LIBRARY Myr‘fir‘ft‘zr- 35%: L wry ,,\. ‘Mfiuu -. - 91w: 25¢ per «y per item RETURNING LIBRARY MATERIALS: N ‘3‘ "M, Place in book return to remove . *“W‘ '4 charge from circulation records AN EXAMINATION OF SAFETY STOCK POLICIES IN MULTI-ECHELONED DISTRIBUTION SYSTEMS BY Robert Lorin Cook A DISSERTATION Submitted to Michigan State University. in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Marketing and Transportation Administration 1980 SEWice F distribut 35 lead 1mg de] used to the COKE, ABSTRACT AN EXAMINATION OF SAFETY STOCK POLICIES IN MULTI-ECHELONED DISTRIBUTION SYSTEMS BY Robert Lorin Cook An accurate determination of channel system safety stock requirements is desirable as one aspect of customer service policy. Safety stock is located throughout a distribution system to buffer uncertainties due to demand and lead time performance. An accurate determination of safety stock require— ments depends on two factors: (1) accuracy of the technique used to formulate safety stock policy; and (2) understanding the combined effects of safety stock and uncertainty on customer service. There has been little prior research which studies the customer service effects of safety stock levels and locations, particularly in multi-echeloned distribution systems. The objective of this research was to measure both the accuracy of a statistical approach commonly used for setting safety stocks and effects of alternate safety stock policies and uncertainty levels On customer service performance in single and multi- echeloned channel systems. Two :sing a dyn- 5'3erous 51' of safety : mi mlti-t results we: Part compa channel sy astatisti stocks. T emined e acertaim (if each C} may stc ISSearCh : the most . in Single Echelon s ”Edict S as OPPOSe the “flat eche10nec‘ to be ina intEIrela IOCatiOnS Safety st Robert Lorin Cook Two series of dynamic simulations were performed using a dynamic simulation model of a distribution channel. Numerous simulations were made using alternate combinations of safety stock policy and uncertainty level for both single and multi-echeloned channel systems. The customer service results were examined using a two-part analysis. The first part compared the simulated customer service results of both channel system designs to the customer service predicted by a statistical approach commonly used for setting safety stocks. The second part investigated the individual and combined effects of alternate safety stock policies and uncertainty levels on the simulated customer service results of each channel system. The following conclusions for safety stock planning and control were drawn from the research results. First, the statistical approach, for the most part, should not be used for setting safety stocks in single or multi-echeloned channel systems. In single echelon systems, the statistical approach did not accurately predict simulated customer service. Lead time uncertainty, as opposed to demand uncertainty, had the greatest effect on the relative accuracy of the statistical approach. In multi- echeloned systems, the statistical approach was also found to be inaccurate due, in part, to a failure to consider the interrelationship of inventory performance at sequential locations. The statistical approach does not consider safety stock location within the channel. Sa asignifi sslti-eche the initia significar ascertain: positioni: Safety stc resulted . litrod‘xe Customer LCV‘ér ech Ser‘v’ice S at the SE Rsecond itl that 935.610“ : bSt'n'een . E’Cheloh 65501th inventOI Prism} “fig “4 t H ‘1 «\r C Robert Lorin Cook Safety stock level and location was found to have a significant effect on customer service in both single and multi-echeloned channel systems. In single echelon systems, the initial increments of safety stock provided the most significant increases in customer service, regardless of uncertainty level. In multi-echeloned systems, safety stock positioning had significant impacts on customer service. Safety stocks introduced at the lowest channel echelon resulted in higher customer service than safety stocks introduced at the second echelon. This difference in customer service increased as uncertainty level increased. Lower echelon safety stock additions increased customer service slowly, while additional increments of safety stock at the second echelon rapidly decreased in effectiveness. A second echelon positioning policy increased the probabil- ity that retail replenishment orders were filled, but second echelon safety stocks did not buffer lead time uncertainty between the two echelons. Partial postponement of safety stocks at the second echelon resulted in higher customer service than either absolute postponement or absolute speculation because inventory is necessary at each echelon since inventory performance at sequential locations is interrelated. This higher customer service was accomplished without increasing safety 51 channel a n highe: ofsafet Robert Lorin Cook safety stock levels and carrying costs. Thus, a total channel approach to setting safety stock policy results in higher customer service performance for a given amount of safety stock. 