969). p. B-93. 5J. L. Heskett, "A Missing Link in Physical Distri- bution System Design," Journal of Marketing (October, 1966), pp. 37-41. 6Naylor, p. 18. 7D. J. Bowersox, "Forces Influencing Finished Inventory Distribution," Readings in Business Logistics, edited by D. McConaughy for Amefican Marketing Associa- tion (Homewood, Illinois: Richard D. Irwin, Inc., 1969), p. 88. 8Naylor, p. 4. 9C. McMillan and R. F. Gonzalez, Systems Analysis: A Computer Approach to Decision Models (Homewood, Illinois: Richard D. Irwin, Inc., 1968), p. 25. 10J. W. Forrester, Industrial Dynamics (Cambridge, Massachusetts: The M.I.T. Press, Massachusetts Institute of Technology, 1961), pp. 13-19. 11M. A. Geisler and W. A. Steger, "The Combination of Alternative Research Techniques in Logistics Systems Analysis," Operations Management Selected Readings, edited by G. K. Groff and J. F. Muth (Homewood, Illinois: Richard C. Irwin, Inc., 1969), pp. 324-332. 12Ibid., p. 332. 13A. A. Kuehn, "Logistics of Physical Facilities in Distribution," Readings in Physical Distribution Manage- TEE: edited by D. J. Bowersox, B. J. LaLonde, E. w. Smykay (New York: The Macmillan Company, 1969). 74 75 l41bid., p. 263. 15Bowersox, Smykay, LaLonde, p. 326. l6Starr, p. 10. 17Heskett, p. 137. 18Ibid., p. 143. 19Ibid., p. 140. 20W. J. Baumol and P. Wolfe, "A Warehouse Location Problem," Operations Research, Vol. 6 (March-April, 1958), pp. 252-263. 21A. A. Kuehn and M. J. Hamburger, "A Heuristic Program for Locating Warehouses," Management Science, Vol. 9 (July, 1963), pp. 543-666. 22D. J. Bowersox, "An Analytical Approach to Warehouse Location," Handling & Shipping, Vol. 11 (February, 1962). 23Heskett, p. 140. 24Ibid., p. 143. 25R. A. Howard, "Dynamic Programming," Management Science, Vol. 12, No. 5 (January, 1966), p. 317. 26Ibid. 27 R. H. Ballou, "Dynamic Warehouse Locatibn Analysis," Journal of Marketing Research, Vol. V (August, 1968), pp. 271- 276. 281bid., p. 271. 291bid., p. 271. 0Forrester. 31Ibid., p. 14. 32R. E. Bellman and S. E. Dreyfus, Applied Dynamic Pro- rammin (Princeton, New Jersey: Princeton UniverSity Press, 1962). 33Hadley. 4 Bowersox. 35Bowersox, Smykay, and LaLonde, p. 29. 76 36P. Kotler and R. L. Schultz, "Marketing Simulations: Review and Prospects," The Journal of Business (The Graduate School of Business of the—UniVersity of Chicago: The Univer- sity of Chicago Press) Vol. 43, No. 3 (July, 1970), pp. 237-295. 37 Steiner, p. 21. 38Forrester, p. 7. 39J. F. Magee, "Quantitative Analysis of Physical Dis- tribution Systems," Readings in Business Logistics, edited by McConaughy for American Marketing Association (Homewood, Illinois: Richard D. Irwon, Inc., 1969). 40 Ibid., p. 76. 41R. H. Ballou, "Quantitative Methods--What They Are and How You can Use Them," Readings in Physical Distribution Management, edited by D. J. Bowersox, B. J. LaLonde, and E. W. Smykay (New York: The Macmillan Company, 1969), pp. 235-242. 42Magee, 3Bowersox, Smykay, and LaLonde. 44H. M. Wagner, Principles of Operations Research (Englewood Cliffs, N. J.: Prentice—Hall, Inc., 1969). 45Kuehn and Hamburger. 46Ibid. 47 H. N. Shycon and R. B. Maffaei, "Simulation-—Tool for Better Distribution," Readings in Physical Distribution Management, edited by D. J. Bowersox, B. J. LaLonde, and E. W. Smykay (New York: The Macmillan Company, 1969), pp. 243—260. 48Ibid., p. 244. 491bid., p. 249. 50Ballou, "Dynamic Warehouse . . ." SlIbid., p. 271. 521bid., p. 271. 53Bellman and Dreyfus. 54Ballou, "Dynamic Warehouse . . ." 5Forrester. 56Ibid., p. 22. 77 37Ibid., p. 23. 58Ibid., p. 23. 59J. W. Farrell, "Distribution Dynamics at Work: Carrier Air Conditioning Company," Traffic/Physical Distribution Mana- gement, Vol. 9, No. 6 (June, I970). 60A. H. Packer, "Simulation and Adaptive Forecasting as Applied to Inventory Control," Operations Research (July, 1967), p. 672. 61R. C. Brown, Statistical Forecasting for Inventory Control (New York: McGraw-Hill, 1959). ' 62Packer, p. 662. 63Hannssmann, "A Survey of Inventory Theory from the Operations Research VieWpoint," Progress in Operations Research (New York, 1961). 64R. H. Ballou, "Multi—Echelon Inventory Control for Interrelated and Vertically Integrated Firms" (unpublished dissertation, Univ. Microfilms, Inc., 1965). 65Naylor, et al., p. 10. 66McMillan and Gonzalez, p. 11. 67Ibid., p. 31. 68Van Court Hare, Jr., Systems Analysis: A Diagnostic Approach (New York: Harcourt, Brace & WOEld, Inc., 1967). 09W. T. Morris, "On the Art of Modeling," Management Science, Vol. 13, No. 12, p. B-707-7l7. 70P. J. Kiviat, Digital Computer Simulation Modeling Conce ts (Santa Monica, California: The Rand Corporation, , p. 18. 71 Ibid., p. 19-200 72Naylor, et al., p. 29. 73Bowersox, et a1, MonOgraph. 4Marien. 75M. Asimow, Introduction to Design (Englewood Cliffs, N. J.: Prentice—Hall, Inc., 1962). 6Forrester . 77Naylor, et a1. CHAPTER III APPROACH TO MATHEMATICAL MODEL DESIGN Introduction The conceptual model, required model capabilities, and general methodology for develOpment of the LREPS model were discussed in the Introduction, Chapter I. This chap- ter in successive sections reviews the design criteria, presents the general approach used in formulating the math- ematical model, and discusses several special design con- siderations. In the summary of this chapter, the method chosen for reporting the design evolution process for the LREPS math model is reviewed. Design Criteria The research problem of this thesis has previously been defined in terms of a set of independent variables as one of formulating the mathematical model to assist in making sequential decisions for total physical distribu- tion responsibility over a long-range planning horizon. The design criteria established to achieve this were de- fined in terms of four general categories, which were to: 1. Solve the Specific physical distribution problem statement 78 79 2. Meet the general research requirements 3. Remain within the established model Operating limits 4. Achieve the desired model capabilities. The problem statement required that the general solu- tion approach be heuristic. Simulation, the heuristic technique selected, is according to the literature essen- tially the only modeling technique practical for analysis and design of a problem as complex as a total physical dis- tribution system. Since the problem considered the total physical distribution system, it was also essentially re- quired that the unifying dimension be temporal rather than spatial. The fact that the problem included sequential or staged decisions suggested that the model be dynamic, in- corporating feedback control lOOps and recursive relation- ships. The requirement that the problem consider a long- range planning period made it important that a second ele- ment of dynamics, the ability to modify over time the en- vironmental factor inputs to the model over the planning horizon, be incorporated in the LREPS operating model. One of the general research design criteria was that the model must be of modular construction.1 Using a modu- lar or "building block" approach means that formulation begins with a single module of the system of interest, and by adding modules the total system can be developed as a total integrated system or in terms of its separate com- ponents. There are many benefits offered by the modular approach. 80 A modular approach is appealing from a pedagogical point of View. Designing a model upward from identifiable and observable process or analogies is also a logical pro- cedure with examples of success documented in the liter- ature. Finally, the modular approach provides the model designer with the possibility of considerable flexibility. Additional benefits of modular construction are also dis- cussed in the literature.2 An example of the modular construction in the LREPS model was the development of the inventory management module to Operate with a "heuristic" inventory module with reorder quantity, reorder point, and safety stock set by management or with a theoretical inventory module incorporating the standard reorder point policy, the Optional replenishment policy, and/or a hybrid combination of both the reorder point and optional replen- ishment policies. These two modules were interchanged in the LREPS model without reprogramming. A second general criteria, which is not independent Of modular construction, is the concept of universality. The concept of universality in the context of this thesis means that the model must be applicable, with little re— ALGORITHM LIST TRANSFORMATIONS An Arithmetic Logical sequence of operations LIST OUTPUT SPECIFICATIONS NOILHTOS Figure 3.1--Format for Activity Analysis in LREPS 85 the connecting links for combinations of activities which form the systems hierarchy. Special Design Considerations In formulating the mathematical model several addi- tional concepts not previously reviewed in this thesis were given consideration as they related to the objectives of the LREPS model. These three concepts were: (1) work flow structure, (2) model simplification methods, and (3) robustness or flexibility. Work Flow Structure Work flow structure is the first important special design consideration. Holstein and Berry define work flow structure as: . . . the pattern of aggregate work flow through the production system . . . and . . . the relation- ship Or pattern of functional processing sequences in the shOp.3 The work presented by these authors is specifically re- lated to job-shop and manufacturing systems, but the gen- eral concept, nonetheless, appears to be applicable to the problem of formulating the system structure of the problem Of this thesis, Figure 1.2. Essentially the authors de- velOp a method for identifying the relative activity levels or importance of the links between individual work centers or nodes of the network. The activity levels or work flow structure in a physical distribution network for example are partially dependent on the source of manufacture 86 for each product, product demand, inventory stocking policy, etc. Holstein and Berry suggest the use of the important or strong links in job ShOp simulations rather than assum— ing that all links are possible. The neglect of the "weak" links, in terms of frequency of and amount of work flow, did not have a major effect on the results of simulations relative to the results achieved by previous authors who had considered all possible links of the job shops. .The above concept, which might be stated in terms similar to the ABC rule frequently used in inventory con- trol--that 20 percent of the links account for over 80 percent of the activity, was used in the develOpment of the structure of the physical distribution network for this model, Figure 1.2. For example, in the problem de- fined in this thesis the assumption was made that the closest manufacturing center, the MCC, always supplies the product to a particular distribution center when more than one MCC manufactures the product. Thus the assumption was that the "weak" link, the small amount of volume or acti- vity from the remaining MCC'S for the product, would not have significant effect on the design alternatives. A second example where the above concept was incorporated was the situation where a remote distribution center has a "stock out" for a particular product. 87 Using the above "strong link" concept the assumption was made that even though shipments of the product from a "second" best distribution center would actually be made occasionally these shipments would not have a significant effect on the design alternatives. These "strong link" assumptions will be investigated via sensitivity analysis to determine if the concept was valid for this physical distribution simulation model. Model Simplification The second Special area for design consideration is "model simplification" methods. Simplification methods can be divided into two main categories: (1) first-order methods, which directly reduce complexity of the model, and (2) higher-order methods which simplify a system in- directly through a series of steps. Direct attempts at system simplification usually in- volve the actions of "elimination" and "grouping." Either of these actions decreases the distinctions that need to be made in a system definition. Van Court Hare states that: We simplify by elimination when the system Objective requires Optimization, isolation, and search of detailed action. We simplify by grouping, classi- fication, and consolidation of detail when the sys- tem Objective requires estimation, comparison, and test between blocks of detail. The approaches to elimination that were considerd in this project were similar to the following three general methods: 88 1. Restricted ranges of measure, of interest, 2. Logically or statistically restricted com- binations, or patterns of acceptance and 3. Threshold and discrimination methods.S Higher-order simplification is accomplished by work— ing with the system's control structure hierarchy--the system goals, objectives, values, and measures of effective- ness.6 The higher-order approach is concerned with the system's potential for improvement, growth, change, and optimization. It is a strategic approach. The higher- order approach stresses relevance rather than the complete— ness or precision as stressed in the direct simplification methods. In this model design the hierarchy was LREPS model, system, subsystems, components, and activities. A primary design problem related to higher-order simplification was thus to coordinate the subsystems into a model that would enhance the over-all purpose(s) of the total system. Van Court Hare states that: The most likely trouble-spot in the design of a complex system, or the operation of an existing complex system, is not that the individual blocks do not Operate"efficiently" or even effectively regarding their own stated goals, but that the goals guiding these Operations do not, when com- bined, result in either efficient or effective Operation of the entire system.7 Just as conflicting subsystem goals may restrict the achieve- ment of the full overall system objective, it is possible that there are conflicting multiple goals at the total sys- tem level. Consideration Of constraints, risks, and 89 commitments, are also important in the higher level defini- tion. Modification of these makes possible higher-order simplification. Morris also discusses Simplification of models.8 He states that if a model in its current version is "tractable" (well behaved) it can be enriched or SOphisticated, other- wise it may have to be simplified by making variables into constants, eliminating variables, using linear rela- tions, adding stronger assumptions and restrictions, and/or suppressing randomness. Enrichment involves just the oppo- site type of modification. Robustness-Flexibilipy The third area of special consideration previously not discussed is "robustness." This term is defined by Morris to mean: How sensitive is the model to changes in the assumptions which characterize it?9 Robustness also is defined as the measure of flexibility in a planned sequence of investment decisions by Gupta and Rosenhead.lo The measure of robustness of a decision in the investment case is stated in terms of the numbers of "good" end-states for expected external conditions which remain as Open Options. An example of robustness reported by Gupta and Rosenhead is given for facility location in which the robustness-score is the ratio of the number of occurrences Of a given potential location, among the set of good systems, to the number of good systems. 90 This was a useful concept for the LREPS model. One key problem in selecting the "best" set of staged decisions from among many good sets was the uncertainty of the envi- ronmental assumptions or inputs over time. An approach such as robustness aids in reducing the risk associated with decisions under uncertainty. For example, the loca- tion that appears most frequently in the final set of "good" systems facility network alternatives for various environ- mental and management inputs should be a lower risk (more flexible) decision than selecting a location that appears only in a few cases. Summary This chapter presented the basic design approach used in formulating the LREPS mathematical model. Before pro- ceeding to the next three chapters, two points should be made concerning the method selected for reporting the model. The first point concerns the method of reporting the itera- tive design process which occurred during the actual devel- Opment of the mathematical model. Two extremes were possible for reporting this process. One extreme would be to present the model in its final form with specifications for output, input, and the transforma- tions without reporting the alternatives and design efforts that were judged unacceptable for the final model. The second extreme would be to emphasize the iterative process by reporting all of the alternatives considered, including those rejected for the initial version of the LREPS model. 91 For this point a compromise position was taken. In the chapters that present the model the iterative process of design evolution is discussed for those activities and combinations Of activities that are most critical to the model, appear to be of more general interest, and/or rep— resent a possible contribution to the state of the art. For most activities, however, only the final selected alternative(s) are reported. The second point is related to the order Of presenta- tion of the mathematical model. The activities could be reported generally either in the order in which the design process occurred or in the sequence of Operation of the model. In the former case, the order of presentation at each level of the systems hierarchy would be outputs, in— puts, and transformations. Thus, the order of presentation at the systems level would be Report Generator System, Supporting Data System, and Operating System. In the latter case, reporting by sequence of Operation, the order would be inputs, transformations, and outputs. The author made the decision to report the higher level sys- tems, subsystems, etc., in the general order of model Opera- tion. Therefore, the order of presentation for the systems is Supporting Data System (Input), Operating System (Trans- formations), and Report Generator System (Output). CHAPTER I I I - -FOOTNOTE REFERENCE S 1T. H. Naylor, et al., Computer Simulation Techniques (New York: John Wiley & Sons, 1966). 2J. W. Forrester, Industrial Dynamics (Cambridge, Mass.: The M.I.T. Press, Massachusetts Institute of Tech- nology, 1961). 3Holstein & Berry, "Work Flow Structure; An Analysis For Planning and Control," Management Science, XVI (February, 1970), 324-337. 4Van Court Hare, Jr., §ystems Analysis: A Diagnostic A roach (New York: Harcourt, Brace & World, Inc., 1967), p. I57. SIbid., p. 160. 6Ibid., p. 200. 71bid., p. 210. 8W. T. Morris, "On the Art of Modeling," Management Science, XIII (August, 1967), 715. 9 Ibid., p. 716. 108. K. Gupta, and J. Rosenhead, "Robustness in Sequen- tial Investment Decisions," Management Science, XV (October, 1968), 18-29. 