'P Iv d Jah‘ 4 a expert a dis the r iHClu to ur ACKNOWLEDGMENTS This research became a reality with the aid of many fine individuals who contributed their professional expertise, financial assistance, and encouragement. The committee was composed of Dr. Donald J. Bowersox, Professor; Dr. M. Bixby Cooper, Associate Pro- fessor; and Dr. David J. Closs, Assistant Professor; all of the Department of Marketing and Transportation Adminis- tration at Michigan State University. Their professional expertise and encouragement will long be remembered. Dr. Donald J. Bowersox, Chairman of the Committee, a distinguished distribution scholar, conceived and directed the research. He supported my efforts in a myriad of ways, including the provision of computer time which enabled me to undertake the research, many significant editorial contributions, and constant encouragement. For this, I am forever grateful. Dr. M. Bixby Cooper provided invaluable contribu- tions, especially to the methodology and analysis portions of the research effort. For this, and his continuous support, I am indebted. Dr. David J. Closs met each of the countless inter- ruptions with a willingness to help. His in-depth knowledge ii of distrit itowledge this, I a: Dr. and Trans; excellent his intere .zs research, greatly a; I a Harold, f< during th of distribution system modeling and ability to impart that knowledge has greatly benefited the research and me. For this, I am deeply grateful. Dr. Donald A. Taylor, Chairman of the Marketing and Transportation Administration Department, provided an excellent environment for professional deve10pment. For his interest and ever-present moral support, I am grateful. Mrs. Grace Rutherford typed the final draft of this research. Her excellent performance and professionalism is greatly appreciated. I am deeply grateful to my wife's parents, Kay and Harold, for their love, confidence, and constant support during this research. My mother will long be remembered for the love and encouragement she provided. Her quiet determination was an inspiration to me. My father supplied the opportunity for higher education. For this and his love and help throughout my work, I am indebted. To my sister, Susan, I owe a special thank you, for providing a strong sense of purpose which motivated me throughout this work. To my wife, Karen, I am forever grateful. Her love, friendship, and incredible support made this research a reality. iii II TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . . . . . LIST OF FIGURES . . . . . . . . . . . . . . . . Chapter I. INTRODUCTION . . . . . . . . . . . . . General Research Situation . . . . . Statistical Technique Accuracy . Relationship--Safety Stock Policy and Uncertainty . . . . Detailed Problem Statement Problem I . . . . . . Problem II . . . . . Research Procedure . . . Dissertation Outline . . II. LITERATURE REVIEW . . . . . . . . . . . Introduction . . . . . . . . . . . . Nature of Safety Stock Determination Demand . . . . . . . . . . . . Lead Time . . . . . . . Forecasting . . . . . . Order Quantity-Cost . . Reorder Point . . . . . Customer Service Policy System Structure ,, . . Safety Stock Techniques . . Intuitive . . . . . . . Mathematical Formulations Statistical Techniques . Simulation . . . . . . . . O O O O O O O O O O O O O O O O O O O O O Multi-Echeloned System Inventory Contro Literature . . . . . . . . . . . . Mathematical . . . . . . . . . . Simulations . . . . . . . . . . . iv O O O O O O O O O O O O Page vi viii Chapter III. HY IV. RE APPENDIX 3‘“. UlUNIOGR‘A Chapter III. HYPOTHESES AND RESEARCH METHODOLOGY . Introduction . . . . . . . . . . . Problem I: Single Echelon Systems Hypotheses . . . . . . . . . . Methodology . . . . . . . . . . Problem II: Multi-Echeloned Systems Hypotheses . . . . . . . . . . Methodology . . . . . . . . . . Statistical Analysis: Problems I and IV. RESULTS OF ANALYSIS . . . . . . . . . Introduction . . Results: Problem Part Part Results: Part Part Problem 0 0 Ho 0 H. 0 0000000 .0000 o o 0.000 ooooooo ooooooo 0000000 U3? U3? VO CONCLUSIONS O O O O O O O O O O O O O IntrOduction O O O O O O O O O Conclusions for Safety Stock Planning and Control . . . . . . . . . . . Problem I: Conclusions . Problem II: Conclusions Summary . . . . . . . . Research Considerations . Research Limitations Future Research . . . APPENDIX O O O O O O O O O O O O O O O O O O BIBLIOGRAPHY O O O O O O O O O O O O O O O O Hooooooo H Page Table 2.1 2.2 3.] 3.2 LIST OF TABLES Table 2.1 Safety Stock Protection at Various Levels of Standard Deviation . . . . . . . . . . . 44 2.2 Summary of Safety Stock Factors in Multi-Echeloned Case . . . . . . . . . . . . 61 3.1 Uncertainty Levels: Problem I . . . . . . . 76 3.2 Inventory Policies: Problem I . . . . . . . 78 3.3 Simulations: Problem I . . . . . . . . . . 79 3.4 Simulation Output: Problem I . . . . . . . 81 3.5 Inventory Policies: Problem II . . . . . . 86 3.6 Simulations: Problem II . . . . . . . . . . 88 3.7 Simulation Output: Problem II . . . . . . . 89 3.8 ANOVA: Part A . . . . . . . . . . . . . . . 91 4.1 Abbreviations . . . . . . . . . . . . . . . 95 4.2 Mean Differences in Simulated and Predicted Customer Service Levels . . . . . 97 4.3 Analysis of Variance: Mean Difference in Simulated and Predicted Customer Service Levels O O O O O O O O O O O O O O O O O O O 101 4.4 Mean Values of Simulated Customer Service Levels O O O O O O O O O O O O O O O O O O O 108 4.5 Analysis of Variance: Simulated Product Customer Service Levels . . . . . . . . . . 108 4.6 Mean Differences in Simulated and Predicted Customer Service Levels . . . . . 115 vi Table 4.7 Page Analysis of Variance: Mean Difference in Simulated and Predicted Customer Service Levels O O O O O O O O O O O O O O O O O O O 116 Mean Values of Simulated Customer Service Levels O O O O O O O O O O O O O O O O O O O 126 Analysis of Variance: Simulated Customer Service Levels . . . . . . . . . . . . . . . 128 Summary of Safety Stock Level Comparisons . 135 vii Figure 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.1 3.2 4.1 4.2 4.3 Figure 2.1 3.2 4.1 LIST OF FIGURES Demand Uncertainty . . . . . . . . . . . Lead Time Uncertainty . . . . . . . . . Economic Order Quantity . . . . . . . . Illustration of Variable Order Quantity and Average Inventory . . . . . . . . . Relationship Between Safety Stock and Locations O O O O O O O O O O O O O O O Channel System Structure . . . . . . . . Normal Distribution . . . . . . . . . . An Arborescence . . . . . . . . . . . . Series and Parallel Structured Multi- Echelon Systems . . . . . . . . . . . . Representative Channel System Configuration: Problem I . . . . . . . Representative Channel System Configuration: Problem II . . . . . . . Mean Values of Simulated and Predicted Customer Service Levels for Safety Stock Policy R1 Under All Uncertainty Levels . Mean Values of Simulated and Predicted Customer Service Levels for Safety Stock Policy R2 Under All Uncertainty Levels . Mean Values of Simulated and Predicted Customer Service Levels for Safety Stock Policy R3 Under All Uncertainty Levels . Mean Difference in Customer Service for Each Safety Stock Policy Under A11 Uncertainty Levels . . . . . . . . . . . viii Page 16 17 25 27 35 36 42 48 49 72 83 98 99 100 102 Figure 4.5 4.9 4.12 4.13 Mean Difference in Customer Service for Each Uncertainty Level Under All Safety Stock Policies . . . . . . . . . . . . . . . Mean Values of Customer Service Level for Each Safety Stock Level Under All Uncertainty Levels . . . . . . . . . . . . . Mean Values of Customer Service Level for Each Uncertainty Level Under All Safety StOCk POliCies O O O O O O O O O O O O O O O Simulated and Predicted Mean Values of Customer Service Level for Safety Stock PeliCies With R1 O O O O O O O O O O O O O O Simulated and Predicted Mean Values of Customer Service Level for Safety Stock POIiCies With R2 O O O O O O O O O O O O O 0 Simulated and Predicted Mean Values of Customer Service Level for Safety Stock P01 ic ies With R3 O O O O O O O O O O O O O O Mean Difference in Customer Service Level for Each Safety Stock Policy Under All Uncertainty Levels . . . . . . . . . . . . . Mean Difference in Customer Service Level for Each Uncertainty Level Under All Safety Stock Policies . . . . . . . . . . . Mean Values of Customer Service Level for Each Safety Stock Policy Under All Uncertainty Levels . . . . . . . . . . . . . Mean Values of Customer Service Levels for Each Safety Stock Level Under a Distribution Center Safety Stock Positioning Policy . . . Mean Values of Customer Service Levels for Each Safety Stock Level Under a Retailer Safety Stock Positioning Policy . . . . . . Mean Values of Customer Service Levels for Each Safety Stock Level Under a Distribution Center-Retailer Safety Stock Positioning Policy . . . . . . . . . . . . . . . . . . . ix Page 104 110 112 117 118 119 121 123 129 130 131 132 Figure 4.17 4.21 Page Mean Values of Customer Service Levels for the Safety Stock Positioning Policies Under Safety Stock Level SSL-.5 . . . . . . 137 Mean Values of Customer Service Levels for the Safety Stock Positioning Policies Under Safety Stock Level SSL-1.0 . . . . . . 138 Customer Service of Safety Stock Policies Under Low Uncertainty Levels LlDl, LlD2, L1D3 O O O O O O O O O O O O O O O O O O O O 142 Customer Service of Safety Stock Policies Under Intermediate Uncertainty Levels, Lle’ L2D2’ L2D3 O O O O O O O O O O O O O O 143 Customer Service of Safety Stock Policies Under High Uncertainty Levels, L301, L3D2, L3D3 O O O O O O O O O O O O O O O O O O O O 144 Mean Values of Customer Service Level for Each Uncertainty Level Across All Safety StOCk POIiCieS o o o o o o o o o .‘ o o o o o 1.46 Statistical Approach-Application in Single Echelon Channel Systems . . . . . . . 154 Statistical Approach-Application in Multi-Echeloned Channel Systems . . . . . . 162 CHAPTER I INTRODUCTION General Research Situation The formulation of a customer service strategy is an important part of physical distribution performance. Overall, this strategy requires both a specified level of inventory availability and a desired speed and consistency of delivery. A critical aspect of a customer service strategy is inventory placement. Only by having the correct quantity of inventory at the right place and when demanded can a prescribed customer service level be realized. Two types of uncertainty are experienced in the placement of inventory throughout a distribution channel. The first uncertainty is demand which may be greater than that forecast. The second is delay in replenishing inventory to a stocking location. Managers attempt to overcome the effects of both types of uncertainty by using safety stocks. When demand exceeds forecast or when replenishment is delayed, safety stock may be required to fill orders. In both situations, safety stock provides a degree of protection against stocl unavz safet deter b-v servi range tistic The Inc stock statis dezand 10:5) is Sts 515§le SFStem .0: 5 fet 41 1 .. “he S‘JI ‘ 1 stock-outs. A stock-out occurs when inventory is unavailable to satisfy an order. Thus, because the safety stock level influences inventory availability, determination of such levels is a major aspect of customer service strategy. Numerous techniques have been developed to assist in the selection of safety stock levels.1 These techniques range from judgment and simple mathematics, to complex sta- tistical formulations, and to various forms of simulation. The most commonly used techniques for determining safety stock level involve statistical probability. Selected statistical techniques provide methods for estimating both demand and lead time uncertainty in a single formulation.2 Inventory is stocked at one or more stages (eche- lons) of a physical distribution system. When inventory is stocked at only one stage, the system is defined as single echelon. The structure of most physical distribution systems, however, consists of two or more stocking stages; for example, products stocked at distribution centers and retail locations. When two or more stocking stages exist, the system is defined as multi-echeloned. A multi-echeloned channel structure adds complexity to planning inventory level and positioning because per- formance at sequential locations is interrelated.3 Thus, decisions regarding the level and positioning of safety stocks can be expected to influence performance at all locations in a multi-echeloned distribution channel. Statistical techniques used for establishing safety stock level have not taken into consideration the inter- relation of echelons in multi-echeloned situations. With minor exceptions, no research has been done supporting the validity of using identical statistical techniques regard— less of the echeloned structure.