92 CHAPTER IV SUPPORTING DATA SYSTEM Introduction The Supporting Data System is the first stage of the three stage LREPS model. The primary functions of this system are to generate the supporting data analyses and the data input required for the Operating System. The supporting data analyses and data input are presented via a subset of activities for each of the operating subsystems of the model. Each activity analysis is defined in terms of the desired outputs, input requirements, and selected mathematical transformations. The major sections of this chapter and order of presentation within the chapter are: l. The Demand and Environment Subsystem 2. The Operations Subsystem 3. The Measurement Subsystem 4. The Monitor and Control Subsystem An important point to keep in mind is that the model was designed to be universal for any firm that fits the description of Figures 1.1, 1.2, and 1.3. The supporting data analyses become very critical in applying the model 93 94 since it is via the supporting analyses that the input data and decision rules are prepared for the application of LREPS to different situations. The subset of activities for each subsystem con- sisted of analyses and preparation of data that remain constant throughout the planning horizon and the intro- duction of exogenous change in the experimental factors. In addition, special subsets of activities were required for the Demand and Environment Subsystem to develop the demand input. In the first section of this chapter the outputs, inputs, and system transformations for each of the data support activities of the Demand and Environment Subsystem are developed in detail. Demand and Environment The Supporting Data System--Demand and Environment provided analysis of company data and environmental or external data. The output of the subset of support activities for the Demand and Environment Subsystem con- sisted of two major streams of data; the Order File (or demand) Generator and the input data for the Demand and Environment Subsystem. The subset of activities used to develOp the desired outputs are presented in the Demand and Environment section in the following order: 1. Invoice Analysis 2. Customer Type Analysis 3. Product Item Analysis 4. Regional Analysis 95 5. Customer Demand Generation 6. Basis for Demand Generation and Processing 7. Demand Unit Analysis 8. Order File Generator 9. Demand Allocation to Customers 10. Customer Sales Quota Invoice Analysis An analysis of the invoice file of the research sub- ject firm being modeled was performed to study the rela- tionship between the category or independent variables such as distribution center, class of customer, month of year, etc. versus dependent variables such as dollar per order, weight per order, sales per pound per order, invoice lines per order, cubic feet per order, and cases per order. Figure 4.1 presents the activity analysis diagram in terms of the outputs, inputs, and the transformations used to perform the Invoice Analysis. A flowchart of the Invoice Analysis is illustrated in Figure 4.2. This analysis in some cases could be performed on the total invoice file, but for most firms that would utilize this model, the large number of invoices per year, for example over a hundred thousand, would make it imprac- tical to perform analysis of all invoices for one year. Therefore, a sampling procedure was used to select the invoices to be analyzed. 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W mumsam ozu ."mm cosm ucosowmcme an own no mammamcm ouwo>c« Eouu mouumwumum novuo ovsmmm .ouo .unwaos .mumaaov .mocwa .mommo «mm Loam uovuo non Hanuov uoaboua poxumuH “nu-zonedmttn~.¢ anemia MAHh «memo OGDmmm >muw>auooo humeesm uO smug mafia mm muonvoun vouooHom Oumuocmo .m umpuo ovaoma new muoapoua poxomuu Oumuocoo uoouo ovsoma COL mocwa uo popes: ocHELOuoo Q N H monHcu OHQEMO co ounmoanm uOSpoua poxompu some mafia mo nopssz umwa nonpoua voxomue . uoavoun (’1‘? poxomuu sumo u0w muwumwumum novuo .N meuop uoavoum .H mesmzH LJI-‘thLJE— O 7 mHm>q aeovcoaoveu on» Suvaoum .u.Om~ vuuuodo- era 0» n.0mn mcacuanL oz“ Oueuoaoaaw< .nu«:3 ucqaov ~q3v~>accu an caucus no an. easy umN ecu gouaum .luuu on» Inna won: on o. ..omu a-ca. do “.3a «gs Suasom “cacao ascoquuam an up Iuev o» vouuopeou ovou nun so none nuvoo gas on. nauseousmuo co wanna noueoo «accuuoom man an eu-v cuquocau .ch .uonoa acumen .noqnn aucuOu .aouuaaaaon .o.« movou na~ up oo«»uluo.c« o~aq«u¢> ucoeeoeovc— .OAAU melon-So ha ova-n one node. uquOU .0.“ "luau Ibuu sauna-neucu :c_.euc_—< noose: .o~na«-> “concuaovea evacuaun zone new you» snacku cucuua0unam ask .oOOOSn no unseen uo\veo museum can any.» cuzouw oma~0>1 vuucmaaz wean: vauuuaa. moan-«ua> unoccuawpc. :Uuuuuaoxm 0;» ac soon we couuuoaoun one caauno £322 .83 -uuaum omu .uuo> anon on» new umN coco ecu coau-ILOucu can-«un> ucovcoauvcu ash .ooo~ no.» on. new acauqasaon «gaudy-o "sausage new .¢.um~ any .u.:a ecu so neaneuuu> unencuaoveu vauuoiua on» you cuov no.» one» ecu «unease .«ovOl ecu no. vauOOLOa uo~nc«~o> acoueoaovcu on» no on." < E .OOAIn Beau “undone .uuo .aeaqu «any.» .uuaca ¢6H undocuaovea EFF uo nunsducu coda-aouLOO anoepem .euuu oz» scum Quin nuns. anaec< .co«uq:~e>o ecu oo~nu«~¢> uauvcunovca no and; at:u_c co—u-oo«~< veqaeo \\. OLZu // maz~ umN V .:- ecuauo: unacccma ecu sea :a soda wen ecqsov no. gonna .v n.um~ vauoo~oa no u-«A .n .10» cans as“ you own guns ~me uconeeaeocu .u I ...III «UVOI uzu new vauuofioe nouzeuua> ucuvcoaov:« «0 «cu; .— \\ omz~ _H=u ¢<> wk: 51 \aazwnmmmlww u.om~ Ouauulo~u¢< .0 tom: 0; cu n.0mN uo uuu~ ecu “oeuom n Loueuocou nuev oms nosuuacou .c rm xmozH ogre_ue> ucoeeoaovca coco nuanoum .n Fum’xn Hm8 IUVr—u COED UMQQOHL .N *1 m~m>4 uo manhuncu ccuu-aouuou .~ LPLM \lIlHI>iJ/E ?\\ QMHUwqmm V ovOO man up vascunn> uCOfiCOQUVCu £060 new case .n seam Beau «new guano unacc< .N au~nauuq> aceteeaovcu aqua .u thLZu macs aaza / m>se maza "cu-suen< suu>uuo+-::> 137 Using forecasts made by the Bureau of Census and supplied by the firm, growth rates for each independent variable were develOped according to various geographical break- downs. Three regional approaches were considered to develop the average compound growth rates: 1. The firm's existing service areas 2. Grouping of Zip Sectional Centers 3. Individual or groups Of states. A comparison of the state growth rates with the rates of growth for the firm's service areas indicated that the service areas encompassed states of widely vary- ing compound growth rates. Such service area classifica- tion would result in a distortion of the independent variable over a ten year planning horizon. Similarly, the zip groupings combined states of widely varying rates of growth. The approach chosen was that of grouping states with similar rates of independent variable growth rate. Four groupings of states were selected and a weighted average growth rate was computed for each grouping. The selection of Zip Sectional Center as the demand unit structure presented the problem of developing the projections by demand unit of the independent variables over the 10 year planning horizon. Growth rate informa- tion was not available by Zip Sectional Center at this time. Therefore, growth rates develOped based on the states were applied to Zip Sectional Centers within the geographical limits of the states. As additional census 138 data is collected the growth rates can be developed dir- ectly by Zip Code. The data does exist now by Zip Code from commercial sources, but the cost to purchase each year of data by Zip Code was prohibitive for this project. The appropriate growth rate was then applied to the base level (1969) of each independent variable to develop the estimated projection for each demand unit for each future year of the planning horizon. The equation for calculating the future values of the independent variables is of the form: X(IDU,O) * (1+R(IDU) )Y'l X(IDU,Y) = where: X(IDU,Y) = The independent variable level for the Yth year for demand unit, IDU Y = Year of the planning horizon (1, ...., 10) X(IDU,O) = The base value (1969) for the demand unit that was read in R(IDU) = The rate of change for the demand unit, IDC. The projection of the independent variables used in conjunction with the list of ZSC's, the data by Zip Code from the firm, and the independent variable infor- mation by Zip Code provided the necessary input to develop the total ZSC data file. An activity titled the ZSC Data Generator accomplished this by merging and accumulating the Zip Code area data into the ZSC areas. 139 The ZSC Data Generator merged the following inputs: 1. Total firm sales and sales by each customer type 2. A data deck containing Zip Sectional Center number (or range of numbers), Zip Code agglomeration, Zip Code inde- pendent variable information, identifi- cation Of domestic or non-domestic Zip Codes, number of customers in the Zip Code area, and the number of competitors in the Zip Code area 3. A deck containing Zip Sectional Center number, the firm's annual sales in dollars and pounds by Zip Code. The analysis included a merge run in which the data by Zip Code was accumulated into all Zip Sectional Centers. The percent dollar sales for each ZSC and the percent for each customer type was calculated relative to the total firm sales. This analysis produced the data file for each Zip Sectional Center. There were certain problems associated with using the ZSC's in the large metrOpOlitan areas such as; Chicago, New York, Los Angeles. For example, ZSC 600-606 inclusive comprises the Chicago 3-digit Zip Code Sec- tional Center area. The southern half is not meaningful because post Offices in each half are assigned codes in alphabetical order, so that there is no geographic line dividing the two groups of offices. There are also difficulties in gathering accurate marketing data for Evanston (602), Oak Park (603), and Chicago prOper (606) since the areas served by these post Offices do not necessarily corres- pond with the limits of these cities. 140 Hence, most users of zip marketing data will find it more convenient to consider the entire Chicago area (600- 606) as a unit, and treat other major metrOpOlitan areas similarly. An agglomeration of the 561 ZSC's was then necessary to merge the ZSC's in major metropolitan areas into one ZSC. The basis of the agglomeration was taken from Rand McNally ratings on ZSC's in terms of how well they actually represent true trading areas.2 The codes used allowed the 560 sectional areas to be reduced to just under 400 agglomerated Zip Sectional Center demand units. The ZSC data, the selected independent variable growth rates and the basis for selection of the desired number and list of ZSC's provided the information neces- sary to select the ZSC's, agglomerate other ZSC's to the selected ZSC list, and project the independent variables for the agglomerated ZSC's. The output of this analysis provided the basis to develop the relative demand for each demand unit for each year of the total planning horizon. Relative Demand to DC.--The relative demand to the distribution centers was determined using a weighted index. This weighted index based on the independent variables was determined as follows: * 100 WTDINDX(Y,IDU) m m 2 X r (I) 2 X(Y,I,IDU) IDU IDU = g .EEl£L__ * X(YIIIIDU) I 141 where: Percent of total sales for period, ITP allocated to DU,IDU WTDINDX(Y,IDU) r2(I) = Correlation analysis coefficient of independent variable, I against sales for the year X(I,IDU,Y) = Value of independent variable, I for demand unit, IDU for time period, Y I = Independent variable identifica- tion number IDU = Identification number of the DU Y = Time period in years. The demand allocated to a demand unit was thus a function of the level of the Ith independent variable within the demand unit and the correlation coefficient of the Ith variable against sales. The relative demand to a DC was determined by summing the weighted indices for all DU's assigned to the in-solution DC. Customer Sales Quota The purpose of domestic forecast analysis was to develop the daily forecast basis which was used in the D&E to generate daily sales quota for each distribution center. The Options considered in developing forecast data for the model included: 1. Developing a forecast method for the firm such as exponential smoothing 2. Using the existing forecasting model already in existence in the firm incorporating it in the simulation model 3. Using output of the firms existing forecast model to establish the annual forecast exogenous to the LREPS model. 142 The decision was made to use the research subject firm's existing forecasting model. The reason was that most large firms, already have an existing sophisticated computer forecasting model and/or "grass roots" forecast- ing model where salesmen forecast for each territory then summarize and modify at region, district, domestic, etc. Therefore, the model was designed to accept, exogenously, the total annual forecasts in dollars for each of the years Of the planning horizon. The M&C Subsystem presents a method of modifying this forecast to indicate the effect of high service (or low service) by increasing (decreasing) the forecast. This analysis developed the daily forecast factor used in conjunction with the Weighted Indices to estab- lish the daily sales level for each in-solution DC. Figure 4.18 presents the activity analysis in terms of the outputs, inputs, and transformations required for development of the sales quota. Figure 4.19 presents the sequence of development in flowchart format. The firms daily sales history is analyzed to deter- mine the variability Of sales for the days of the week. This is accomplished in the Analysis of Daily Sales/Week Activity. A Monthly Sales Analysis is also conducted using the sampled invoices to determine the variability of sales by month. Option 1 for this activity involved the assumption that the variability within the days of the week and by month is not critical for a long range 143 cacao moaum uoEOumzo manna unmoouom magma mammm ammoouom AHHmo ao~o>oo woaumwumum moamm aafima coauma>op pumpcwum paw oweuo>m .xooz «0 saw Sp mwamm O>wumaou uo comHHMOEOU >u0umwz monm mawmo moaumfiumum moamm >Hsucoz modumaumum monm mafimp can manocoa onu wumuocow mammamc< oowo>cH toanamm Boom OHHL ooao>cw m.Eun Scum mooao>cw pOHaEmm munch ammo now mummoouOu Hmscc< "unecononIIoH.q ouswum x3xmmqAHuAzH ZONHmom Uszzfiuoqoo .m mmqHmcm monm >Hnucoz .H moneu0umws monw macucoe a Adamo .m H madame» mwmxamcm oowo>cw poadamm .N co~«»on < wcficcde uo>o mummoouOm Hmocc< .H w a mFszH 144 planning model such as LREPS. For the firm used in this project the variability was low and therefore the assump- tions presented no problem. Option 2, for the sales quota which would not require any major revisions would include an activity to generate a day of the week factor and monthly variability factor to correct for seasonal and weekly buying pattern variability. The daily factor is used in conjunction with the Weighted Index in the D&E to determine the daily sales by DC. Summary The completion of the above activities was required to provide the supporting data analysis and to prepare the data for the Operating System--Demand and Environment Subsystem. The next major section of the Supporting Data System presents the Operations Subsystem analysis and data preparation activities. Operations The Supporting Data System-Operations provided the analysis and data preparation for the basic components of the physical distribution system, which as previously stated, are transportation, unitization, communications, inventory, and location. In addition Special supporting analyses were required for the manufacturing control cen- ter to distribution center (MCC-DC). 145 Tranpportation Component For the inbound and outbound transportation components in the Supporting Data System--Operations the following analyses were required: 1. Development of transit times 2. Establishment of shipping policies 3. Development of shipment statistics 4. Development weight break Transit Times.--The development of transit times for the outbound and inbound transportation links required con- sideration of the modes of transportation, and reliability or consistence of the transportation. The location and num- ber of demand units relative to the distribution center was considered for outbound transit times and the relative loca- tion of manufacturing control centers for inbound. Figure 4.20 illustrates the activity analysis in terms of the out- puts, inputs, and transformations required for the transpor- tation activities. Figure 4.21 presents the flowchart for the transportation component analysis. The shipment modes considered for each DC-DU link of the outbound transportation network were primarily truck and rail. In some cases air freight was also evaluated for the universality aspect of the model. Preliminary analysis indicated that truck should be the normal mode for outbound tranSportation, whereas rail should be the normal mode for inbound shipments. 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O '4qu monHuoucw mean on .c AOSOAOAwmo mo mao>oa now must wcwumuoao .m co«umumnoud paw wcwmmOOOCS povuo new mums wcwumpono .N mucoeoufisvmu oomam on .H mksmzH LPCL; O mHqur this component is presented in Figure 4.28. Communications Network.--This component analysis cOnsidered the universal aspects of communications in ‘tkiat decentralized, regional, and centralized networks Can be simulated. A decentralized communications network is where OITders are transmitted to remote distribution centers frtnm the customer demand units with replenishment orders oriiginating at the decision of the remote distribution center. Regional network referred to a communications network where customer orders are transmitted to re’gional distribution centers (order processing centers) StuChas the primary distribution centers. 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Development of product categories to group individual products 3. Use of all individual products 4. Development of list Of tracked products. Analysis indicated that to test the effect of different policies it would be necessary to track a representative number of individual products. The work by Packer indi- cated that the use of a statistical sample of products would enable testing of various inventory policies representative to the total product line.3 The procedure for selection of the tracked products was presented in the Product Item Analysis of the supporting analysis for the Demand and Environment Subsystem. The selection of the inventory policies for the LREPS model is discussed as part of the supporting analysis of the Monitor and Control Subsystem. Backorder Procedures.--Two basic approaches were considered for handling backorders. The first approach required generation of a new order with each backorder for the unfilled amount of each tracked product. The procedure required the generation of the backorder, holding the backorder until the replenishment shipment Of all the tracked products arrived at the distribution center. The backorder then would be resubmitted into the order stream and processed. This appeared to be inefficient to implement because of the additional pro- gram complexity, core storage, and additional process- ing required. The second method completely filled each 170 customer order allowing the inventory to go negative (or more negative). This negative inventory was relieved with receipt of the replenishment orders for each of the individual tracked products. The order processing and preparation time, CT2, is not increased as a result of stockouts using this approach. However, an average delay due to stockouts (backorders) of tracked products CT3 is calculated as part of the total customer order cycle. As previously stated, the Order Cycle Analysis is pre- sented in the Supporting Data System-Measurement. Reorder Lead Time.--The reorder lead time analysis developed the replenishment order cycle in terms Of the reorder transmittal time from DC-RC, RTl’ the reorder processing and preparation time at the RC, RTZ' and the shipment dispatch policy delay time at the RC, RT and 3. the transit time from RC-DC, RT4. The procedure for develOpment of the values for each of these order cycle time elements is presented in the Order Cycle Analysis. Initial Inventories.--The initial inventory for each tracked product was established by stocking each distribution center based on six weeks of average demand. Location Component The analyses performed for the location component within the Supporting Data System--Operations included the calculation of the initial sizes for each existing facility in terms of the five size intervals established and designa- tion of the initial DC location. 