“ The validity of using probabilistic statistical techniques to set safety stocks is questionable, due to the interactions of demand, lead time, multiple order cycles, and multiple echelons. Determination of the level and positioning of safety stocks, without consideration of the above noted interactions, could result in higher or lower than planned customer service. In the first instance, inventory carrying cost increases because of excessive safety stocks. In the second instance, sales are lost unless orders can be backordered. The attainment of a prescribed customer service level depends on two factors: (1) the accuracy of the technique used to formulate the safety stock policy; and (2) understanding the relationship of alternative safety stock policies and uncertainty levels on customer service performance. The objective of this research was to seek a better understanding of each of these two factors in both a single and multi-echeloned inventory system. eat? Gail ave: We» 4.“ Statistical Technique Accuracy The first factor deals with the accuracy of a statistical approach used to determine safety stocks. This approach involves two formulations. A convolution formulation and a service level formulation are jointly used to determine the safety stock level required to real- ize planned customer service performance. Customer service performance is defined as a fill rate (quantity sold in units divided by quantity demanded). The convolution formulation combines demand and lead time uncertainties. Specifically, the formulation mathematically combines the variance about the average daily demand during lead time with the variance about the average lead time. The formula is as follows: co = lrtcdz + d’otz where: co = combined standard deviation of demand during lead time (units); t‘= average lead time (days); 0 2 = variance of demand over lead time (unitsz/day); d = average demand per day (units); and o = variance of lead time (daysz).s The product is the combined standard deviation of demand during lead time in units. This measure can be used to determine the probability of a stock-out during replenish— ment.6 For example, given a situation where normal demand and lead time distributions are assumed, the policy of having a safety stock level equal to one standard deviation would mean that stock-outs would occur, on the average, during only 15.87 percent of the lead times.7 This measure of customer service performance does not directly yield fill rate. The actual quantity fill rate, over time, depends on the number of replenishment orders. The number of replenishment orders required over a planning period is directly related to order quantity. The conversion of the probability of a stock-out, during a given replenishment cycle, to a quantity fill rate, over time, is accomplished by the service level formulation introduced by Robert Brown.8 The formula is: (K) 0c SL=1- 00 where: SL = service level as a quantity fill rate; K = safety factor or protection provided by (SK) x (cc) units of safety stock; SK = the number of combined standard deviations of safety stock placed at a location; co = combined standard deviation of demand over lead time in units; and 00 = replenishment order quantity.9 The resulting output is the quantity fill rate expressed as a percentage. The accuracy of this statistical approach can be tested by making a statistical comparison of customer service levels predicted by that approach to those obtained from dynamic simulation. Relationship--Safety Stock Policy and Uncertainty The second factor deals with an evaluation of safety stock policies and combined demand and lead time uncertainties. Both the safety stock poliCy employed, and the uncertainty level experienced, have impacts on channel system customer service performance. Thus, to achieve a prescribed customer service level, it is desirable to understand the relationship between safety stock policy and uncertainty. In a single echelon channel system, the safety stock policy consists of setting a safety stock level. The determination of a specific safety stock level must be closely related to the combined demand and lead time variability, since the function of safety stock is to buffer uncertainty. Thus, a joint probability distribution of demand over lead time must be estimated and related to safety stock level and customer service performance. Recent research has indicated that demand and lead time variability may interact causing a "cancellation effect" in total variability.1° This interaction of demand and lead time variabilities reduces the accuracy of current techniques used in estimating the impact of uncertainty on channel system performance. However, the impact of uncertainty on channel system performance must be pre- cisely defined, since both over and underestimation of safety stock requirements penalize the firm. In a multi-echeloned channel system, the safety stock policy consists of setting a safety stock level and position. An additional safety stock policy consideration is that inventory performance of echeloned locations is interrelated. For example, a wholesaler who derives demand from a retailer may set a safety stock level based on the combined variability of demand over lead time. The retailer may set safety stock level in the same manner. Thus, by setting safety stocks independently, both have set aside stock to cover the same variability in demand. The result is excess safety stock in the channel. Therefore, safety stock level and position must be considered simultaneously when setting safety stocks in multi-echeloned systems. The relationship between safety stock policy and uncertainty and its impact on customer service performance must be