171 Summary The completion of the above activities was required to provide the supporting data analyses and to prepare the data for the Operating System--Operations Subsystem. The next major section of the Supporting Data System presents the Measurement Subsystem analysis and data preparation activities. Measurement The Data Supporting System-Measurement provided the analysis and data preparation for the target variables of service and cost. Chapter VI, Report Generator System cdiscusses the target variable flexibility. In addition a special supporting analysis was required for calculating tine distance between point-to—point locations. Measures of Service Preliminary analyses indicated that the following “measures of service to customers and distribution centers VKDuld provide a sufficient range of measurement criteria: 1. Customer Service a. Normal customer order cycle, NOCT b. Total customer order cycle, OCT c. Outbound transit time, CT4 d. Percent of sales volume for various order cycle times 2. Distribution Center Service a. Reorder cycle time, ROCT b. Stockout delays c. Percentage of case units backordered 172 Figure 4.31 presents the activity analyses diagram in terms of the outputs, inputs, and transformations for the development of the measures of service. The flowchart for the service analyses are illustrated in Figure 4.32. Customer Service.--The customer service analyses provided the approach used to calculate the average and variance values for elements of the normal and total customer order cycles. The main elements of the normal customer order cycle (NOCT) as defined included: 1. Customer order transmittal time 2. Customer order processing and prepara- tion time (DC), CT2 3. Outbound transit time (DC-DU), CT4 As previously discussed the order transmission time, CTl is composed of time from dispatch of the order from the customer demand unit to the arrival at the processing distribution center. The order processing and preparation time, CT2 consisted of the time for processing of written orders and the materials handling required to prepare the physical order for shipment. The CT4 element represented the transportation time for the DC-DU link. The NOCT thus does not include any delay due to stockouts at the DC. The procedure for developing a penalty order delay time due to stockouts is presented later in this section. 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The product of the sum of the weighted indices :ftoz: the quarter times the domestic sales forecast estab- lished the sales forecast for the DC for the day. The daily sales forecast for the DC was next adjusted by the Sales Modification Factor, SMF, to obtain the simulated actual sales or sales quota. The SMF, previously defined in the Supporting Data System-- Demand and Environment, is an exponentially smoothed .r21tzio of actual to desired service level calculated at the end of each quarter. The SMF factors were generated fOr each DC and region via a feedback-control loop within tI-lle Monitor and Control Subsystem. The transformations ‘iéi‘veeloped for calculating the simulated actual sales or Salles quota by DC were of the form: DCSALS(ID) = DSQ(ID) * WI(IQ) * NWSMF(IQ) Whes—re: The simulated actual daily sales dollars for the DC for the day, (ID) DCSALS(ID,IDC) DSQ(ID) = The daily sales quota (forecast) for day, (ID) WI(IQ) ' = The sum of the weighted indices for all DUs assigned to the DC for quarter, IQ NWSMF(IQ) = The current exponentially smoothed value of the ratio of actual to desired service. 232 Iflnea daily domestic sales quota or forecast was thus used tx: calculate the actual simulated sales for each DC 1J1-solution on the particular day. Select Order Group.--An order group containing the sets of customer order blocks was then read in to provide tile: total basis for demand generation for the DC for the current clock day. As stated in Chapter IV, Supporting Data System--Demand and Environment, the total number of equivalent orders within the order blocks of the order group was established to provide the larger size DC's Wi th the average number of orders normally processed per (i£1§g. Process Customer Type.--The next major step involved Processing of sales and orders by the customer types Se:Lected via the customer type analysis. The percentage Sales allocated to the customer types for the region being p1‘<>cessed was used to calculate the simulated sales allo«- cated to each customer type for the DC. The transforma- tion for this calculation was: CSTSAL(ICT,IDC,ID) = DCSALS(ID,ICT) * CSPLTP(ICT) VV11€EIK3: Customer type ICT simulated sales dollar allocation for day, ID, for DC (IDC) CSTSAL(IDC,ID) Simulated actual daily sales dollars for the DC(IDC) for day, ID DCSALS(ID,ICT) CSPLTP(ICT,IR)= Regional, IR customer, ICT dollar split percentage. 233 A random variate generator was then used to select an order block from the appropriate customer's order block file. The sales accumulated for the DC being processed was then compared against the sales quota or allocation of the DC for the current day to calculate the value of an (order block modifier, OBM. The OBM, the percentage of the <3ustomer order block being processed, was required to ggenerate the simulated sales allocated to the DC for the (flay; The transformation was of the form: OBM(ICT,IDC,ID) = (CSTSAL(ICT,IDC,ID) - CSTDAC(ICT,IDC,ID))/ORDBLK(ICT) VVIuere: OBM(ICT,IDC,ID) Order block modifier (OBM) for the customer types, ICT; DC,IDC and day, ID CSTSAL(ICT,IDC,ID) Customer type, ICT sales dollar allocation for DC, IDC for day, ID Accumulated customer type, ICT sales dollars for DC, IDC for day, ID CSTSAC(ICT,IDC,ID) ORDBLK(ICT) = Sales dollars for customer type, ICT order block ready to be processed. Process Orders at DU.--The next major step initiated the processing of the N equivalent individual orders of ‘the customer order block at the DC-DU level. In the .initial version of LREPS each order block contained ten (Drders (N=10) for each of the three customer types. A Irandom variate generator selected a DU from among the DU's 'assigned currently to the in-solution DC being processed. 234 The basis for the Monte Carlo procedure was the DU's weighted indices for sales allocation. The probability distribution for selection of the DU's within a DC ser- vice area was developed as shown below assuming hypo- thetically that only five DU's were currently assigned to the DC: For Each DC-IDC Number DU: ZSC WI No. Code WI ZWI Prob. Cust. Types 1 110 0.001 0.001 10% 1,2 2 101 0.003 0.004 30% 1,3 3 112 0.001 0.005 10% 1,2 4 100 0.004 0.009 40% 1,2,3 5 108 0.001 0.100 10% 1 Each DU selected was then checked to determine if ‘tlne DU contained the Special customer type being pro- Cxessed. If for example the customer type being processed VIhas Type Number 2 and the initial DU selected was DU Num- ber 2 the DU would be unacceptable since it does not Ckontain the type of customer being processed. In this (Base another DU was selected until any one of DU's Number 1., 3, or 4 was selected. Once the appropriate DU was fiselected the individual order was processed for the DC-DU link. At this point in the operating sequence the Opera- ‘tions Subsystem Activity-Individual Order (INDORD) pro- <2essed the orders allocated to the DU by accumulating the <3ollars and weight at the DU level. This routine is 235 presented in more detail in the Operations Subsystem. The above sequence was repeated until N orders of the order block had been processed. The Operations Subsystem Rou- tine-Order Summary next developed the product detail and all the summarized sales information at the DC-level. This routine is presented in the next section of the Operating System. The decision block next checked the amount of accumulated dollar sales for the customer type being (processed against the allocated sales. An additional order block for the customer type was randomly selected unless the accumulated sales dollars were less than or equal to one half percent (0.5%) below the allocated sales. When the allocated sales were achieved a new «order group was selected to process the next DC for the current day. End-of-Day.--The final Operations Subsystem Routine, ZEnd-of-Day performed the end of day activities such as .inventory update for the orders processed during the «day. The Operations Subsystem presents this routine in lmore detail. Once all of the DC's have been processed for the day the control of the LREPS model was returned ‘to the Monitor and Control Subsystem for scheduling and ;processing of the next event. Summary The Daily Sales Quota and Sales Processing events Presented in this section develop the input necessary 236 for the Operations Subsystem. The Operations Subsystem, the next section of this chapter, presents the events, routines, and activities developed to simulate the opera- tion of the physical distribution system structured for the LREPS model. Operations Subsystem The Operations Subsystem deals with the flow of products and information through the physical distribution system. The orders allocated by the Demand and Environ- ‘ment Subsystem must be processed at the remote distribu- tion centers. Thus, for each remote facility in the physical distribution network, orders will arrive each day from the customer demand units. The batch of orders from each demand unit is then assigned a communications delay referred to as the customer order transmittal time. This time delay is the first element of the total order cycle, CTl. The order transmittal times are selected from a discrete probability distribution based on the expected variation around the average time delay. The orders are then processed to determine if sufficient inventory for each of the tracked products in the orders is available. If sufficient product units are in stock the order is prepared and a shipment dis- patched to the demand unit. The order processing and preparation are assigned a combined time delay which is also based on a discrete probability distribution, CT2. 237 The transit time from shipment dispatch until ship- ment arrival at the demand unit is based on the reliability of achieving the average service time stated for the dis- tance from the distribution center to demand unit, CT4. A discrete probability distribution formed the basis for developing the reliability function. If the inventory for a particular product is insuf- ficient, back orders are created. As inventory reorder points or periods are triggered, replenishment orders are dispatched to the firm's replenishment centers. The ship- ment (replenishment) is then scheduled to arrive at the distribution center after a time delay due to order trans- mittal to, order processing and preparation at, shipping schedules at, and transit time from, the replenishment center. The information from these time delays deter- mines the replenishment reorder cycle statistics which are used to generate the mean and standard deviation of reorder cycle time. The average customer order cycle time is thus a function of the customer order transmittal time, the customer order processing and preparation time, the average stockout delay time, and the customer transit time. The inventory policies tested in the model for the tracked products include a daily reorder point system, an Optional replenishment system and a hybrid combina- tion of the reorder point and replenishment systems. The information for the tracked products is extrapolated to the total line of products of the firm. 238 The effect of information flow for various communi- cations networks can be tested using different values of, and functions for, the various order transmittal and order processing time delays in the Operations Subsystem. The Operations Subsystem performed the above func- tions via a series of fixed and variable events. The fixed time activities included the following four areas: 1. The processing of individual orders which included the allocation of and accounting for sales information at the demand unit plus the generation of and accounting for customer service statistics at the distri- bution center level (INDIVIDUAL ORDER) The processing of the tracked product-multi order summarys, the order block's, both sales and product detail information at the distribution center level (ORDSUM) The distribution center End-of-Day Activities by which the distribution center's tracked product inventory levels are checked with the appropriate inventory management policy vari- ables to determine if reorder for product replenishment should be dispatched from the distribution center to the supplying manufac- turing control centers (DC-EODAY) The End-of—Day Activities at the distribution center to determine if any shipments are ready to be diSpatched to the distribution cen- ter from the supplying manufacturing control center's (DC-EODAY). The variable time events, which do not occur every basic time unit, in this model the day, for the DC-MCC links were grouped under two major categories: 1. 2. The arrival of a multiple-product reorder at a MCC which was placed by a DC, (MCORAR) The arrival of a replenishment shipment at a DC for a supplying MCC, (DCSHPAR). 239 Fixed Event-Individual Order The processing of the Individual Order Routine called by the Daily Event previously discussed in the Demand and Environment Subsystem, allocated the sales information to the demand units and generated the customer service statis- tics at the distribution center. Figure 5.6 presents the activity analysis in terms of the outputs, inputs, and transformations for the Individual Order Routine. The flowchart for this routine is presented in Figure 5.7. Order Cycle Time CTl.--The first activity of the Individual Order Routine generated the CT1, customer order transmittal time for the DC-DU link. The generation of CTl both constant and variable times as previously pre- sented in the Supporting Data System--Measurement were develOped using sets of concentric rings for the constant and Monte Carlo selection procedures with values of 0, l, or 2 for the variable element. The next step depended on the type of distribution center being processed. If the DC was a full-line, RDC-F, the entire individual order was allocated to the DC. If, however, the DC was a partial-line the percent of the individual order allocated to the RDC-P must be calculated. The basis for splitting the order between the RDC-P and its assigned PDC as presented in the Supporting Data System was the accumulated weight of the RDC-P's tracked products. The transformation required was of the form: 2‘4C) undusom wovuo Hospu>wvcu "uumnosonIIn.m ousmam uso>o maueuoooue sedan m a o 0:» cu ensued an sea 09 caduceuOusu sodo- ocu ensuedu< soda aeIuo ago now ooapuoe no sous-ens any eoaopov ou nauseous: sown-shone“ «annalsuu< «so .uluu uaeseuu vssoauso any one who .uluu soausuenoue use nanosecond notes 0:» oucasoaeu and sea cu noose as» us owausouuoe any «unusuuao ocuu Heuuuee no Iuasw a mu on: sea accuse: one-hone: ED .83 Annual-scan uovuo on» synagogue a mfldcm an >¢um xbuo< ago + «no ulna: N QAwvcH "anneaa=< sua>3uoov .vum van oucuo>< .m mucuoasasuoo 9002 Mo sewuaw>ov .vun vac cumuo>< .e macauuoeouo muovuo use w modem Huoz .n on osHHIHuuuuue use .ocHHIHHDH now moaom .u3 :90 .N on mafia Iamwuumo can .oCHHIaasw paw modem 99c .~ wannabe noamm no ouoooaa< .o mmusmmos mow>uom oumasasou< .n «Ho .oEau ufimcauu vcsonuso mamasoamo .c New .oafiu coaumuo Icons can wcfimmoooue novuo oumasoamo .m qunm ecu cu umpuo ozu mo owmucoouoe ouoaaofimu .N ~HU .OEHu touuafimcmuu uwtuo OumHSUHwo .~ mon9cw mafia Hoauuom .ca owe: ommo you unmask ammuo>< .m~ .woc wean mafia oou>uom soEOumsu .Na sausages“ swam 0c .au omen on he unassumcoo zuaomaoo .oa nucoaoanm unseemsu Adamo one no usoouom .o one you ucoaoazn sagas w azauxwa «H .w macauocsu oosmauo> mafia oou>uom .5 ucoscwammo cow was one» on .o mowuowouoo huoucu>sa no.0: Hmuoa .m commoooun weave xooHn novuo quOumso .e novuo on» now vouooflom an .m commououe wagon opoo on Huaucouom .N vommuooun wagon on couusaonIsH .~ mesmzH 0390.39 mHmrAHQZH QIrIsolidated shipments to the DU's a procedure was EEsrtablished for scheduled shipment dispatch of a percent- EiSJe to the customer orders. If the maximum daily ship- n“ent (SDSM) to the PDC, was greater than the customer ‘Cfirder being processed (IORD) a random number was gener- 6ited to determine if the order being processed was one ‘Crf a set percentage (CSDP) of orders that received daily S.I'Iipment dispatch. All other orders less than SDSM plus Eill orders greater than SDSM were shipped on the next $3cheduled shipment day, for example Monday, Wednesday €ind.Friday of simulated calendar time. The CT2 for the (Drders that were shipped on the day ready to ship was 'generated in the same manner as the CT2 for the PDC's, 243 the RDC-F, and RDC-P. The CT2 designated for the scheduled distribution was based on the order processing and preparation time plus any additional delay resulting ffirwom the ready to ship date to the next scheduled ship- rneerat day. The transformation was: IF(DCSLQD(IDC) is > ULOPC(IDC) * DCCAPC(IDC) volleere: Sales volume in dollars for the DC(IDC) quarter-to-date DCSLQD(IDC) Upper limit on throughput, or sales volume as percent of design capacity before delay occurs in order processing and preparation ULOPC(IDC) Design capacity of DC(IDC) in throughput dollar volume DCCAPC(IDC) tZIIEHH CT2 = PARM + 1 where : PARM = A Monte Carlo function of the form: Probability Normal Order Processing of Delay and Prepgration Time 70% l-day 20% 2-day 10% 3-day Order Cycle Time CT4.--The generation of the ship- Inent time for outbound transit CT4 for the DCeDU link ‘flas next calculated based on the same procedure of cone Centric service rings for constant time element and the 244 variance functions for the variability time element as used to generate the CT1 element. Service Measures.--The next activity accumulated the information required by the Measurement Subsystem to calculate the measures of service for the DC-DU link. This activity accumulated the information necessary to develop the measure of the amount of sales dollars and orders within a certain interval of normal customer order cycle time days (NOCT = CTl + CT2 + CT4). Based on the NOCT generated for the individual orders the following table was constructed for each quarter for the DC being processed: NOCT-INTERVAL No. Days 1 0-3 2 3-5 3 5-7 4 7-9 5 >9 DC(IDC) QTD Dollars % SLSDOLS(1) PCD(l) SLSDOLS(2) PCD(Z) SLSDOLS(3) PCD(3) SLSDOLS(4) PCD(4) SLSDOLS(5) PCD(S) QTD Orders % SLSORDS(1) Pco(1) SLSORDS(2) PCO(2) SLSORDS(3) PCD(3) SLSORDS(4) Pc0(4) SLSORDS(5) Pco(5) The same measures of service also can be developed for the elements of the NOCT such as the percent of sales and/or orders within the CT4 outbound transit time intervals. The above table provided the measure of actual service which when compared against desired service produced the sales modification factor, SMF. The SMF in addition to adjusting 245 sales based on service also determined the need for DC addition or deletion in the Locate algorithm as will be presented in the Monitor and Control Subsystem section of this chapter. The final activity block allocated the sales infor- mation to the DU from the DC being processed. The amount of the order block allocated to the DU was established by the following transformations: DCDUSLS(IDU,IDC) 1/CBF * ORDBLK(ICT) * RDCPC (or RDCPLPC) where: DU sales information i.e. dollars and weight DCDUSLS(IDU,IDC) CBF = Customer blocking factor, ICT ORDBLK(ICT) = Sales information in order block RDCPC = Percent allocated to RDC-F equals 100% RDCPLPC = Percent allocated to RDC-P equals <100% IDC = Identification of DC IDU = Identification of DU ICT = Identification of customer type. The control was returned to the D&E Sales Processing Event after completion of this final activity. The next routine of the Sales Processing Event was the Order Summary. Fixed Event-Order Summary The Order Summary Routine processed the order blocks summarized sales information and product detail at the DC 246 level. Figure 5.8 presents the activity analysis diagram in terms of the outputs, inputs, and transformations for the Order Summary Routine. The flowchart is presented in Figure 5.9. The first step of the ORDSUM Routine was to deter- mine whether the DC being processed was an RDC-F or RDC-P. If it was an RDC-P, the order block summary had to be allocated (split) between the RDC-P and the PDC. The total order block was allocated to the DC being pro- cessed if it was either an RDC-F or a PDC. The next activity accumulated the sales information at the DC level. The sales for a RDC-P was based on the partial- line percent, RDCPLPC calculated in the Individual Order Routine. Accumulation of the number of orders processed at the DC was the next activity. For a RDC-F or PDC the number of orders was a simple accumulation of the indi- vidual orders processed quarter-to-date at the DC. However, for an RDC-P the assumption was made that two orders were required for each order received and split at the RDC-P. Therefore, for each split order one order was accumulated at the RDC-P and one at the regional PDC. The next activity accumulated the shipment weight allocated to the DC-DU links in the appropriate customer weight categories: 224'7 ocauaom humaasm uovuo "uumsoaonIIm.m ouswfim .osuusom unannououm modem m a a on ensued .xuo~m scene can Iona sues: cease ausvoue an vsseIcOIooqu0uso>su uusvoun suave» .eowuoUUUco huouce>su Hue aeououm .uouuououeu mucuso>cu ocfiaIaqauuam uo seamlaasm neoooum .huouOucu anode: euauunounes «so aw genus: ususewea scone uovuo euaaslsuo< .oa o:«HI-:h ho undulaluuuem onu as nausea uo non-so sandalsuo< .oa oauauaaas no ocoauaoouuaa can as coda-lacuna nouns ouuaslsuo< .09 ocuaIaeuuuem no oaaaIaaaa no no so «nauseous on songs .osuaInusm no usquueuuu-m .Ho>oH on as hue-lam soon: noose aeoooum % a mu4wuomH on otu um Hamuov gaseous can mwawm xuoan noose mo acuuoaoaou mmmmmmm modem uosvoua mmoooum unwaoa usosaasm oumassSoo< .a .e .n muovuo mo unease oueasasoo< .N O :IF‘m Z>F mumw4mGH .0 moauomoumo mucuso>sH .m unwaoa ucoaeaxm Moods uwvuo .q on «to on muoouo mo nonauz .n on use now coaumah0uca moamm .N o: ocHHIHmauumo no ocaaIafiom .a mesmzH D503200 3 >200:l,000 4 >1,000 The transformation for accomplishing this was: WTCAT(IWC) = PWTCAT(IWC) + l/CBF * ORDBLKWT(ICT) * where: WTCAT(IWC) CBF = ORDBLKWT(ICT) RDCPC = RDCPLPC = IWC = ICT = The Monitor and RDCPC (or RDCPLPC) Weight category, IWC Customer blocking factor Order block weight, ICT Percent allocated to DC if an RDC-F equals 100% Percent allocated to DC of an RDC-P equals uuuounm uovno out .ofi mwuaoahuem am>auem + ucwaauzm on .m— mwamm ammo oustcea voxonuu .ANEmem. 