evaluated, and then represented in safety stock . techniques. Customer service levels resulting from dynamic simulations were analyzed statistically in evaluating the relative impacts of safety stock policy and uncertainty on customer service performance. Detailed Problem Statement Two specific problems are examined in studying the two factors upon which desired customer service performance depend. Problem I The first problem is a comparison of predicted and simulated customer service performance in a single echelon channel system. It is divided into two parts so that each part can be compared to that of Problem II. Part A. Part A determines the accuracy of a statistical approach for determining customer service levels under selected safety stock policies and uncertainty levels. Part B. Part B evaluates the relative impact of the safety stock level employed on customer service performance under selected uncertainty levels. Problem II The second problem is a comparison of predicted and simulated customer service performance in a multi- echeloned channel system. It also is divided into two parts. Part A. Part A determines the accuracy of a statistical approach for determining customer service levels under selected safety stock policies and uncertainty levels. Part B. Part B evaluates the relative impact of the safety stock level employed and echelon positioning on customer service performance under selected uncertainty levels. Research Procedure Ideally, each problem could be researched by performing a series of controlled experiments using actual distribution channels. The researcher could then observe channel system performance related to changes in safety stock policy under different uncertainty situations. Direct experimentation is not feasible because of an inability to control relevant variables. Therefore, this particular research problem was solved using a channel system model. A model is a representation of an object, system, or idea in some form other than that of the entity itself.11 Two broad model categories exist for analysis of physical distribution systems--mathematical programming and simula- tion.12 A mathematical model describes the system, its components, and their interactions in quantitative terms. In order to develop and use a mathematical model, all 10 system relationships must be completely understood and quantified. This can be a difficult task. As Closs states: Although it is not difficult to quantify the relationship between total transportation costs and the elements contributing to total cost, it is very difficult to establish with any degree of certainty a quantifiable relationship between customer service and resultant sales.13 Another major weakness of employing mathematical modeling in distribution research is the inability to treat day- to-day dynamics of distribution system Operations. Simulation is an alternative form of modeling that has been successfully employed to replicate physical distribution systems.‘“ One definition of simulation is: the process of designing a model of a real system and conducting experiments with this model for the purpose of either understanding the behavior of the system or of evaluating various strategies (within the limits imposed by a criterion or set of criteria) for the operation of the system.15 Computer simulations are designed as static or dynamic. Static simulation models measure the state of variables and relationship at a given point in time. Dynamic simulation measures the state of the variables and relationships over time. Dynamics permit the researcher to investigate time-dependent relationships between both the parameters and variables of the system simulated. Simulations may also be deterministic or stochastic. In deterministic simulation models, the relationships 11 between model variables are constant. Models, in which at least one relationship is represented by a probability function, are stochastic.16 Two significant stochastic variables found in simulation models are demand and lead time. Therefore, a dynamic/stochastic simulator is suitable for experimentation of safety stock policies. The specific simulation model employed in this research is the Simulated Product Sales Forecasting (SPSF) model.r7 The model is capable of measuring both channel system cost and service performance; it incorporates the ability to simultaneously handle several channels of both single and multi-echeloned structure; it is dynamic and stochastic; and it replicates both spatial and temporal systems' dimensions. Two series of simulations were required by the research designs. They combined all possible combinations of three safety stock policies and nine uncertainty levels. The series of simulations pertaining to Problem I replicated twenty-seven different single echelon channel systems. The series of simulations pertaining to Problem II replicated eighty-one different multi-echeloned channel systems. The increase in simulations for Problem II stems from the echelon-positioning of three safety stock levels. For Problems I and II the customer service results are analyzed for each experimental simulation. In Part A, 12 of both Problems I and II, the formulated and simulated customer service levels are compared statistically. In Part B of the same problems, the simulated customer service levels are analyzed to determine the individual and combined effects of the experimental treatments on customer service performance. In both problems, the statistical analysis consists of analysis of variance, post hoc multiple comparison procedures, and t-tests. Dissertation Outline This dissertation is presented in five chapters. Chapter II reviews the nature of safety stock determination, specific safety stock techniques, and the literature per- taining to multi-echeloned inventory control. Chapter III discusses the hypotheses tested, the research methodology utilized, and statistical analysis procedures. Chapter IV reports the results of the analyses and reviews the general hypotheses. Chapter V presents conclusions for safety stock planning and control and suggests areas for future research. FOOTNOTES-~INTRODUCTION 1For a review of safety stock techniques, refer to Chapter II pp. 37-46 below. 