2H0 .¢~ modem wmeu assessu coxossu .u«umw50o aka .na wcausox wsouuaze:oom uzwdm: ucrIUc .m— mfimmououm smoILOIucu on "uuozuzoEIIZ.m flaw; v.33. em: :36; Exam: ~38. .: memes ozoIcsxocum coumhmwucqnoaak .o— N couches» upstate camcom GPO .o 6:622: com 1. com .w Jamison may suave: uusvoua naus- .ee> u.— .uusvoue coo—om: two :2. 56.307. ucwmwsm .N anon saves on : «9.20.20... :3 missions“ 2:... .w 3!. nus—cone sumo-nu 05 noon muscuosp utscotc uflqauass we .02 .a 3 uninsusv ou dunno roman-u unison: 52:9: 536.3 out Lemma; .m C332: 5 nus—eons ..qu up; mweE of: Contact :33 233.. .N mucouomu uu:touc vocab—:E we .o: Hence .a among .3333» nevus?— = sou-house Finn 3.3»: .n all white: .vsuqsvuu houses.— »uuuoa use-£350.19. 1:330 .n ESP—.5 2E3. 22.3.? 322.33. .2 >030.— usuoe hour—cu: ..n Ragga we: 3;: Levee: Bones .2 "51. 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The transformation for this activity was: TINTIOH(ITP,ID) = TINTIOH(ITP(ID-l)) + IOH(ITP,ID) where: TINTIOH(ITP,ID) = Time-integrated (QTD) inventory-on-hand for end-of-day, ID for tracked product, ITP TINTIOH(ITP,(ID-l)) = Time-integrated (QTD) inventory-on-hand for end- of-day, ID-l for tracked products IOH(ITP,ID) = Inventory-on—hand for end- of-day, ID for tracked products, ITP. and: AVGINV(ITP) = TINTIOH/NWKDYS where: AVGINV(ITP) = The average inventory-on-hand for tracked product, ITP quarter-to- date TINTIOH(ITP) Time-integrated inventory-on-hand for tracked product, ITP quarter- to-date NWKDYS = Number of workdays, quarter-to-date. The stocked out situation required updating of two vari- ables. A time-integrated stocked out cases variable was updated by adding the number of case units that were stocked out for the current day. The transformation for the second condition.was: 253 TINTSOCU(ITP,ID) = TINTSOCU(ITP,(ID-l)) + -IOH|(ITP,ID) where: TINTSOCU(ITP,ID) Time-integrated (QTD) stocked- out cases for end-of-day, ID for tracked product, ITP TINTSOCU(ITP,(ID-l)) Time-integrated (QTD) stocked- out cases for end-of-day, ID-l for tracked product, ITP Absolute value of negative inventory-on-hand for end-of- day, ID for tracked product, ITP. I-IOHI (ITP,:D) This variable provided the Measurement Subsystem with the information to determine the customer service penalty time, CT3 for inventory stockouts. As previously stated in the Supporting Data System-Measurement the normal cus- tomer order cycle, NOCT plus CT3 equaled the total custo- mer order cycle, OCT. The calculation of CT3 is presented in the Measurement Subsystem. The second variable calculated for measures of stock- out was the stockout days for the product. This variable, updated each day that a product was stocked out, enabled the calculation of the average and standard deviation of the product stockout days given that a stockout had occurred. The transformations to calculate the stockout days were: NDASO(ITP,ID) = NDASO(ITP,(ID-l)) + l where: NDASO(ITP,ID) = Number of days (QTD) a stock- out occurred for tracked pro- duct, ITP for end-of-day, ID 254 NDASO(ITP,(ID-l)) = Number of days (QTD) a stockout occurred through day, ID-l for product, ITP. If there were any DC product reorders outstanding the reorder quantity, ROQ was added to the time-integrated inventory-on-hand to approximate the total average inventory for this product at the DC. The transformation was stated as follows: If a reorder is outstanding for the product from the DC, then TOTINTIOH(ITP,ID) TINTIOH(ITP,ID) + ROQ(ITP) wnere: TOTINTIOH(ITP,ID) Total time-integrated (QTD) inventory-on-hand for the end- of-day, ID for tracked product, ITP TINTIOH(ITP,ID) Time-integrated (QTD) inventory- on-hand for end-of—day, ID for tracked product, ITP ROQ(ITP,ID) = Reorder order quantity outstand- ing for tracked product, ITP at end-of—day, ID. Looping through all of the tracked products within an inventory category was necessary since the inventory policy was assigned to categories rather than individual products and certain summary data was accumulated only by inventory category. Selection of the inventory policy was the next major activity of the routine. As previously discussed in the Supporting Data System--Operations and Monitor and Control 255 three basic inventory management policies, level-3, were developed: 1. Optional replenishment system 2. Reorder point system 3. A hybrid of the reorder point system and the optional replenishment system. 'The details of these three policies are presented as a Monitor and Control Subsystem Routine-Inventory Management Module. In this section the emphasis is on the operation of inventory control, the level-l and level-2 inventory problem. The assigned policy was selected for the inven- tory category using an inventory policy indicator set at the initialization of the run. The assumptions were made that all tracked products in an inventory category would be managed by the same inventory policy. If the policy was an optional replenishment policy with periodic review the routine checked to determine if the current day corresponded to the time for inventory review for the inventory category. If it is time for a review the reorder transformation was as follows: ROQ(ITP) = S(ITP) - IOH(ITP), If IOH(ITP)uuu< Hm>wuu< wovuo out "uumsoaoamnnma.m muswwm nocuo out unamadmdd huw>uuuaouou 2 auuvuoou unavoua “uasa no nobssz .N . a ..mSSomxm: .55 3 533. 7.5.5: $38.. e no nauseoua vo>wuouu our unmouum .H 2 o whomhao uovuouu so Hanna: usage: waned: .n unuao: accuses. Manna any ounce: meHmm< unwouou uusvoua canvas .H «mama co: monHm .n H 3303 5 3268.. 3. 5:85 coo; @ , 355:. «o 2.3 .a < "mouabquuuu uso>m M<¢oox .a e < whamzH a snag uazu Hmumuuu new use-nus. axon cu nonvoun vv< comm mauuun unvuo out on on a ouououa Add: unzu UnauQOH :olau o~n¢wun>= M< do out 264 The number of reorders was updated by a linear, first-order difference equation as follows: DCMCCOR(IMC,IDC) DCMCCOR(IMC,IDC) + l where: Total number of orders on the MCC(IMC) dock ready for ship- ment to the DC(IDC). DCMCCOR(IMC,IDC) The total weight of the shipment currently being assembled at the MCC was incremented with each order for the given DC if a shipment had been made to this DC within the past ten days. The transformation was a linear, first-order difference equation as follows: DCMCCWTAL(IMC,IDC) DCMCCWTAC(IMC,IDC) + ORWT(IMC,IDC) where: Accumulated shipment weight for the next shipment for the MCC(IMC) - DC(IDC) link DCMCCWTAC(IMC,IDC) Weight of an order for shipment from MCC(IMC) to DC(IDC). ORWT(IMC,IDC) Variable Event--DC Shipment Arrival The last routine of the Operations Subsystem, also a variable Event processed the shipment arrival of pro- ducts to update the inventory status variables at the DC. Figure 5.14 presents the activity analysis in terms of the outputs, inputs, and transformations for the DCSHPAR Routine. The flowchart is presented in Figure 5.15. 265 ocfiusom maammuooum wsuwmououm Ha>uuu< Hm>euu< ucoEafizm on "uumnozoahnlma.m ouswum usuanwam on "mumhflma< huw>uuuov vumvsaum . mucuaasssoou maaov usOJUODu unauu>< . vouovuoxomn wages ammo unmouum . acetone you name usoxUOum usumuum . can: so mucuno>nH . h o n nusoxUOun uosvoua mo kebabs .vuc .c : ..gusomxm: .53 3 533. 3332: com 9.35333 + com .n a . N H . ~n>uuu~ .IIIIIII o ucuaauno :« nauseoua ado caucusu coo; mammaao .3332: . .2352 cam uonou .ucasusouhu0u=o>=a zen ca 30H cu suaucasv uueuoou vu< .N HzmzmHMm cu suuuaasu novuoou «acetone ov< cam aa< mouammoa unexUOuu mauve: .H on _ mzouegomng huaueasu pounce» anououm com acumowvsw com mauvsmuuuso + com .c H can: so huouao>su .n 2 nauseous poxumuu we posses Hmuoe .N nous-d0. adm: ovou on sofiusaoulsn .v n u30300ua hu0uco>cu suave: .oa um HDOMUOHm uuvuouu sq muusvoum .o W H.295 anon usu>m . A Ha>wuum mo mafia .m < "mouabauuua usu>m muuuuoa nu vansncouxuOuco>cw a“ com coauouou uuusvoun Han noououm ~a>uuua unclean» on cu out a uuououn and: yoga «nausea «Ida cannuun> 266 The products listed on the shipment were checked against the DC inventory-on-hand. If a product on the shipment was stocked-out the percentage of case units backordered, and the mean and standard deviation of pro- duct stockout delays were updated. The final activities updated the IOH for all tracked products received in the shipment from the MCC. The transformation was a linear, first-order difference equation as follows: IOH(ITP,(ID+1)) IOH(ITP,ID) + ROQ(ITP,ID)) where: Inventory-on-hand for beginning of day, ID+l for tracked pro- duct, ITP IOH(ITP,(ID+1)) Inventory-on-hand for end-of- day, ID for tracked product, ITP IOH(ITP,(ID) ROQ(ITP,ID) = Reorder quantity received for end-of-day, ID for tracked pro- duct, ITP. Summary The Operations Subsystem events; the three fixed-time events Individual Order, Order Summary, and DC End-of-Day, and the two variable events MCC Order Arrival and DC Ship- ment Arrival, provide the activities and sequencing nec- essary to simulate the operation of the total physical distribution system structured for the LREPS model. The next section of the Operating System presents the Measure- ment Subsystem, which develops the measures of cost, ser- vice, and flexibility, 267 Measurement Subsystem The function of the Measurement Subsystem is to process the results of the previous operating period to develop values of the target variables cost, service, and flexibility (robustness). These variables provide the basis for evaluation and selection from among the various sets of sequential decision outcomes of the LREPS model. The design criteria for the Measurement Subsystem required that it provide service, cost, and flexibility information that is suitable for strategic decision making. Extrapo- lation of inventory characteristics was also required. The output included a measure of total physical distribution costs, which required consideration of fixed investment cost of the physical distribution cen- ters, inventory costs, distribution center operations (throughput) costs, transportation costs, and communica- tions costs. Basic measures of customer service included the total order cycle, percent customers served within a set of designated service times, percent sales volume served within a set of designated service times, stock- outs and order cycle delays due to inventory policy, service to major customers, and finally, a measure of service relative to competition. The final criteria was that the subsystem develop the necessary output to develOp measures of flexibility (robustness) or as pre- viously defined, the degree of "non" risk associated with a particular decision. 268 The general flowchart illustrating the processing sequence for the Measurement Subsystem and the order of presentation in this section is presented in Figure 5.16. In summary, at the end of each quarter the Monitor and Control Subsystem triggered a fixed event which called the Measurement Subsystem Routine. The routine selected a region, IR, and a DC, IDC, within the region. The service, cost, and flexibility subroutines were then pro- cessed and the output recorded for each DC, IDC in-solu— tion during the past quarter in the region, IR. This procedure was repeated for each region, IR, where IR = l,...,NR and NR equals the number of regions. The Mea- surement Subsystem is presented via three major routines. In order of presentation they are: l. The Service Measures Routine 2. The Inventory Extrapolation Routine 3. The PD Cost Routine. Service Measures The first set of activities of the Measurement Sub- system is the routine to calculate the measures of ser- vice. Figure 5.17 presents the activity analysis in terms of the outputs, inputs, and transformations for the service activities which are performed for each in-solution DC. The measures of service developed in the Measurement Subsystem were: 1. Customer service penalty time, CT3 2. Mean and standard deviation of customer normal order cycle time, NOCT fl MEASUREMENT:> SUBSYSTEM PD SERVICE WW INVENTORY EXTRA? PD TOTAL COST b PD FLEXIBILITY C D 269 Measurement Subsystem includes Service, Cost, Extrapolation and Flexibility. Set of Service Activities. Set of Inventory Extrapolation Activities. Set of Cost Activities. Accumulation of data to develop "Robustness" in Report Generator System. Return to fixed time schedules - M & C Subsystem. Figure 5.16—-Flowchart: Measurement Subsystem 270 3. Mean and standard deviation of customer outbound transportation time, CT4 4. Total customer order cycle time, OCT 5. Percentage of case units backordered 6. Mean and standard deviation of product stockout delays 7. Normal order cycle time proportions 8. Domestic average service time 9. Average lead time for each DC-MCC link. The flowchart for development of the service measures is presented in Figure 5.18. Customer Service Penalty Time.--The customer service penalty time, CT3, resulted from DC stockouts of tracked products during the past quarter's operations. The normal order cycle time, consisting of the DU to DC order trans- mission time, CTl, the order processing and preparation time, CT2, and the DC to DU transit time, CT4, when increased by CT3 is defined as the average total custo- .mer order cycle time. The calculation of the CT3 custo- mer penalty time was performed for each inventory category and then a weighted average, based on total tracked pro- duct sales was developed for the DC as follows: ITNPC Z AVINCP(ITP,IDC) ITP=l ITNPC Z PRCTDC(ITP,IDC) ITP=l DCCPT3(IDC) for: 271 casemuco0num~.m ouamwm .ocuusou nuahud nouuaav1uouvco u a r a» census .-u«ua«uauoeuezo huouoo>cu L<¢me ua aueaonauuxo o» ocuuaou ca 00 H4< .aaua outage no.0 uoxuua you and» toad cease): ouaaauuuo Umuo¢ ou1->a oauaulov euausuuau u4e house unison ou-Hsugqu unuom "Suwzuacamv-rq. .aA-qov uaoxuou- suspend uo coauq.>ov vuavcnua use can! ouo~=u~uu .voeooeoxusn agar: oqau no Unau:0usoa confine—nu .Uqu o~o>u bongo uauou ouch»). euc~augau .oaau noun-uncon:auu vcaonuao tunesoau mo ecuuna>ov uu-vcnua we. can- oua~su~ao .uauu euuxu sovuo ~useo: easesnsu uo caduudpov vu-vcaun use coal ou-a:u~qu .nh ucavav '«u 004’u0I hacumvu ouanaeuau .nouanool oua>uou outloo nee annoy-so eua«=u_qu .uou:aaol ood>uoe euodsu-u iii _:cxu: as uq,.0 z.:m§xu:n .us< -_ s i x aw e 4.1. ns_em “co . 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Deviation of NOCT.--The calculation of the mean and standard deviation of the previously defined normal customer order cycle time (NOCT) was calcu- lated using the QTD order sales and the accumulated NOCT for all orders. The procedure included the following transformations: AVNOCT(IDC) _ ACNOCT(IDC) ’ DCQDOSL(IDC) and § 2 STDNOCT(IDC) = (Eggggéi?ggc) - (AVNOCT(IDC)) ) 273 where: AVNOCT(IDC) Average NOCT for DC(IDC) Accumulated NOCT for all orders for DC(IDC) ACNOCT(IDC) DCQDOSL(IDC) QTD order sales for DC(IDC) IDC = DC identification number Standard deviation of NOCT for DC(IDC) STDNOCT(IDC) MNOCT(IDC) Mean of the square of accumulated NOCT for all orders for DC(IDC). Mean and Standard Deviation of OBT.--The calculation of the mean and standard deviation of customer outbound transit time, CT4, required the accumulation of QTD out- bound transit time and order sales for the DC. The cal- culation was made as follows: ACOBT(IDC) AVOBT(IDC) DCQDOSL(IDC) and 1 MNOBT(IDC) (AVOBT(IDC))2 7 STDOBT(IDC) =(DCQDOSL(IDC) ' > where: AVOBT(IDC) = Average OBT for DC(IDC) ACOBT(IDC) Accumulated QTD outbound transit time for DC(IDC) DCQDOSL(IDC) = QTD order sales for DC(IDC) STDOBT(IDC) = Standard deviation of OBT for DC(IDC) MNOBT(IDC) = Mean of the square of accumulated OBT for all orders for DC(IDC) IDC = DC identification number. 274 Total Customer Order Cycle.--The sum of the normal customer order cycle time, (CT1+CT2+CT4) NOCT and the customer penalty time, CT3, previously defined as the total order cycle time, was calculated as follows: AVOCT(IDC) DCCPT3(IDC) + AVNOCT(IDC) where : AVOCT(IDC) Average total OCT for DC(IDC) DCCPT3(IDC) Penalty time, CT3 for DC(IDC) AVNOCT(IDC) Average NOCT for DC(IDC) IDC DC identification number. Percent Backorders.--The next activity developed the percent of tracked product case units backordered due to inventory stockouts, relative to the total tracked product case units sold for all inventory categories. This activity required the accumulated days delay due to stockouts and the total case units sold for all tracked products QTD for each DC. The transformations used were: PCUBO(IDC) = ggfigélnc) * 100 PRCTDC(ITP,IDC) ITP where: PCUBO(IDC) = Percent case units backordered for DC(IDC) CUBO(IDC) = Case units backordered for DC (IDC) PRCTDC(ITP,IDC) = Total case units sold for tracked product, ITP for DC(IDC) ITP IDC 275 Tracked product identification number DC identification number. Stockout Delays.--The mean and standard deviation of tracked product delivery delays due to product stockouts required the accumulated QTD days delays and the stockouts QTD for all inventory categories. The transformations were performed as follows: and where: AVSODL(IDC) STDSODL(IDC) AVSODL(IDC) ACSODL(IDC) STDSODL(IDC) MNSODL(IDC) PRCTDC(ITP,IDC) ITP IDC = ACSODL(IDC) [PRCTDC(ITP,IDC) ITP 1 MNSODL(IDC) _ (AVSODL(IDC))2 7 Z PRCTDC(ITP,IDC) ITP Average stockout delay in days Accumulated stockout delay in days, QTD Standard Deviation of the stockout delay in days Mean of the square of accumulated stockout delay, QTD Total case units sold for tracked product, ITP for DC(IDC) Tracked product identification number DC identification number. 276 NOCT Proportions.-—The proportions of DC(IDC) sales dollars and sales orders delivered to its customers within a set of specified normal customer order cycle time (NOCT) intervals were calculated using the transformations: PCD(IOT) PCD(IOT) where: PCD(IOT) Pco(IOT) SLSDOLS(IOT) SLSORDS(IOT) IOT NOT NOT SLSDOLS(IOT) Z SLSDOLS(IOT), and IOT=l NOT SLSORDS(IOT) X SLSORDS(IOT) IOT=l Percent sales dollars within normal customer order cycle time interval, IOT for the DC(IDC), QTD Percent sales orders within NOCT interval, IOT for the DC(IDC), QTD Sales dollars within interval IOT for the DC(IDC) QTD Sales order within interval IOT for the DC(IDC) QTD NOCT intervals Number of order cycle intervals. Domestic Service Time.--The domestic average total customer order cycle time, a weighted averaged based on customer orders, was as follows: DOMACT calculated at the end of each quarter NDC Z TORDSDC(IDC) * AVGOCT(IDC)/ IDC=l NDC Z TORDSDC(IDC) IDC=l 277 where: DOMACT = Domestic average total customer order cycle time weighted by all DC's TORDSDC(IDC) Total orders for the DC(IDC) AVGOCT(IDC) Average total customer order cycle time, OCT for DC(IDC) IDC = DC identification Number of DCs. NDC Reorder Lead Time.--The average total reorder lead time for each DC-MCC link for an in-solution DC was defined as the sum of the DC-MCC reorder transmission time, RTl, the reorder processing and preparation time, RT2, the waiting time prior to shipment from the MCC, RT3, and the MCC-DC shipment transit time, RT4. The data requirements to calculate this measure of service were the total number of multiple product reorders and the number of MCC's in-solution. The transformations used for this activity were: 2 ROCT(IDM,IRO)/NMORDS(IDM) IRO AVDCMCLT(IDM) where: AVDCMCLT(IDM) The average DC-MCC reorder lead time for each DC-MCC link, IDM ROCT(IDM,IRO) The reorder cycle time for the DC-MCC link, IDM for reorder, IRO NMORDS(IDM) The number of multiple product reorders for the DC-MCC link, IDM 278 IDM = Identification number of DC-MCC link IRO = Reorder identification number. Inventory Extrapolation The next major set of activities, EXTRAP developed additional measures of inventory characteristics. This routine was necessary to extrapolate or generalize the average inventory characteristics developed from the results of activities of the tracked products to the total product line. Figure 5.19 illustrates the activity anal- ysis in terms of the outputs, inputs, and transformations required for development of the inventory characteristics. Figure 5.20 presents the sequence of calculations for the set of activities. Categornyodifier.--The first activity of the Inventory Extrapolation Routine calculated the category modifier, CM, which was used to extrapolate the inventory characteristics for a particular inventory category. CM was calculated by the following transformation: CM(IC) = TNCTPD(IC)/TKPDCT(IC) where: CM(IC) = Inventory category modifier to extrapolate inventory characteristics to all products in the category, IC TNCTPD(IC) = Total number of products in the inven- tory category, IC TKPDCT(IC) = Tracked products in the inventory category, IC IC = Inventory category identification. 279 coaumaoomuuxm >u0uco>cm .oauuaou n.0usucul ouu>uou mdmx ou unseen .mouuowOunu huouao>ca swaounu oooq .auosvoua pose-nu :u30unu goo; .huouco>a« uqanu owauo>o n.uu=voun nuanonauuxm .usaluao>=« on oucuo>a u.uuavoun auaaoacuuxu .huowoueu cu nauseous voxuauu «an ouoooum .ouovuoou unavoun Ioawsue can ausoxooua ouqaoaauuxm .muuumu nuouuauanu n.5hououao muouao>cu nanu ouoaonauuxo cu nouuauos ozu ouausouau .aowuomouao muounobsa Han aaououm .nouu sausage-none huoucoean on cannon-nunm mafiusom uuumsoaoamlno~.n ouswwm % Q unau amoyzm>zH m2u on aduhxm 9:539. a mSoxooS mica _ «Humane: >&OOMHcu "mummams< >ua>wuuCH cwmuw>m pouoaoamuuxo on .d mHDmHDO mucuco>cu ownso owmu0>m m.uo=poua oumaoomuuxm .Q ucosumu>Ca on ommuo>m m.uusvouo oumaoomuuxm .m muovuoou suspend mfiwcfim tam monoxUODm oumaoomuuxm .N umfiuapoe Showcase wumasuamc .~ wchh¢OHZm>ZH 'C.su huuaaoau ouausoaau .ouuuolov use coduou .8 new :3 33335.00 3:315 .a.on as» :wsousu avoow uo uaulo>ol .uuuou nannusounu «undouauu .Unluu: .muuou noun-uuonncauu essencw «unusuuao .Dnloa .ouuou noduauuonacuuu manoeuao ouausuaou .u0uuesv avoweoun one you uueoo unused-cu om «unusuaau fizOHzm>zH UAsuu<-us~.m shaman mumou muaawoow on .n mumoo mcowuwowcsssoo on .c mumoo uoenwaoucu on .n umou cofiumuuoamcmuu casebau on .N umoo cowumuuoomcmuu masonuao on .~ whamhpo umoo ucoaumo>cfi xuaawomw mamasuamo .n mumoo mcoaumUHcsasou monasoamo .q mumou usmzmzounu mumdsoamu .m mumou coHumuuoamcouu canons“ oumaaoamu .N mumOu c0wuwuuonmcmuu oc30buso oumaaoamu .~ monH .mm owumosov can .cofiwwu .on new umtuo nod umou oanmwum> .nm owumoeov can .cowwou .on new mumOU mcofiumoucassoo voxam .eN mmamm mean sea HmuOu on .mu moamm wovuo aha Hobo» on .qm ecuumm umoo cofiumowcsssoo uwumoson .mw nobomm umoo cofiumuacsssou Hmcowwom .NN neuomw umou :ofium0ficsssoo on .- oezu vcm anew on hp dump umoo yonzwsoush .cm uOu~uach ouwm on .¢~ weapowoumu ucwwoz 0cm use can uo .oz .w~ uzmwos ouzuoe kuafiassou< .n_ moumu uzwfiouu ouzuoo .ou nouumw wcwxufipos mum» unusawcm voaooe cam .m~ neuumw newuuouuoo much was» on .q~ powwooouo wcHon m.zc mo noses: Hmuoe .m~ osau kumasswm no new» .- :w: can :u: muwfiwavos wmmouucw ouch doom .- :v: v6“ :0: .mucofiowwwooo cowumsvo ceammouwom .c~ muowwwvos dump pwumwuowoc :b: can :m: Hmcowmom .m vummwoouo mcawp coawox .m mmHmm uswwoa aha Hmuou on .5 .pH .scwfima en mufimm use muons a alone .0 mscsfl salon oucaumse sauna“: .n ucoscwfimmm Dom tam waxy on .c commoooua wcwob an .n unwwos vca mucuacwfimma Donna .N commooouo wagon on couuaaomlsw .H wHszH ODE-*9. Hzmzomzou Hmou Om Q24,000 lbs. The weight for each MCC-DC link was accumulated in the Operations Sub- system. The calculation of inbound transportation cost for the MCC-PDC used the identical transformation, but the freight rate for the >24,000 weight interval was applied to all weight accumulated for the PDC links. Throughput Cost.--The throughput cost activity cal- culated the cost of preparing the customer orders for shipment. The transformation was of the form: THRUPC(IDC) = THRUCF(IS,IT) * WTSL(IDC) 288 where: THRUPC(IDC) Throughput cost for DC(IDC) for the quarter THRUCF(IS,IT) Throughput average cost factor by DC size interval, IS,IT WTSL(IDC) = Throughput average cost factor by DC(IDC) for the quarter IS = DC size interval identification IT = DC type identification. The basis for the throughput cost factors was discussed in the Supporting Data System--Measurement. The total weight moved through the DC was accumulated via an Operations Subsystem activity. Communications Cost.--The cost of order transmittal and preparation up to the point of the physical prepara- tion of the order were defined as communication cost. The transformations which develop the fixed cost and variable cost for the DC were of the form: COMFCDC(IDC) = CMFCDC(IS.IT) where: Communications fixed cost for DC(IDC) for the quarter COMFCDC(IDC) Communications fixed cost for DC size interval IS, type IT CMFCDC(IS,IT) and: COMVCODC (IDC) CMVCODC (IS , IT) * NMORDS (IDC) where: COMVCODC(IDC) = CMVCODC(IS,IT) = NMORDS(IDC) and: COMVCLDC(IDC) = where: COMVCLDC(IDC) = CMVCLDC(IS,IT) = NMLNS(IDC) The fixed and variable five size intervals IS 289 Communications variable cost for orders processed for DC(IDC) for the quarter Communications variable cost factor for orders for size, IS, type IT Number of orders processed for DC(IDC) for the quarter. CMVCLDC(IS,IT) * NMLNS(IDC) Communications variable cost for lines processed for DC(IDC) for the quarterly Communication variable cost factor for lines for size, IS, type IT Number of lines processed for DC(IDC) for the quarter. cost factors were developed for the and three types IT (PDC, RDC-F, and RDC-P) as previously discussed in the Supporting Data System--Measurement. Communications costs were also developed at the regional and national levels to allow the flexibility of simulating regional or centralized order processing sys- tems. The transformations for the regional costs were of the form: COMFCRG(IR) = CMFCRG(IS) where: COMFCRG(IR) CMFCRG(IS) and: COMVCORG(IR) where: COMVCORG(IR) CMVCORG(IS) NMORDRG(IR) and: 290 Communications fixed cost for region, IR for the quarter Communications fixed cost for regional size interval, IS CMVCORG(IS) * NMORDRG(IR) Communications variable cost for orders processed for region (IR) for the quarter Communications variable cost factor for orders for regional size inter- val, IS Number of orders processed for region, IR for the quarter COMVCLRG(IR)==CMVCLRG(IS) * NMLNSRG EVENT Events filed by day and within FILE day by FIFO. SELECT Select next imminent event from the NEXT list of possible; BOYC, DAILY, EVENT MONTHLY, QUARTERLY, HALF-YEAR, YEAR and BOCYC. If end of planning horizon, "stop" by processing BOCYC. <::RETURN :) Return to Fixed-Time Scheduler. Figure 5.23--Flowchart: Supervisor Function-Executive Routine 297 variable events were presented in the Operations Subsys- tem and thus are not discussed in this section. Tfiua fixed time event, BEGINNING-OF-CYCLE, essentially consisted. of a set of initialization activities required for emufii simulation cycle of a complete planning horizon. The flowchart is presented in Figure 5.24. The BOCYC event included: 1. Exogenous input 2. List of in-solution DC's 3. DC-DU link information 4. Beginning inventory levels and control information 5. Calculation of modified annual domestic forecast 6. A call to the Daily Event to process the first days sales activities. The fixed time events, DAILY, MONTHLY, QUARTERLY, HALF YEAR, and YEARLY were generally similar in processing sequence. Each of the events was called by the Executive Routine on the Clock Time "TNOW" corresponding to the appropriate calendar day of the year. Figure 5.25 pre- sents the activities from which each event was constructed. flflmzsequence was to process the daily activities included in thelxflly Event each calendar day. The Daily Event linkedtflw Routines; Daily Domestic Sales Dollar Forecast and Sales Processing each of which was discussed in the Ikmmndanm.Environment Subsystem. Upon completion of the daiLyguocessing for all in-solution RDC's, and the PDC ‘r’ieet Q (:g BOCYC EXOG CALC MDD FORECAST RETURN 298 Beginning of cycle event activity. Link to routine to read LREPS exogenous inputs. Link to routine to make DC facility initialization. Link to routine to develOp DC to DU link information. Link to routine to initialize DC inventories plus calculate inventory parameters. Calculate modified annual domestic forecast. Link to routine to process first days activities. Link to GASP EXECUTIVE Figure 5.24—-Flowchart: Beginning-Of-Cycle-Event 299 mmqaamzom MZHH nmxHh OH ZMDHmmA mHh v mNHAm mafia poxfim uuumnosoamnlmm.m muswfim anus Nauod .muo .sua NH a .HH .muc .m-H NH s .~.H H a mmzHHDom MDZHHZOU ZOHHmoezm>z~ m5mm wm4m moozmooozm m9m mzue amme zmemsmmam aomaz OU Qz< MOHHZOZ squam» mm zmo seems a .moH>mmm .Hmoo qummmooxm mmam v 300 for each region the control was returned to the Fixed-Time Scheduler to generate the next fixed time event. The Monthly Event consisted of the Daily Event activities plus End-of-Month and Beginning-of-Month activ- ities. In the initial version of LREPS the only addi- tional activity in the Monthly Event was the calculation of the Monthly Sales Forecast, using linear regression as follows: TDSF(IMO) = a + IMO * b where: TDSF(IMO) = Domestic sales dollars forecast for coming month, IMO IMO = Month identification a,b = Regression coefficients. The Quarterly Event consisted of processing the activities of the Daily and Monthly Events, and the End- of-Quarter, the linkages to the control, and Beginning- of-Quarter routines. The End-of-Quarter routine devel- Oped the measures of cost and service, which were pre- viously presented in the Measurement Subsystem, and prepared the results for output to the Report Generator System. The control linkages are presented in the next Section of this chapter. The BOQ activities served as the routine to initialize the endogenous variables for the next quarter's activities. After processing of the Quarterly Event, control was returned to the Fixed-Time Scheduler. 301 The Half Year Event in the initial LREPS version was a dummy event placed in the system for future flexibility. The annual or Yearly Event included the processing of the routines Daily, End-of-Month, End-of-Quarter, and End-of-Year Events, and the control linkages, the Begin- ning—of-Year, Beginning-of-Quarter, and Beginning-of- Month routines. The two new activities performed by the Yearly Event were to increment year by one and develop a new monthly sales forecast. The transformation for incrementing the year was a linear, first-order difference equation of the form: Year(IY+l) = Year(IY) + l where: Year(IY+l) = Coming year, IY + l Year(IY) = Previous year, IY IY = Year identification number. The new monthly sales forecast was calculated using linear regression of the form previously illustrated in the Monthly Event. The End-of-Cycle Event, EOCYC, ended the execution of the simulation run for a planning hori- zon. Gateway.--The three primary routines that made up the Input/Output or Gateway subfunction were: 1. End-of-Quarter routine, EOQ 2. Exogenous input routine, EXOG 3. Beginning-of-Quarter routine, BOQ. 302 The EOQ routine prepared and was responsible for the output of the End-of-Quarter results from the Operating System. This output was used by the Report Generator System to develop the special and standard management reports. The flowchart for the EOQ routine is presented ism I?i§pare: 5.226. The first major activity of this routine looped through all the DU's to develop exponential averages of DU dollars and weight sales for the quarter. The trans- formations were of the form: DUSD(IQ,IDU) = Alpha*(DUSF(IQ,IDU) + DUSP(IQ,IDU)) + (l-Alpha)*(DUSD((IQ-l),IDU)) where: DUSD(IQ,IDU) New exponential average sales dollars for DU(IDU) for quarter, IQ Alpha = Smoothing constant, initially set at 0.25 DUSF (IQ , IDU) Demand unit sales QTD for DU(IDU) from full-line DC's DU$9U0,IDU) Demand unit sales QTD for DU(IDU) from partial-line DC's DUSD(IQ, IDU) Previous exponential average sales for DU(IDU), through quarter, IQ-l. mm, DUSW(IQ,IDU) Alpha*(DUWF(IQ,IDU) + DUWP (IQ,IDU)) + (l-Alpha)*(DUWD(IQ-l),IDU)) C... D 0 DU EXP AVGS TOTAL cosrs a. SALES I (mm) 303 Routine to prepare and output end-of- quarter results. Process each DU. Prepare exponentially averaged DU sales dollars and weight looping through all Du's. Develop the measures of cost and service for each in-solution DC. Call Measurement Subsystem routine to calculate measures of cost and service. Sum PD total lost and sales for DC, region and domestic. Call Report Generator Subsystem routine output in-solution DC statistics, regional statistics, domestic statistics, and data base. Return to the Monitor and Control Quarterly Event. Figure 5.26--Flowchart: End-Of-Quarter Routine 304 where: DUWD(IQ,IDU) = New exponential average sales weight pounds for DU(IDU) for quarter, IQ Alpha = Smoothing constant, initially set at 0. 25 DUWP(IQ,IDU) = Demand unit sales weight in pounds QTD for DU(IDU) from full-line DC's DUWP(IQ,IDU) = Demand unit sales weight in pounds QTD for DU(IDU) from partial-line DC's Previous exponential average sales weight for DU(IDU) through quarter, IQ-l DUWD((IQ-l).IDU) IDU = DU identification IQ = Quarter identification. The next set of activities looped through the DC's by region to calculate the measures of service and cost via the link to the Measurement Subsystem. The transfor- mations used for the individual cost components were presented in the Measurement Subsystem. After returning to the Monitor and Control Subsystem, the total cost per DC, per region, and for the domestic were calculated next in the EOQ routine using the following transformations: DCCST(IDC,IQ) = OTBD(IDC,IQ)+INBD(IDC,IQ) + CMDC(IDC,IQ) + FINVC(IDC,IQ) + THRUPC(IDC,IQ) + INVNC(IDC,IQ) where: DCCST(IDC,IQ) = Total DC cost for DC,IDC for quarter, IQ -= - ............:' 305 Outbound transportation cost for DC,IDC for quarter, IQ OTBD(IDC,IQ) Inbound transportation cost for DC,IDC for quarter, IQ INBD (IDC , IQ) Communications cost for DC,IDC for quarter, IQ CMDC(IDC,IQ) Facilities investment cost allo- cated to DC,IDC for quarter, IQ FINVC(IDC,IQ) THRUPC(IDC,IQ) Throughput cost for DC,IDC for quarter, IQ INVNC(IDC,IQ) = Inventory cost for DC,IDC for quarter, IQ and: REGCST(IR,IQ) = Z DCCST(IDC,IR,IQ) IDC where: where: Total PD cost for region, IR for quarter, IQ REGCST(IR,IQ) Total PD cost for DC,IDC in region, IR for quarter, IQ DCCST(IDC,IR,IQ) IR = Region identification and: DOMCST(IQ) = Z REGCST(IR,IQ) IR Total domestic PD cost for the quarter, IQ DOMCST(IQ) Total PD cost for region, IR for quarter, IQ. REGCST(IR,IQ) 306 The sales dollars by region and domestic total used transformations of REGDOL(IR) where: REGDOL(IR) DUSF(IDU) DUSP(IDU) and: the form: 2 DUSF(IDU) + Z DUSP(IDU) IDU IDU The sales dollars QTD for all DC-DU links in region, IR Demand unit sales dollars QTD for DU(IDU) from full-line DC's Demand unit sales dollars QTD for DU(IDU) from partial-line DC's DOMDOL = 2 REGDOL(IR) IR where: DOMDOL REGDOL(IR) The calculation of The total domestic dollars QTD for all DC-DU links in the system The sales dollars QTD for all DC-DU links in region, IR. sales weight by region and domestic required transformations of the form: REGWT (IR) where: REGWT(IR) DUWF(IDU) DUWP(IDU) E DUWF(IDU) + 2 DUWP(IDU) IDU IDU The sales weight in pounds for QTD for all DC-DU links in the region, IR Demand unit sales weight in pounds for QTD for DU(IDU) from full-line DC's Demand unit sales weight in pounds for QTD for DU(IDU) from partial-line DC's. 307 and: DOMWT = 2 REGWT(IR) IR where: DOMWT = The total domestic sales weight in pounds QTD for all DC-DU links in the system REGWT(IR) = The sales weight in pounds QTD for all DC-DU links in the region, IR. The last major activity of the EOQ routine provided the link to the Report Generator System, via which the output information was passed for off-line print-out of the management reports and special analyses. The LREPS exogenous inputs required for the Operat- ing System are listed in Appendix 1. These variables were read in via the Monitor and Control routine EXOG. The final routine associated with the Gateway subfunction was the Beginning-of-Quarter, BOQ, activity which reinitialized endogenous variables for the next quarter's activity. Fixed-Time Scheduler.--The Fixed-Time Scheduler used current clock time generated within the LREPS model to schedule the next imminent event. Figure 5.27 presents the sequence of processing of the Fixed-Time Scheduler. The initial activity advances the clock time to the next day, since a call is made to the Fixed-Time Scheduler only after completion of the activities for the day, TNOW. The transformation for advancing the clock was a linear, first- order difference equation as follows: a“; ‘5 . Iii - ‘ '1." L. ‘ :- <:E?('T1Pfl) SC§:) AJHUUNCE CLOCK. 1 SCHEDULE EVENT 1 SCHEDULE EOCYC I (:RETURN :> 308 Start Fixed Time Scheduler. Processing for day complete - advance clock to next day incremental TNOW by one day. Schedule next imminent fixed-time event by comparing TNOW against fixed-time events. Schedule end of cycle event if end planning horizon. Return to EXECUTIVE ROUTINE. Figure 5.27--Flowchart: Fixed Time Scheduler a...“ 309 TNOW(ID+1) = TNOW(ID) + l where : TNCWV(ID+1) = Clock time of day, ID + l TNOW(ID) = Clock time of day, ID. Inna next activity scheduled the imminent fixed-time event by selecting the event that equaled the day TNOW(ID+1). m For example, using the calendar of 252 working days; 21 w per month, 63 per quarter, and 126 per year, if current clock time, TNOW(ID+l) equaled day 63 the fixed-time scheduler placed the quarterly event code in the event file of the Executive routine. Control then transferred to the Executive routine which first selected for processing any variable events scheduled previously for the 63rd day in FIFO order. After completion of processing of the vari- able events the Executive selected and processed the quarterly fixed time event. Once the fixed time event or variable event was called the routines which make up the events were processed. In summary, the sequence of control using the Fixed-Time Scheduler and Executive routine for each day, ID, of the simulation was as follows: 1. Compare clock time with fixed event time using the Fixed-Time Scheduler, selecting the appropriate fixed time event for the workday, ID Schedule the fixed time event for day, ID, via the Executive routine sequence file, placing the event code in the file ITansfer control to the Executive routine 6. 