2Robert B. Fetter and Winston C. Dalleck, Decision Models for Inventory Management (Homewood, 111.: Richard D. Irwin Inc., 1971), pp. 50-52; and Robert G. Brown, Decision Rules for Inventory Management (New York: Holt, Rinehart & Winston, Inc., 1967), pp. 108-109. 3There are numerous sources, including: Jay Forrester, Industrial Dynamics (New York: John Wesley & Sons, Inc., 1961)? and Andrew J. Clark, "An Informal Survey of Multi-Echelon Inventory Theory," Naval Research Logistics Quarterly, December 1972, pp. 621-650.7—For additionaI' discussion, see Chapter II of this dissertation, pp. 47-60. ”Refer to Table 2.2, Chapter II, pp. 61-62 below. 5For a more complete derivation of this formula, as applied to inventory control, see Fetter and Dalleck, Decision Models for Inventory Management, pp. 50-52. 6For a discussion of using standard deviation as a measure for setting the level of safety stocks, see Chapter II, pp. 43—45 below. 7Since stock-outs only occur when demand is above the expected level, a one-tailed distribution is utilized. One standard deviation above the mean for a one-tailed normal distribution includes 84.13 percent of the area under the normal curve. 8Brown, Statistical Forecasting for Inventory Control, pp. 107:119. 9Ibid., p. 109. l°George D. Wagenheim, "The Performance of a Physical Distribution Channel System under Various Conditions of Lead Time Uncertainty: A Simulation Experiment" (Ph.D. disserta- tion, Michigan State University, 1974). 11Robert E. Shannon, Systems Simulation--The Art and Science (Englewood Cliffs, N.J.: Prentice Hall, Inc.,1975), p. 4. 13 Foreca and Va Univer thsic of Bus 14 12Robert G. House and Jeffrey J. Karrenbauer, "Logistics System Modeling," International Journal of Physical Distribution and Materials Management, May 1978, pp. 194-196. l3David Joseph Closs, "Simulated Product Sales Forecasting: Mathematical Model, Computer Implementation, and Validation" (Ph.D. dissertation, Michigan State University, 1978). 1"Donald J. Bowersox et al., Dynamic Simulation of Physical Distribution Systems (East Lansing, Mich.: Bureau of Business Research, Michigan State University, 1973). 15Shannon, Systems Simulation--The Art and Science p. 4. 16Thomas H. Naylor et al., Computer Simulation Techniques (New York: John Wiley & Sons, Inc., I9667, p. 17. 17Donald J. Bowersox, David J. Closs, John T. Mentzer, Jr., and Jeffrey R. Sims, Simulated Product Sales Forecastingf-Documentation (East Lansing, Mich.: Graduate School of Business Administration Research Bureau, Michigan State University, 1978). CHAPTER II LITERATURE REVIEW Introduction Chapter II provides a review of the nature of safety stock requirements determination and an examination of the literature concerning inventory control in multi-echeloned physical distribution systems. The literature review is organized into three sections. The first section discusses the nature of safety stock, and reviews the major factors affecting the determination of safety stock requirements. The second section provides an overview of safety stock techniques. Section three reviews inventory control literature pertaining to multi-echeloned channel systems. Nature of Safety Stock Determination Safety stock, also referred to as buffer or pro- tective stock, is locational inventory. Safety stock is placed in certain locations in an attempt to buffer the uncertainty that is inherent in the forecasts of customer demand and lead time performance of the firm. Figures 2.1 and 2.2 illustrate the two types of uncertainty.1 In Figure 2.1, demand occurs in excess of 15 16 Inventory Level \\ Forecast of Demand \ Demand Stockout \\ 1 2 3 4 5 6 7 8 9 10 Days Figure 2.1 Demand Uncertainty. 17 .aucwmuuwoss mafia puma N.N musowm mama ma vH ma NH HA OH m m h o m e m N H (I}\|( usoxooum / / / / @5500 m0 ammowuom/ / / umwoumm umwoomm muoucm>cH anoucm>cH no mo Hm>oq mafia Hmzuo¢ mafia cmccmam . muoucmecH 18 forecasted demand during the period. This results in an out-of—stock condition at the end of the sixth day. Customer orders received by the retailer during the next four days will not be filled. Figure 2.2 depicts the second type of uncertainty: time delays in excess of the planned time for replenishing inventory stocks between two locations. As Figure 2.2 illustrates, replenishment of inventory stocks is planned to occur just as on-hand inventory reaches zero. However, because of unexpected delays, actual replenishment occurs five days later. Thus, an out-of-stock condition exists for the five-day period. Both types of uncertainty may result in inventory shortages. Safety stock, strategically placed, provides the firm with a specified degree of protection against inventory shortages. Two prerequisites to the successful determination of channel system safety stock requirements are: (l) the identification of the principal factors affecting safety stock; and (2) the choice of a safety stock technique which accurately reflects the uncertainty faced by the firm. The principal factors that affect a safety stock calculation are discussed in the remainder of this section. When managers seek to deploy safety stocks success- fully, a question that must be answered is: ”On what does the level of safety stock required at each location depend?" 