7. 310 Process all variable events tagged for occurrence on day, ID, in FIFO order Select the fixed time event previously scheduled for day, ID Process the routines of fixed time event Transfer control back to the Fixed-Time Scheduler, advance the clock time to day, ID+1 Repeat steps (l)-(7) until clock time is equivalent to the planning horizon at which time the End-of-Cycle event is called and processed ending the simulation cycle. Controller Function The Controller, which generated the information feed- back responses for sequential decision making, consisted of two major sets of routines: l. The set of routines that reviewed and developed the endogenous feedback responses, REVIEW: a. The routine of calculating the DC and regional sales forecast modification factors, DCSMOD b. The routine of calculating a new regional total to tracked product weight ratio for MCC shipment weight extrapolation, RWRC c. The calculation of new inventory con- trol variables and selection of new inventory management pOlicies, INVMGT d. The facility location algorithms for determining the requirement for, and scheduling any DC facility systems additions or deletions, LOCATE e. The facility expansion algorithms for determining the requirement for, and scheduling a DC expansion, EXPAND 1'... n-e- -— h..- A i..__ _A.-.. 311 2. 'The set of routines that activated any exogenously or endogenously scheduled activities for changing the PD system, UPDATE: a. The quarterly activity of implementing any scheduled DC facility additions, PUTDCN b. The quarterly activity of implementing any scheduled DC facility deletions, DELDC c. The quarterly activity of implementing any scheduled DC facility expansions, MODIFY.. Each of the above routines is presented within the con- troller function in the order listed above. Sales Modification Factors.--The routine DCSMOD calculated the DC and regional Sales Modification Factors, SMF's. These factors were used to modify sales forecast for deviations of service from the desired level. Figure 5.28 presents the activity analysis in terms of the out- puts, inputs, and transformations for the Sales Modifica- tion routine. The flowchart is presented in Figure 5.29. The first activity used the actual service in terms of the percentage of sales dollars within the established order cycle intervals, i.e., (IOT = 3,5,7,9, > 9 days) and the desired service percentage within a specified inter- \mfl.to develop the new exponentially smoothed SMF for each:hrsolution DC. The transformation was of the form: EDCSMF(IDC,IQ) = Alpha*ACDCSMF(IDC,IOT,IQ) + (l-Alpha)*EDCSMF(IDC,(IQ-1)) 312 ll.‘.‘ acessom mzm cosmmm ec< ea "unusuaosmula~.n ouawsm .uco>o mauoouqsv Houosou a uouacox co apnoea .hxm «occuwou voweuo>¢ haacuosoaonxo so: ecu arm «occuwou neon-ac uso«>oun oeo uuaasouau .co«uou some umoooum .MZm vomauo>a unanuusocoaxo so: ouensoueo .uuuwsvsu nacho nacho osu cucuua onovuo vac auaaaov mouse no ocoouon uo mason cw woouasc ago you on no.0 you ooa>uum Hasooa coausoaau .souosaoalcw um Loco cocoons .n.mzw Houseman can on uneasoaao zuahmd hxm Km Awuo\ .—I Mimics mo mwmuo>m Hmfiucmcoexm .q mrm Hmcofiwmu mo owmum>m Hmwococomxm .m mzm Hmsofimmu nuances maofi>oum .~ g DE-‘D-a C mZm .uooomu cowumofiufipoa moamm on . mesmeso him owmuo>m Hmfiucmconxm .m mHmwAw Hmwucmconx6 on oomHsono .u mZm onomm nz< on monHuom mo Ho>oH confines .q mconou coaoSHomlcw mo .02 .m m.uc cowusaomnca mo .02 .N mowmucoouoa umaaov moamm «Homo umpuo uoEOomso deuce ._ wPDmZH a < P‘< ta z.& D F and: ACDCSMF(IDC,IOT,IQ) where: EDCSMF(IDC,IQ) Alpha ACDCSMF(IDC,IOT,IQ) PCD(IDC,IOT,IQ) DSDSV(IR,IOT,IQ) EDCSMF(IDC,(IQ-1)) IOT 313 PCD(IDC,IOT,IQ)/DSDSV(IR,IOT,IQ) New exponentially smoothed sales modification factor for DC(IDC) for quarter, IQ Smoothing constant, initially set at 0.25 Actual sales modification factor for DC,IDC order cycle interval, IOT for quarter, IQ Percent sales dollars within interval, IOT for quarterly, IQ Desired service stated for initial LREPS as percent sales dollars within interval, IOT for region, IR for quarter, IQ Previous exponentially smoothed sales modification factor for DC(IDC) for quarter, IQ-l Order cycle sales interval identification. The new exponentially smoothed sales modification factor was calculated for each in-solution DC. The next activity of the routine calculated the sales modification factor for each region using accumulated sales by region within each order cycle interval to develop the percentage by order cycle interval, IOT. The exponentially smoothed regional SMF's were calculated using transforma- tion of the identical form used for the DC calculations as follows: 314 ERGSMF(IR,IQ) = A1pha*ACRSMF(IR,IOT,IQ) + (l-Alpha) *ERGSMF(IR,(IQ-1)) and: ACRSMF (IR, IOT, IQ) = PCD (IR, IOT, IQ) /DSDSV(IR, IOT,IQ) where: ERGSMF(IR,IQ) = New exponentially smoothed sales modification factor for region (IR) for quarter, IQ Alpha = Smoothing constant, initially set at 0.25 PCD(IR,IOT,IQ) Percent dollars within interval, IOT for quarter, IQ for region, IR DSDSV(IR,IOT,IQ) Desired service stated for initial LREPS as percent of sales dollars within interval, IOT for region, IR for quarter, IQ ERGSMF (IR, (IQ-1)) Previous exponentially smoothed sales modification factor for region, IR for quarter, IQ-l IOT = Order cycle sales interval identification. Regional Weight Ratio.--The regional weight ratio calculated a new regional total to tracked product weight ratio for MCC shipment weight extrapolation each quarter. Figure 5.30 presents the activity analysis in terms of the outputs, inputs, and transformations for the regional weight ratio calculation. The flowchart is presented in Figure 5.31. 131.5 ocHosom ofiumm unwed: HddOfiwox "oumnosoamnlam.m ouswwm .zuw>wuom oco>o «<30 0 a 2 cu cpsuox .mGOHmou coHusaomucH HHm swooucu moo; .cofiwwu ecu oaumu armada oumasonu .m.oo sofioaaomncu Ham swoonro noon .ucwfiws HmuOD m.cofiwou co unwfims m.uo unmanagoo< .cofiwou onu :H on coausaomnc« :omo mmoooum .cowwmu some mmmooum .owumu uswfios Hmcofiwoe 3m: ouaflaoamo on oewoaou cofiumflauamo oases unmfloz Hmcoswwm ZMDHmm OHHsuoc_ unu::swzl_, ,,.m ._;s_i ocosumccqx secoco>=~ "uaaxasc< >ua>aoou sum .m peso two“ nephew» m>q uuznuo .e Aw>e~ suooco>cs Lasoscv gospOLa tsxoeuu we .n ‘\.- . ~u>msgm ooavOua texueeo on .~ V n m.mCm oosv0ua vsxoeuu on .— .Ua ccwu3HOmncu some new Au>MAIm In. . 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The next series of activities calculated the speci- fic tracked product inventory control variables for each in-solution DC. For each DC-MCC link the average daily demand for each tracked product of the DC being processed was developed using the following transformation: ADEM(IQ,ITP) = PTPDEM(IQ,ITP) * DCWI(IDC)*NWKDYS/4 where: ADEM(IQ,ITP) Average daily demand for tracked product, ITP for quarter, IQ Predicted total demand for tracked product, ITP for quarter, PTPDEM(IQ,ITP) IQ DCWI(IDC) = Cumulative weighted index for DC(IDC) NWKDYS = Number of workdays in the year, 252. The next activity determined the standard deviations of average reorder lead time, review period, and average daily demand. The standard deviation of reorder lead time was calculated assuming the lead times were poisson distributed as follows: 1 SDLT(ITP) = AVGLT(ITP) 2 where: SDLT(ITP) = The standard deviation of lead time for tracked product, ITP AVGLT(ITP) = Average reorder lead time for the tracked product, ITP. 321 The standard deviation of the average review period length was calculated assuming a uniform distribution using the transformation: SDRP(ITP) = AVGRP(ITP)/ (12) where: SDRP(ITP) = Standard deviation for the review period for tracked product, ITP AVGRP(ITP) = Average review period length for tracked product, ITP. _The standard deviation of daily demand was calculated assuming that demand was a poisson distribution using the transformation: SDEM(ITP,IQ) ADEM(ITP,IQ) where: Standard deviation of the daily demand for tracked product, ITP SDEM(ITP) 'ADEM(ITP,IQ) Average daily demand for tracked product, ITP for quarter, IQ. The next activity calculated the buffer stock and economic order quantity, EOQ, for each tracked product for the DC being processed. The transformation for the buffer stock was: BUF(ITP,IQ) = NSD(ITP)*(SDLT(ITP))*SDEM(ITP) + ADEM(ITP,IQ) * SDRP(ITP) where: BUF(ITP) = Buffer or safety stock for tracked product, ITP 322 Factor for the number of standard deviations or level of safety desired for the tracked product, ITP NSD(ITP) The standard deviation of lead time for tracked product, ITP SDLT(ITP) The standard deviation of the daily demand for tracked product, ITP SDEM(ITP) ADEM(ITP,IQ) Average daily demand for tracked product, ITP The standard deviation of the review period for tracked product, ITP. SDRP(ITP) The BOQ was calculated using the standard EOQ formula as follows: EOQ(ITP,IQ) = ((2*PTPDEM(ITP,IQ)*DCWI*ORDCST(IDC,IQ))/ l DICC*63*CGCU(ITP))§ where: EOQ(ITP,IQ) = Economic order quantity for tracked product, ITP for quarter, IQ PTPDEM(ITP,IQ) = Predicted total demand for tracked product, ITP for quarter, IQ DCWI(IDC) = Sum of weighted index for DC(IDC) ORDCST(IDC,IQ) = Order cost for DC(IDC) for quarter, IQ DICC = Daily inventory carrying charge CGCU(ITP) = Cost of goods sold per case unit for tracked product, ITP. After calculating the buffer stock and the EOQ the next activity selected appropriate inventory policy for 323 the tracked product being processed. If the product category was assigned a reorder point policy or a hybrid system the transformations for the reorder point, ROPl were: BUF(ITP,IQ) = NSD(ITP)* SDLT(ITP)*SDEM(ITP) and: ROPl(ITP,IQ) = BUF(ITP,IQ) + AVGLT(ITP)*ADEM(ITP,IQ) where: BUF(ITP,IQ) Buffer or safety stock for tracked product, ITP, for quarter, IQ NSD(ITP) = Factor for the number of standard deviations for tracked product, ITP SDLT(ITP) = The standard deviation of lead time for tracked product, ITP SDEM(ITP) = The standard deviation of daily demand for tracked product, ITP ROPl = Reorder point level-l, used for reorder point policy and hybrid policy AVGLT(ITP) = Average reorder lead time for the tracked product, ITP ADEM(ITP,IQ) = Average daily demand for tracked product, ITP for quarter, IQ. At this time the value of ROP2 was set equal to ROPl if the product category policy was the reorder point system. If the product used the replenishment policy or hybrid system the transformation was: ROP2 = BUF(ITP,IQ) + ADEM(ITP,IQ)*(AVGLT(ITP) + AVGRP(ITP)/2) where: ROP2 BUF(ITP,IQ) ADEM(ITP,IQ) AVGLT(ITP) AVGRP(ITP) 324 = Reorder point level-2, used for the optional replenishment sys- tem and hybrid system Buffer or safety stock for tracked product, ITP for quarter, IQ Average daily demand for tracked product, ITP for quarter, IQ Average reorder lead time for the tracked product, ITP Average review period length for tracked product, ITP. If the DC was new the initial inventory was calculated as follows: where: INIV(ITP) INIV(ITP) EOQ(ITP) BUF(ITP) EOQ(ITP) + BUF(ITP) Initial inventory for tracked pro- duct, ITP - Economic Order Quantity for tracked product, ITP Buffer for safety stock for tracked product, ITP. The standard S-level was calculated for each inven- tory policy as follows: where: SLINV(ITP) SLINV(ITP) EOQ(ITP) ROP2(ITP) EOQ(ITP) + ROP2(ITP) S-level inventory for tracked product, ITP Economic Order Quantity for tracked product, ITP Reorder point level~2. 325 These activities were performed for each tracked product for each in-solution DC. After completion of these activities control was returned to the Executive routine-Review. The inventory management routine demon- strates an example of modular and universal aspects of the LREPS model since this routine should be flexible to handle the policies of a large variety of multi-product companies. The theoretical inventory management module can also be replaced by a specific heuristic inventory policy module for a particular company. This was accom- plished during initial runs of the LREPS model. Facility Location.--The facility LOCATE algorithm reviewed the need, selected the location(s), and scheduled the addition and/or deletion of DC's in the PD system con- figuration. The LOCATE algorithm included the following routines: 1. Review of domestic constraints 2. Review of regional decision rules for feasibility and priority for PD system changes 3. Process list of regions to select region for PD system change 4. Process list of DC's to select location for addition or deletion 5. Implement DC addition 6. Implement DC deletion. Figure 5.34 presents the activity analysis in terms of the outputs, inputs, and transformations for the LOCATE algorithm. 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Review of domestic constraints 2. Review of regional decision rules 3. Process list of regions to select region for PD system change 4. Process list of DC's to select DC for expansion 5. Implement DC expansion. The first routine reviewed the domestic constraints to determine if any expansion could take place. If not, the EXPAND algorithm was bypassed and control returned to the Monitor and Control Quarterly Activity. The domestic con- straints for the expansion algorithm allowed expansion if and only if the following constraints were not violated: (NMINPS < MXIPAS), and (INVSPS < MXIVPS), and (INVSTS < MXINVS) where: NMINPS = Domestic number of DC's in-process of addition MXIPAS = Maximum domestic number of DC's in-process of addition INVSPS = Domestic total dollar investment for in-process DC's MXIVPS = Maximum domestic total dollar investment for in-process DC's INVSTS = Domestic total dollar investment for in-solution DC's MXINVS Maximum domestic total dollar invest- ment for in-solution DC's. The next routine, given that the domestic constraints were not violated, checked the regional constraints. The 342 region could expand one or more of its DC's if and only if the following constraints were not violated: (INVSTREG(IR) < MXINVSREG(IR)), and (NMINPSREG(IR) < MXIPASREG(IR)), and (INVSPSREG(IR) < MXIVPSREG(IR) where: Dollar investment for in-solution DC's in region, IR INVSTREG(IR) MXINVSREG(IR) = Maximum allowable dollar invest- ment for in-solution DC's in region, IR INVSPSREG(IR) = Dollar investment for DC's in- process in region, IR MXIVPSREG(IR) = Maximum allowable dollar invest- ment for DC's in-process of addition in region, IR NMINPSREG(IR) = Number of DC's in-process of addition in region, IR MXIPASREG(IR) = Maximum number of DC's in-process of addition in region, IR. If expansions could take place in the region the in-solu- tion DC's of the region were checked to determine which if any DC required expansion. This was accomplished by first calculating the ratio of current sales to capacity for each in-solution DC as follows: SRATIO(IDC) = DCSLS(IDC)/DCCAPAC(IDC,IS) where: SRATIO(IDC) = The ratio of sales dollars to sales dollar capacity for the DC, IDC 343 DCSLS(IDC) Sales dollars for the DC,IDC for the quarter DCCAPAC(IDC,IS) Capacity of the DC,IDC of size, IS in sales dollars. This ratio was then compared to a specified ratio, LMTRATIO which was set as a management parameter by the exogenous input. A DC was defined as requiring expansion if and only if: SRATIO(IDC) > LMTRATIO(IS) where: SRATIO(IDC) The ratio of sales dollars to sales dollar capacity for the DC,IDC LMTRATIO(IS) Ratio of sales dollars to capa- city for DC size, IS at which expansion decision sould be made such as 60 percent. Each DC above the LMTRATIO was then entered in RLISTEX as a DC requiring expansion. If the list contained any DC's after all DC's were processed the DC with the largest sales to capacity SRATIO above LMTRATIO was selected and scheduled for expansion. The time for expansion was set in the same manner as the time for addition and deletion of a DC. The transformation was of the form: TNOW + TMEXP TMINEX(IDC) where: TMINEX(IDC) Day of simulated calendar when DC(IDC) expansion comes in- solution 344 TNOW = Day of simulated calendar when decision made to expand DC TMEXP = Delay time required for expand- ing DC. The domestic and regional in—process constraint variables were then updated as follows: INVSPS INVSPS + FINV(IDC,IQ) - FINV(IDC,(IQ-l)) NMINPS NMINPS + l INVSPSREG(IR) INVSPSREG(IR) + FINV(IDC,IQ) - FINV(IDC,(IQ-l)) where: INVSPS = Domestic investment in-process Capital investment for DC(IDC) in-solution at quarter, IQ after expansion FINV(IDC,IQ) FINV(IDC, = Capital investment for DC(IDC) (IQ-1)) in-solution at quarter, IQ-l before expansion NMINPS = Domestic number of DC's in- process INVSPSREG(IR) Investment in-process in region, IR. The domestic constraints were then checked to determine if any other expansions could be made in the PD system. If the constraints were not reached the routine returned to the list of candidates for expansion and to attempt to expand another DC. If the constraints were reached the control was returned to the Monitor and Control Quar- terly activity. Implement DC Addition.--The last set of routines of the Controller were the Update routines. These routines 345 implemented the scheduled changes to the PD system. The first routine within the Update Function of the Controller was the quarterly routine of implementing any scheduled DC facility addition, PUTDCN. Figure 5.38 presents the activity analysis in terms of a DC addition. The flow- chart is presented in Figure 5.39. The first activity checked to determine if it was time for the DC to come in-solution. The DC was brought in-solution if and only if: TMINDC (IDC) TN OW where: TMINDC(IDC) = Day when DC(IDC) now in-process was scheduled to come in-solution TNOW Current work day of simulated calendar. Assuming that the DC was due to come in-solution the next activity updated the following in-solution variables using linear, first-order difference equations: NUMDCS = NUMDCS + 1 NDCREG(IR) = NDCREG(IR) + 1 INVSTREG(IR) = INVSTREG(IR) + FINV(IDC) INVSTS = INVSTS + FINV(IDC) where: NUMDCS = Domestic total number of DC's in-solution NDCREG(IR) = Number of DC's in-solution in region, IR 34465 cosssee< ea uceaosasm "upmcuzosm--om.m assess ucu>m mumm cmo use“ m.oa msssmmmu Co sass vascmu use :9 some mmoooum sadness ImMEOt tam seamco«mmu I totem mewmb mo mmoooueucfi m.oo mo Cohen: oospom 3028 um poocosofiasq meson on some ecu moabmeua> we cofiusflomncfi women: can onfifimfiuwcH 302s om 30c soHusHOmucH osoo cu we mmmo0pnucw on «H ocfisumomp co xoono oceoaou cofiomucosofinsfi cofiufippm on zmzhmx Do zon m.Ua m0 emu; omxz mmmuoxmlzu wusomx H mm<> on mHfiooofilm uosvoua poxomuo on .HH ocoaumo>cw mmooouanca oaumoaoa .oH ucoaumm>=a so«o=HomI:« oaomosoa .o m.oo mmoooueucu mo .0: Son .w m.oo cowosaomlca «0 .oc mom .n ucosumo>ca mmmooualcfi deceamom .o ucosumo>c« coaosaomnca Hmcofiwox .m ppmnnm.oa mmooouaucu mo .0: sum .q nonsuoa on cofiosaomucH .m moanmfiun> on coeusaomncH .N m.uo coeusaomuca No .02 .H mmmmmmm pooomaom on ceau3H0mncfi omen Hausa n.0o odbfimmou wo umfia no us» c« on some mmoooum .m so some mmoooum .s moabnfium> mmoooueucw museum .m on mcwaoo:a no“ moabmwum> on newosaomch women: can onwamaoucH .N tween on an on we onesewoop cu xooso .H mone:u w>< .o owcmgo onus + omcmzo on mo mass .m moamm umHHop w>m axe on .n ucmscwammm com + mesa on .o mofiuwomamo onwm on .n muospoun poxUMHu mo .0: Hmuoa .q m.:o on p.09 oabwwmou wo uqu .m m.=o «0 .oc Annoy .N 30:9 .oEau poumasaam we see .H mHDLZH onHHQo< . J i _ m m _ on HzmzmAAXH ' p...- L < T . “-fl 347 Dollar investment for in-solution DC's in region, IR INVSTREG(IR) Domestic total dollar investment for in-solution DC's. INVSTS The next activity reduced the necessary domestic and regional in-process variables using linear, first- order difference equations of the form: NMINPS = NMINPS - l INVSPS = INVSPS - FINV(IDC) NMINPSREG(IR) = NMINPSREG(IR) - l INVSPSREG(IR) = INVSPSREG(IR) - FINV(IDC) where: NMINPS = Domestic number of DC's in-process of addition INVSPS = Domestic total dollar invest- ment for in-process DC's NMINPSREG(IR) Number of DC's in-process of addition in region, IR Dollar investment for DC's in-process in region, IR. INVSPSREG(IR) The remaining activities of the routine linked each DU to the best insolution DC that could serve it. The basis for selecting the best DC was a heuristically pre- determined ranked list of DC's that could feasibly serve the DU being processed. Each of the feasible DC's for the DU starting with Rank 1 or best, was checked against the list of in-solution DC's until a match occurred. The DU was then assigned to the matched DC for service for the forthcoming quarter(s). 348 Implement DC Deletion.--The next major Update routine presented is the deletion of DC's from the PD system con- figuration. Figure 5.40 presents the activity analysis in terms of the outputs, inputs, and transformations for deletion of in-solution DC's the DELDC routine. The flow- chart is presented in Figure 5.41. The routine consisted of reducing the in-solution and in-process variables. The form of the difference equations for these trans- formations were previously presented for bringing a DC in-solution, PUTDCN. The final activity of this routine deleted the DC's remaining inventories-on-hand and assigned any outstanding stockout commitments to the regional PDC. Implement DC Expansion.--The activity analysis for implementation of the DC Capacity Expansion routine, MODIFY, is presented in terms of the outputs, inputs, and transformations in Figure 5.42. The flowchart is pre- sented in Figure 5.43. For this routine if the current time, TNOW, was the scheduled time for expansion the DC size indicator was incremented to the next appropriate size interval. The next activity reduced the domestic and regional in-process variables, number in-process and investment in-process. The in-solution variables invest- ment for the region and domestic were increased to reflect the larger capacity size interval DC. 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The MCC-DC Weight Accumulation Report consisted of a report for each MCC(IMC) which served as a supply point for the given DC(IDC). Each report contained the follow- ing information for each quarter the DC was in-solution: l. MCC(IMC) supply point being reported 2. Quarter (IQ) being reported 3. Weight accumulated in each of the weight break intervals: 2000 i 5000, >5000 : 24,000, and >24,000 pounds. 366 Report Generator System Summagy This chapter, the Report Generator System, presented the basic information output content, frequency, and for- mats developed for the initial LREPS model. In addition an initial measure of the target variable flexibility- robustness was presented. The final chapter considers the results and implications for future research. CHAPTE R VI- -FOOTNOTE REFERENCES lBowersox, et al., Monograph. 2Marien. 3Bowersox, et al., Monograph. 41bid. 367 CHAPTER VII RESULTS AND IMPLICATIONS Introduction This chapter presents in two sections the results and implications of the formulation of the LREPS mathe- matical model. The first section discusses the results in terms of the relative achievement of the design cri- teria previously defined in Chapter I. The implications for future research are presented in the second section. Results Relative to Design Criteria The design criteria, stated in Chapters I and III, were defined in terms of the following three categories: 1. General research criteria a. Modular construction b. Universal model application 2. Physical distribution problem criteria a. Total physical distribution system b. Long-Range planning horizon c. Sequential decision problem 368 369 3. Model operating criteria a. Operating time b. Operating capabilities c. Operating realism d. Operating input requirements General Research Criteria The concepts Of modular construction and universality were defined in Chapter III. The development of the LREPS mathematical model to achieve these concepts was considered a primary objective in the research project. Modular Construction.--The purpose of modular con- struction was twofold. First, it allowed the design, construction, and implementation of the LREPS model in a series of steps. At each step additional modules and more sophisticated modules were implemented and tested until the total LREPS model was operational. Second, once designed the modular construction provided the flexibility of modifying the LREPS model via substitution of various modules without redesign, reprogramming, or change in the data base. The criteria of modular design was achieved in the development of the mathematical model as illustrated by the following two examples. First, parallel development of the subsystems, components, and activities was possible after the input-output requirements for the activities of each subsystem were defined. The LREPS model was then 370 constructed and implemented using the activities as building blocks or modules.l Second, the LREPS model as formulated contains numerous modules which by simple substitution and essentially no reprogramming can be replaced by modules with different transformations but requiring the same information input and capable of generating the same information output. Examples of activities where more than one module option was imple- mented included the: 1. Locate algorithm 2. Inventory management routine 3. Order file generator. The first modules implemented for the locate algorithm added DCs at fixed time intervals in the sequence presented in a fixed list of potential loca- tions. The second algorithm allowed exogenous addition and also included decision rules for adding DCs via information feedback loops. The third algorithm allowed addition and deletion via both the monitor and control exogenous routine and the information feedback control loop--the locate algorithm. The inventory management routine was implemented with two modules. For the first module safety stocks and economic order quantities were developed by heuristic ,management rules whereas the second used the standard inventory EOQ formulation. Both modules used the inven- tory policies presented in the Monitor and Control Subsystem, Chapter V. 371 Two modular options were implemented for the Order File Generator. Option 1 included only actual customers in the order file whereas Option 2 also included pseudo orders and pseudo customers. The above discussion illus- trates a partial list of activities where more than one option has been implemented. Universal Model Application.--The concept of univer- sality, also defined in Chapter III, referred to the applicability of the model to a broad range of firms that fit the general system audit and structure of Figures 1.1 and 1.2. The final test of the achievement of this design criteria will be the application of the LREPS model to a number of manufacturing firms in dif- ferent industries and/or to a number of divisions in the same firm. However, there are a number of general areas that illustrate the relatively high degree of universality that has been achieved for application of the LREPS model to manufacturers of consumer packaged goods. These areas include: 1. Performance or target variables 2. Market profile 3. ’Product profile 4. Physical distribution system profile. The basic target variables of sales, cost and ser- vice are common to all total physical distribution sys- tems. Each of these variables was classified as a target variable in the LREPS model since the model can be run 372 to search for the set of system configurations over time that maximum sales, maximize service, or minimize cost. The model does not produce the optimum system configura- tion given the objective or desired level of the target variable(s) but using manual or computer search techniques it is feasible to obtain a near optimum or satisficing solution for the given level of input factors and decision rules. The scope of the individual measures of these target variables and the flexibility with which addi- tional measures can be included in the LREPS model illus- trates the relatively high degree of achievement of uni- versality in terms of the performance measures. Two of the important areas related to the degree of universality of the market profile factors are the demand unit structure and the procedure for generating customer demand. The demand unit selected for the initial version of LREPS, the Zip Sectional Center, should itself be somewhat universal for consumer packaged goods. However, the modular development of the model would also allow the use of any of the demand units evaluated in the Supporting Data System--Demand and Environment. These included the county, Standard Metropolitan Statistical Area (SMSA), the state, and the economic trading area (ETA). The LREPS model currently includes the capability for generating demand based on existing customer types and existing order statistics such as average dollar 373 size, weight, lines, cases, and cube via the Order File Generator. The pseudo order matrix portion of the Order File Generator allowed the incorporation of any desired percentage of sales to be generated from new or pseudo customers with existing or different order statistics. The percentage can be set to change over the simulation cycle to reflect the change in customer split via the Monitor and Control Subsystem--Exogenous Routine. This flexibility of the demand unit and options for defining and generating customer demand illustrates again the universal nature of the basic LREPS model. The product profile factors are also important if the model is to be considered universal. In the LREPS model existing products are included in the tracked product list in one of several product categories used for inventory control. Additional new or existing pro- ducts can be added in the existing categories or in new product categories up to a total of fifty products and ten product categories. The product attributes used in the simulation are universal in that only characteristics such as units per case, weight per case, cube per case, freight rate per cst, and so on are required in the transformations. Therefore, the effect of new products can be added and tested relatively easily. The profile of the PD components is also important to the universality of the LREPS model. The inventory policies included in the LREPS inventory management 374 routine reorder point, optional replenishment, and a hybrid combination of reorder point and replenishment should be applicable to the majority of manufacturers of consumer packaged goods. The inventory component also has the flexibility of multiple categories of pro- ducts such as by usage, density, freight classification, and value. The number of tracked products can be varied from one to fifty without reprogramming. Each of the above attributes adds to the universality of the LREPS model. The transportation component included_the capability to simulate the various modes, average transit times, and reliability of transit times via concentric circle ring sets and variance functions. The tranSportation network included the outbound, DC-DU and inbound, MCC-DC links. The capability also exists in the model to simulate the direct transportation link from replenishment center to demand unit, RC-DU for consolidated shipments. These transportation links are common to many of the manufacturers of consumer package goods. Transportation links which the LREPS currently does not explicitly include, but which can be included via adjustments of cost and transit times are the crossshipments between two DC's and two MCC's. The communications component included the capability for simulating various modes, average time delays, and reliability via concentric ring sets and variance func- tions. The network explicitly includes links for order 375 transmittal time from demand unit to distribution center, DU-DC, and distribution center to replenishment center, DC-RC. The communication links for centralized demand unit to the central location, and regional, demand unit to regional PDC can be simulated implicitly via the time delay ring sets and variance functions. The facility network component was restricted in the number of MCC's, PDC's, and DC's that could be in-solution at any one quarter. The current limit for simulating the continental U. S. is five MCC's, five PDC's, and twenty DC's. The modular development of the model does allow the maximum limit for any one of the regions when the region is run separately. The limits of the number of locations therefore does not greatly reduce the universality of the model. The Locate algorithm should prove to be extremely flexible in terms of universal application since the DC's can be added or deleted by exogenous input or via dynamic feedback con- trol loops based on comparison of actual to desired service, and/or cost. The unitization component included the capability to simulate a range of DC sizes, a range of levels of automation, and partial-line and full-line DC operations. The expansion algorithm allowed the expansion of any in-solution DC to a larger size interval based on the ratio of actual DC operating volume in terms of sales dollars to the capacity limit designated for the DC size interval. 376 The above discussion indicates that the general research design criteria were essentially achieved in the LREPS mathematical model. Physical Distribution Problem Criteria The physical distribution problem criteria relate to the stated requirement of Chapter I that the mathe- matical model consider: 1. The total physical distribution system 2. A long-range planning horizon 3. The sequential decision problem. Each of these design criteria was given primary emphasis in developing the LREPS mathematical model. Total PD System.--The total physical distributiOn system as defined in this research included the inter- related activity centers or components from the produc- tion line to the point of ownership transfer. These components were defined as the distribution facility network, inventory allocations, transportation, communi- cations, and unitization. The LREPS mathematical model in both the Supporting Data System and the Operating System listed the desired outputs, the required inputs, and the selected transformations for each of the elements of these components. The presentation in Chapter V of the transformations for the activities for each of the physical distribution components and the demonstration of the scope of the information content of the reports as presented in 377 Chapter VI indicate the high degree of achievement of this particular design criteria. As indicated in the Literature Review, Chapter II the criteria that the model consider all of the compo- nents of the physical distribution system essentially required that the general solution be one of simulation rather than an analytical or optimum technique. The development of a total PD model also required that the service variables be developed in terms of temporal measures such as the average and standard deviation of the customer order cycle. Long-Range Planning Horizon.--The long-range plan- ning or strategic planning horizon can be defined in terms of a generally accepted fixed time period such as five years or ten years, or by a variable time period dictated by the expected rate and significance of technological and marketing environment change in the industry. For example, long-range planning in a highly innovative industry or firm could be as short as two years, whereas in the firm or industry with little innovation long-range planning might be defined as greater than ten years. The initial LREPS model has been designed to simulate forty quarterly periods of Operating time and thus includes a ten year planning horizon which is sufficient duration to be classified as a long-range planning model. The model also has the capability of simulating a forty year horizon if each period is designated as one year. 378 This design criteria required that the LREPS model contain the capability for introducing change in the marketing environmental factors. This was accom- plished by introducing the appropriate factor levels prior to the beginning of each operating period, quar- terly or yearly, via the Monitor and Control Exogenous Routine. Examples of factors that were modified quarterly or annually to reflect the changing market environment included but were not limited to: 1. Sales forecast by demand unit 2. Transportation rates 3. Desired service levels by region 4. Customer split percentages for each customer type 5. Product mix 6. Safety stock factor and inventory policy designation for product categories 7. Desired constraint levels and decision rules for Locate and Expansion algorithms. This approach is one of the two important areas of model dynamics described in Chapters I and II. The second area of dynamics, the information feedback control loops, is discussed in the next section. Sequential Decision Problem.--The sequential decision problem as defined in this research has the property that future decisions are influenced by pre- vious decisions. A solution approach to the sequential decision problem as indicated by the Literature Review, 379 Chapter II, is the dynamic simulation model that incor- porates information feedback control lOOpS. This was the primary role of the control function of the Monitor and Control Subsystem. As presented in Chapter V the initial LREPS model contained the following four major examples of information feedback control loops: 1. The location algorithm 2. The inventory management routine 3. The expansion algorithm 4. The sales modification routine. Each of these algorithms or routines is defined as a first order information feedback control loop in that each includes a sensor to detect the existing system state, a comparator to measure the difference between actual and desired system state, and an effector to cause the desired system change. The Locate algorithm is sequential in that deci- sions at any given time TNOW, related to the addition of a potential DC or the deletion of an in-solution DC effect the location decisions at any time TNOW plus A time in the future. As stated in the Monitor and Control Subsystem this influence was accomplished via an infor- mation feedback control loop. The Locate algorithm detects the calculated actual service in terms of the order cycle time (the Sensor) and compares this to the desired service level (the Comparator). The deviation between the actual and desired is then used 380 to set the priorities for system change by region (the Effector). Finally, the algorithm selects the DC loca- tion to be added or deleted. The inventory management routine likewise was developed to consider the sequential decision problem. At the end of each simulated day, TNOW, the inventories- on-hand (system state) is checked (the Sensor). The system state is compared to the reorder point or review period at which a decision must be made to reorder (the Comparator). If a decision state has been reached or triggered a replenishment order is generated (the Effector) to modify the future system state. The expansion algorithm also illustrates an example of the use of information feedback control loops to solve the sequential decision problem within the LREPS mathe- matical model. The measured level of throughput for each DC at the end-of-quarter (the Sensor) compared against the upper limit or capacity for efficient operation of the DC (the Comparator) determines the need for expansion. The deviation from the desired system state serves as the basis for establishing the priority of selection of the appropriate DC for expansion (the Effector). The adjustment of the sales forecast to reflect the surplus or deficiency of service relative to the desired level represents the fourth and final area of the sequen- tial decision problem to be presented in this thesis. The actual level of service in terms of the percent of 381 sales or orders within a designated order cycle time interval (the Sensor) was compared at the end of each month to the desired percentage (the Comparator). The surplus or deficiency of service was then used as the basis for increasing or decreasing the next period sales forecast (the Effector). The modification of sales of the DC as the result of poor service for example, lowers the sales dollars which were receiving the poor service (longer average service times) thus decreasing the aver- age service time of the region. This in turn improves the actual to desired service ratio. Therefore, the future values of both the sales modification factor and sales are influenced by the current value of the SMF factor. Although each of the above has been presented as an independent information feedback control loop they are interdependent since the decisions for any one control loop in any given quarter effect the future quarter deci- sions of each of the remaining information control loops. These routines and algorithms are examples of the second major aspect of a dynamic simulation model as discussed in Chapters I and II. In summary the above discussion indicates that a high degree of achievement of the physical distribution problem criteria has been obtained in the LREPS mathe- matical model. Each of the components facility network, inventory, transportation, communications, and unitization 382 has been modeled in LREPS thus achieving the design cri- teria that the model include the total physical distribu- tion system. The develOpment of the model to simulate ten years of Operation with the capability of changing the environmental input factors essentially achieves the criteria for a long-range planning horizon. The sequential decision criteria is achieved via development of first order information feedback control lOOps. Model Operating Criteria The Operating criteria or attributes of the LREPS model included the model operating time, the model capa- bilities, and the realism of the model. Operating Time.