19 There is no simple answer to this question. To a large extent, the answer depends on the specific channel system characteristics and the customer service policies of the firm. An examination of the general literature on safety stocks revealed an extensive number of factors which may affect the determination of safety stock requirements. Plossl and Wight stated: The amount of reserve stock required is a function consisting principally of the following elements: the ability to forecast demand accurately; the length of the lead time; the ability to forecast or control lead time; the size of the order quantity; and the service level desired.2 Prichard and Eagle identified the key factors as: level of performance, including reorder point determination, and service level desired; lead time demand; standard deviation of lead time demand; and shortage measures, such as shortage costs.3 Welsh defined the key factors as follows: accuracy of lead time estimate, probability of variations in lead time, accuracy of estimate of usage, cost of carrying "safety" stock, cost of "stockouts," and probability of variations in usage.” A review of each of the numerous factors and their specific functional relationships with safety stock is a large undertaking. To provide a manageable discussion, the key factors from the literature have been grouped into categories. These categories are: demand, lead time, 20 forecasting, order quantity-costs, reorder point, customer service policy, and system structure. A discussion of the impact of these factors on the determination of safety stock requirements follows. Demand The decision as to how much safety stock to establish is partly dependent on demand uncertainty. For this reason, managers are interested in accurately determining the nature of the demand pattern. Specifi- cally, the distribution and level of uncertainty provide a description of the demand pattern which helps managers set safety stock policies.5 A positive relationship exists between the level of uncertainty around average demand during the replenishment cycle and safety stock require-. ments. For example, an increase in the variance of demand during the replenishment cycle requires an increase in safety stocks, if it is assumed all other factors such as desired customer service are held constant. Conversely, safety stock levels may affect demand. Ben Schwartz proposed the idea of Perturbed Demand and suggested the following formula:6 A = Ao/(14-aI) 21 where: lo = the expected demand rate that would prevail with no stockouts; a = the relative number of stockouts (percentage of stockouts); I = a constant parameter of the model related to customer response; and A = the customer demand altered by previous stockout occurrences. Schwartz stated: The effect of a stockout is not to impose a cost ("penalty cost") against the firm at the time of the incident, but rather to modify the demand pattern in the future from that which otherwise would have occurred. This is a manifestation of loss of good will, in which the customer alters his future course of action due to meeting a stockout, rather than causing the firm some immediate, vaguely defined, loss.7 Thus, demand and safety stock are interdependent. The practice of backordering has an impact on safety stock requirements. A customer's order becomes a backorder when it cannot be filled on request and the customer is willing to wait until delivery can be made.8 Backorders represent a sale made when inventory is zero. Thus, backorders are closely related to stockouts. Stock- outs could occur at the time of order placement, at any time until the order is filled, or not at all. This can significantly affect a manager's determination of safety stock needs. For example, in a system where all orders 22 that occur after inventory depletion are backordered, and eventually filled, stockouts are impossible. In such an instance, safety stocks are not required. There is, in essence, a reciprocal relationship between backordering and safety stock. An increase in customer willingness to wait for orders not filled on request reduces the need for safety stocks. Lead Time The inventory replenishment cycle has been iden- tified as a combination of order communication, order processing, order shipment, and update.9 When the replenishment cycle duration is longer than planned, stockouts may occur. For this reason, managers are interested in accurately determining the distribution and level of uncertainty of the replenishment cycle. Once the lead time pattern is determined, managers can set safety stock levels in an attempt to reduce the effects of uncertainty. Thus, lead time uncertainty and safety stock requirements have a positive relationship. Vinson used a computerized cost-minimization model to study the importance of lead time unreliability (vari- ability of lead time from mean lead time) in inventory management. Using different combinations of stockout cost, demand variability, mean lead time, and variability of lead time around the mean, Vinson observed changes in optimum safety stock and inventory costs. Thus I faCto firm . timeS 10w. AS pa to in- SaEEt: 23 The conclusions of Vinson's study were, in part, 1. For a particular mean lead time, as the unreliability of lead time increases, Optimum safety stock increases substantially, other variables remaining constant. 2. In general, to the extent that the two influ- ences are mutually independent, variability of lead time around the mean is much more important than variability in the mean itself in explaining stockouts, stockout cost, and in setting Optimum safety stocks. 3. Unreliability of lead time is a considerably more important factor in explaining Optimum safety stocks than is unreliability in demand, where the two factors Operate independently of one another. 