--The LREPS Operating limits were established in terms of the computer time required to simulate a complete ten year planning horizon. Due to the necessary tradeoff of computer core and computer input/ output requirements the desired operating limit of thirty minutes was not achieved. The actual operating time for a ten year planning horizon required between one hour and one and a half hours depending on the assumed rate of growth of the sales forecast.2 Operating Capabilities.--The desired model capabili- ties, presented in Figure 1.5, in terms of the target, controllable, and uncontrollable variables were essenti- ally achieved as indicated by the activity analyses discussed in Chapters IV and V and the scepe of the output presented in Chapter VI. 383 Operating Realism.--To comment in detail on the realism of the LREPS model requires a complete analysis of the validation results, which was not Completed at the time of preparation of this thesis. In general, however, analysis of the results of the simulation of the reference operating period, 1969 indicated that the critical variables were within acceptable limits. Table 7.1 presents a partial list of the variables included in the validation analysis of the reference year. Operating Input Requirements.--One of the important aspects of the LREPS model is the input information con- tent and required frequency of update. The content of the input information is illustrated to a great extent in Chapter IV, the Supporting Data System and in Appendix 1 which lists the variables. The frequency of updating the input data is a difficult question to answer at this time. There are, however, many variables which a user would have to catalog to ensure that periodic review is conducted on the more critical input variables. For example, transportation could easily account for a large fraction of the total cost of a large distribution system. Therefore, the freight rates might have to be reviewed and changed annually. The invoices used to create the order file generator quite possibly might have to be modified each year to be representative of the changes in the customers TABLE 7.l.--One-Year Validation Results. 384 Information Simulated Versus PD Category Actual Stages Cust Sales Within Limits DU, DC and Within Limits domestic Cust Dollar Sales/Order Within Limits DC and Domestic Cust Wt Sales/Order Within Limits DC and Domestic Line Items per Order Within Limits DC and Domestic Cust Serv-- NOCT-Avg Within Limits DC and Domestic NOCT-Std Dev NO Data Avail. DC and Domestic T4-Avg Within Limits DC and Domestic T4-Std Dev No Data Avail. DC and Domestic Dollar—Preps No Data Avail. DC only Order Preps Within Limits DC only DC-MCC Within Limits DC only Reorder Within Limits DC only Within Limits DC only Within Limits DC only DC Stockouts No Data Avail. DC only No Data Avail. DC only DC Avg IOH Within Limits DC only Cust ship Difficult to DC and Domestic Accums Compare Because of Small Sample Averages in Cust Order Blocks MCC Ship Within Limits MCC only Accums Total Pred Within Limits Domestic only Demand PD Cost Within Limits DC and Domestic Within Limits Within Limits Cum Wt Sales Alloca- DU, DC and Indices tion Basis Regional Within Limits 385 purchasing patterns. In general the cost factors might all have to be reviewed much like inventory control using either a yearly or quarterly review of the cost levels or updating the values whenever a significant change occurs. To prevent the "GIGO" problem of "Garbage-In-Garbage-Out" a standard operating procedure for updating and logging all input data changes is absolutely essential if the model is to remain a viable management tool. Implications for Future Research The implications for future research are defined in terms of the following categories: 1. Enrichment and simplification of the activities within the existing sc0pe of the LREPS model 2. Expansion of the LREPS scepe for distribution systems 3. Expansion of the LREPS scope for manufacturing systems 4. Evaluation of the LREPS model for public systems. Each of these categories is briefly discussed in the order listed above. Enrichment and Simplification.--There are a number of actiVities within the existing LREPS model that should be evaluated for either enrichment or simplification. Enrichment as stated in Chapter III implies further sophistication and possibly greater detail for the activity whereas simplification implies reduction in 386 complexity of the transformations and detail for the activity. A partial list of the activities that should be evaluated for possible enrichment due to their critical nature includes, but is not limited to: 1. 10. The transit time transformations- evaluation of the use of regression equations The locate algorithm-evaluation of the use of linear programming The sales modification routine- evaluation of a feedback control loop with lag and better methods of initialization of the DC-SMF's The shipping policies-evaluation of different policies in effect simultaneously at different dis- tribution centers The partial-line distribution centers- evaluation of different product cate- gories for different partial-line distribution centers The limits on the number of MCC's and PDC's-evaluation of increasing the maximum number of allowable MCC's and PDC's for the total model and the regional model The throughput and communications cost components~evaluation of regression equations for the cost transformations for these components The facilities cost component-evaluation of the use of the time value of money, the uniform annual equivalent series for the fixed investment cost The effect of a greater number of tracked products-evaluation of the use of a larger sample of tracked products The measures of flexibility-robustness- evaluation of additional measures of physical distribution system flexibility 387 11. The improvement of Report Generator System output formats-evaluation of additional output formats including plotting routines for the results of the simulation runs. A partial list of the activities that should be evaluated for possible simplification to reduce the running time of the model includes: 1. The use of a larger basic time unit- evaluation of the use of a larger time unit such as the week rather than the current time unit, the day 2. The use of a larger order block and/or order group-evaluation of the use of larger order or group blocking factors 3. The use of regional modules as the simulation model-evaluation of the use of regional modules that could be run separately from the total domestic LREPS model 4. The use of a smaller number of tracked products-evaluation of the sensitivity of the results to a smaller number of tracked products. Each of the above areas should be evaluated to determine the effect or sensitivity of model results for the recommended areas of simplification and enrichment. Expansion of LREPS Scope for Distribution Systems.-- There are a number of areas of future research that would test the universality of LREPS for physical distribution systems. First, the model based on the results reported in this chapter indicated that the LREPS model should be universal for physical distribution systems of manufac- turers of consumer packaged goods. This, however, has yet to be tested. Second, the application of the LREPS 388 model to physical distribution systems for manufacturers of industrial products presents interesting prospects for future research. Third, and finally the application to pure distribution systems such as warehouse systems, supermarket chains, and shopping center chains also seems feasible. These three areas represent only a sample of the possible applications to test the universality of the LREPS model for planning of physical distribution systems design. Expansion of LREPS Scepe for Manufacturing Systems.-- The LREPS model should be evaluated to determine the feasibility of modeling additional functions related to manufacturing systems. First, expansion of the model horizontally to include unit inventory control and production capacity considerations at the manufac- turing control centers would increase the scope to a production-distribution model. A second additional application that would increase the scope is the use of the LREPS concept to develop a strategic planning model for input materials systems design. The model would provide the capability to assist in strategic planning of integrated input materials system which include components such as purchasing, inventory control, warehouse location, transportation, communications, and warehouse operation for raw materials and/or component parts. 389 The third application involves expansion of the scepe of the model vertically to either a higher level to become part of a total corporate planning model or to a lower level to assist in operational planning. The fourth and final application suggested at this time is expansion of the scope of the model to combine parallel Operations, for example the physical distribution opera- tions of several major divisions within a single corporate structure. Evaluation of the LREPS Model for Public Systems.-- The components included in the LREPS model also exist in non-manufacturing problems where demand is stated in terms of service rather than a product. The LREPS model could conceivably be applicable to the following strategic planning problems of the public sector: 1. School systems 2. Solid waste disposal facilities 3. Airport systems 4. Fire station systems 5. HOSpital systems 6. Equipment pools. In the above situations the demand unit would probably be stated in terms of smaller units than the zip code. Examples of possible demand unit structures for the above systems might include subdivisions, politicial divisions within counties, street boundaries, individual households, or any special grid system developed for a 390 specific problem. The product demand could be stated in terms of pseudo products (service). An example of the demand for service for the school systems could be the number of student classroom hours required for each grade per term by each subdivision or demand unit. The demand for service for the solid waste disposal system could conceivably be stated in terms of the volume requirements per category of waste per day by demand unit. In each of these situations the objective of a LREPS type model would be to aid in strategic planning including but not limited to the amount of resource or service units to stockpile for future demand (Inventory Control), and where to stockpile the service (Location Component). Results and Implications Summary The results presented indicate that the LREPS model has successfully combined and reported possibly for the first time a model which includes all of the physical distribution components, a strategic planning horizon, and the sequential decision process. I The implications of the model are even more excit- ing. The entities and components included in the LREPS model could enable the model to be truly as general as the title implies--Long Range Environmental Planning Simulator. In theory the model should be applicable to any problem that involves the following: 391 l. The inventory problem where there is a cost of holding the resource and the future demand for the resource is uncertain (the Inventory Component) 2. The number of inventory nodes is a decision variable over time (the Location Component) 3. The cost of holding and processing the resource at the inventory node is significant (the Warehouse Component) 4. The movement of the resource and the transmittal of information requires a cost in dollars and/or time for the demand units acquiring the resource at the inventory node and for the inven- tory node replenishment of the resource (the Inbound and Outbound Transportation Component, and the Communications Com- ponent) 5. The demand for the resource exists in either its original form or in pro- cessed form (the Demand Unit and Demand Allocation) 6. The objective of the system is to pro- vide the resource to the demand units in terms of an acceptable average and variance of the availability and cost of the resource. The doctoral program in general and the development of the LREPS research project in particular has provided significant challenge and reward. The implications of this research and the ideas for future research generated throughout my doctoral program and the LREPS project research present an equal if not greater challenge to apply these models and concepts to operating systems in business and society. CHAPTER VI I --FOOTNOTE REFERENCES lMarien. 392 SELECTED BIBLIOGRAPHY Ackoff, R. L. Progress in Operations Research. Vol. 1. New York: John Wiley & Sons, Inc., 1961. Agin, Norman. "A Min-Max Inventory Model." Management Science. Vol. 12, no. 7. Providence: The Institute of Management Sciences, March, 1966. Ansoff, H. Ingor and Slevin, Dennis P. 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Planet: Part IV--Depot Repair and Overhaul Simulator. Santa MoniCa: The Rand Corporation, 1968. Voosen, B. J.: Glaseman, 8.; Young, R. J.: and Judd, J. Planet: Part V--Reports and Analysis Libragy. Santa Monica: The Rand Corporation, 1969. Wagner, H. M. Principles of Operations Research. Engle- wood Cliffs: Prentice-Hall, Inc., 1969. APPENDIX 1 VARIABLES LIST1 1Extracted from E. J. Marien, "DevelOpment of a Dynamic Simulation Model for Planning Physical Distribution Systems: Formulation of the Computer Model" (unpublished dissertation, Michigan State University, 1970). 400 DLT = THE FREQUENCY WITH WHICH THE INFORMATION IS ALTERED C=CYCLIC Q=QUARTERLY A=ANNUALLY D=DAILY TYPE = AN INDICATOR OF SOURCE X=EXOGENOUS N=ENDOGENOUS M-C, OPS, D-E, MEAS = ABBREVIATIONS FOR THE SUBSYSTEMS S=THE PARTICULAR SUBSYSTEM SETS OR ALTERS THAT DATA U=THE SUBSYSTEM USES THE DATA BUT LEAVES IT UNCHANGED DEMAND UNIT INFORMATION VARIABLE DESCRIPTION DLT TYPE M-C OPS D-E MEAS PROPORTION OF SSD#S C X U U X COOR, C X U Y COOR, C X U WEIGHTED INDEX A X U SERVICE RING NO,S Q N S U CUM, WTD INDEX Q N S U DC IN SOLUTION PTR(l-20) Q N S U U U $ SALES EXP. AVE. Q N S WT. SALES, EXP. AVG. Q N S HIWAY DIST. Q N S U 5 SALES, QTD. FULL LINE D N S S $ SALES, QTD. PART LINE D N S 8 WT. SALES, QTD. FULL LINE D N S S U WT. SALES, QTD. PART LINE D N S S U POTENTIAL DISTRIBUTION CENTER INFORMATION VARIABLE DESCRIPTION DLT TYPE M-C OPS D-E MEAS X COORDINATE C X U Y COORDINATE C X U A COEFF.-OBT REG EQ C X U U B COEFF.-OBT REG EQ C X U U Rl-REAL RATE INC. C X U U RZ-REAL RATE INC. C X U U TYPE-P,F,RDC*PDC ASSIGN. Q X U U U U EXP AVG. SALES, $ Q N S EXP AVG. SALES, WT Q N S 401 402 IN SOLUTION DISTRIBUTION CENTER INFORMATION VARIABLE DESCRIPTION DLT TYPE M-C OPS D-E MEAS BACK ORDER PENALTY TIME POTENTIALDC, IN SOLUTION NO. OF DUS IN DC SALES MODIF. FACTOR SUM OF DU WIS TOTAL COST FOR QUARTER AVG. TOT. ORDER CYCLE TIME QTRLY $ SIZE IND NORMAL Av. OCT,S(T1+T2+T4) ST. DEV., S(T1+T2+T4)**2 OBT, AV.T4+S(T4) ST. DEV., S(T4)**2 CASE UNITS BACK ORDERED AVG STOCKOUT DAYS,S(DELAY STD DEV STOCKOUT DAYS,S(S $ SALES, QTD WT SALES,QTD CUBE SALES, QTD CASES SALES, QTD LINES SALES, QTD ORDERS SALES, QTD. CCGC UUUUUUUUUUUUUOOOOOOOO ZZZZZZZZZZZZZZZZZZZZZ mmmmmmmmmmmmmmmmmmmmm mmmmmmmmmmmmmc CCCCCCUDUJUJUJCDCDUJCCDU) REGIONAL INFORMATION VARIABLE DESCRIPTION DLT TYPE M-C OPS D-E MEAS MAX. ALLOW, DCS MAX. ALLOW, DCS ADDED MAX. BEING DELETED QTD TRACKED PRD WT SALES DESIRED SERVICE MAX. ALLOWED $ INVSTMNT MAX. ALLOWED INVSTMNT ADD. SUM DC WEIGHTED INDICES NO. DCS BEING ADDED NO. DCS BEING DELETED DC INVESTMENT $ DC INVST, $ BEING ADDED ACTUAL SERVICE--LAST QTR ACTUAL SERVICE--EXP AVG-SMF RATIO-ALL/SAMPLE PROD LBS TOTAL PD COST MCC SHIP DISP POL--DAYS REORDER COST--MCC NO OF DCS IS PER REG OOOOOOOOOOOOOOOOOOO XXXZZZZZZZZZXXXZ’xXX CCCWWCDMCDMIDUJCDCCCMCCIC} C'. 403 DC--MCC LINK INFORMATION VARIABLE DESCRIPTION DLT TYPE M-C NO. REORDERS MULT PROD S REORDER LEAD TIME ACCUM. S NO. REORDERS OUTSTANDING TOTAL WT ON ORDER+ SDP IND 22222 D D PRODUCTS ON ORDER IND. D D D PRODUCT INFORMATION BY CATEGORY VARIABLE DESCRIPTION DLT TYPE M-C INV SHIP CAT. (RDC—P) C x U TOTAL NO. PRODUCTS C x U INVENTORY POLICY Q x U REVIEW PERIOD LENGTH Q x U SAFETY STOCK FACTOR Q x U PRODUCT INFORMATION BY DC VARIABLE DESCRIPTION DLT TYPE M—C REORDER POINTS 1 AND 2 Q N S S LEVEL Q N S INVNTRY ON HAND OVER TIME D N s INVENTORY ON HAND D N S PRODUCT STOCKOUT DAYS D N PRODUCT CATEGORY INFORMATION BY VARIABLE DESCRIPTION DLT TYPE M—C NUMBER STOCKOUTS D N S NUMBER REORDERS D N S CU-DAYS-STOCKOUTS D N S CASE UNITS SOLD D N 3 OTHER VARIABLES VARIABLE DESCRIPTION DLT TYPE M-C CGS/CASE BY PRODUCT C x U CUBE/CASE BY PRODUCT C x U WT/CASE BY PRODUCT C x U A, OBT RATE MODIFIER—R3 C x U B, OBT RATE MODIFIER-R4 C x U LINKED PROD SOURCE C x U WT BREAKS FOR MCC C x U OPS mmmmm OPS CC C: OPS (DCDUJCIC DC OPS (DCDUJCD OPS D-E MEAS U S D-E MEAS U D-E MEAS S D-E MEAS S S S S D-E MEAS U U U U U 404 OTHER VARIABLES--Continued VARIABLE DESCRIPTION DLT TYPE M-C OPS D-E MEAS WT BREAKS FOR DC U FEASIBLE DC ASSGN., PRIOR ORDER BLKS PER GRP SPLIT COST OF LIVING FACTOR DC CAP, CONSTRAINT BY SIZE FREIGHT RATES REG COMM COST FACTORS DOM COMM COST FACTORS REG CUST $ SPLT PCT-S,H,P PDC, THRUPUT COST BY SIZ RDC-F, THRUPUT COST BY SIZ RDC-P, THRUPUT COST BY SIZ PDC, COMM. COST BY SIZE RDC-F, COMM. COST BY SIZE RDC-P, COMM. COST BY SIZE PD COMP, IN SOL DC COST WEIGHT CLASS ACCUM. SHIP. CAT. WT. BREAKS TOTAL PROD DEM-QTD TOTAL PROD DEM-EA SCH DAY--EVENT ARRAY SERVICE TIME VAR FNS NO. SAMPLE PRODUCTS NO. OF CATEGORIES NO. DUS BEING PROCESSED NO. REGN BEING PROCESSED DAILY INV CARRYING CHARGE MAX INVESTMENT IN DCS MAX BEING DELETED NO. SIMULATED WORKDAYS, YR DELAY TO ADD RDC-F DELAY TO ADD RDC-P DELAY TO ADD CSP DELAY TO DELETE RDC-F DELAY TO DELETE RDC-P DELAY TO DELETE CSP TOT AN DOM SALES FORECAST YEAR OF SIMULATION MAX. SHIP. SIZE FOR CONS. CUST. SHIP. DSPTCH PERCT. MAX NO. DCS ALLOWED MAX NO. BEING ADDED MAX INVSTMNT IN PROCESS NO. DCS BEING ADDED INVSTMNT IN DCS IN SYSTEM INVSTMNT IN DCS BEING ADD. NO. DCS IN PD SYSTEM TOTAL PD COST DOM. AVG. SERV. TIME (DCSCICGCC! CCCCC'. (DUI-U) C.‘ 00100001000003535000000000000000006DUOOOODOOOOOOOOOOO zzzzzzxxxxxzxxx:x:xx:><><::><><:><><><><>