4. Managers and inventory theorists should be particularly careful not to ignore lead time unreliability under the following conditions: when mean lead time is relatively short; when stockout cost is relatively high;_when vari- ability in demand is relatively small; and when lead time unreliability is relatively great.1° Thus, the level of variability of lead time is an important factor in the determination of safety stock requirements. Forecasting Managers design a forecasting system to provide a firm with accurate estimates of future demands and lead times. When forecasts are accurate, forecast errors are low. The result is a smaller safety stock requirement.11 As Packer stated in a study of adaptive forecasting applied to inventory control: "It appears logical to establish the safety stock as a function of the success attained in 24 "12 There is an forecasting demand during a lead time. inverse relationship between the accuracy of forecasting and safety stock requirements. Order Quantity-Cost A major consideration in inventory control is the determination of the order quantity. The size of the order quantity is a factor which must be considered in setting safety stocks. For instance, a decrease in the order size will result in an increased number of smaller orders to obtain a given quantity. Since stockouts can only occur at the end of an order cycle, the increase in order fre- quency increases exposure to stockouts.13 The result is that an increase in safety stock may be necessary to main- tain the customer service level that existed prior to the decrease in order size. In general, order quantity determination is a cost based determination. Therefore, costs affect the determina- tion of safety stock requirements. The classical inventory order quantity model is the Economic Order Quantity (EOQ) which was first derived in 1915 by F. W. Harris.‘“ The formula often is referred to in the literature as the "Wilson Formula." The EOQ is the optimal balance of ordering costs and inventory carrying (maintenance) costs on an annual basis. The costs generally associated with ordering and inventory carrying costs are: 25 Ordering costs--order preparation; order communication; update activities; and managerial supervision.15 Carrying costs--cost of capital; inventory service costs such as taxes and insurance; storage space costs; and inventory risk costs including damage, pilferage, obsolescence, and relocation costs.l Figure 2.3 illustrates the basic relationship.17 The point at which the ordering cost curve and carrying cost curve intersect indicates the number of orders which should be placed per year to minimize the combined costs of ordering and maintaining inventory. Cost Total Cost + ’ Ordering Cost Most Economical Number of Orders + Maintenance Cost 0 Number of Orders per Year Figure 2.3 Economic Order Quantity. 26 A formulation of EOQ is: 2C S EOQ - ° C U m where: Co = cost per order; Cm = cost of maintenance per year; S = annual sales volume, units; and U = cost per unit. As shown in Figure 2.3, order costs have a positive slope, and increase as the number of orders increase. Order costs increase as safety stock requirements rise. Inventory carrying costs have an inverse relation- ship with safety stocks. This can be explained as follows: As the number of orders increase, the size of each order decreases for a given quantity. The average inventory is defined as one-half the order quantity. Since the order quantity is declining, average inventory is also declining and so are the associated costs. At the same time, since more orders are being issued, stockout exposure is increas- ing and so are safety stock requirements. Figure 2.4 illustrates the relationship.18 As order size decreases, average inventory decreases, but the number of stockout exposures increases. 27 Order Inventory Arrival Order Placed 3 0 0 Aver age Inventory 0 60 120 Days Example: Order 600 Inventory 100 Order Order laced l\ rival |\ J\ [\X 50 Av age I ‘\\\\J \\\\\l *\\\>l \\\\Jk \\\\Jk1nveEtQ4 II demand per period; number of lead time periods; 5 II n = number Of demand periods; and p( ) probability Of event in parentheses.“° An 8) probe imes stoci reSpc meth< and : prob; dEte: tech: the . Varic join1 e“Vi: Simu] abilj freqt Over randc Selec pIQCe the t 46 An expansion of this equation determines the exact probabilities for all possible demands during all lead times. These probabilities are then used to set safety stocks by setting the desired level of protection cor- responding tO a probability Of stockout."1 While this method provides an exact answer, it is extremely lengthy and requires the use of a computer for all but the smallest problems. In summary, the most frequently used techniques for determination of safety stock requirements are statistical techniques. Specifically, the standard deviation influences the safety stock level. The technique is adaptable to various types Of distributions and situations where joint probabilities exist. Simulation A simulation technique used for compounding environmental and Operational uncertainty is Monte Carlo Simulation."2 The procedure consists Of assigning prob- abilities tO each event in a manner that reflects the frequency with which the event would be expected tO occur over a large sampling Of events. Then a lead time is randomly selected and subsequently demands are randomly selected for each day Of the lead time. By repeating this procedure a large number of times, the relationship between the two uncertainties is simulated, or approximated. All sitL the PM} tioz thaz con: Carl orI dete "‘1‘ 0031 dis1 the: inVc as - Vari link at m L "arb 47 situations in which the simulated average demand exceeds the expected average demand during lead time are kept for purposes Of formulating a safety stock policy. All situa- tions where the average demand during lead time is less than or equal to expected demand may be eliminated from considerations, since no safety stock is required. Monte Carlo Simulation is especially useful when either demand or lead time do not have a normal or poisson distribution. This section has reviewed the techniques used to determine safety stock requirements in channel systems. The next section provides an overview of the inventory control literature relating to multi-echeloned physical distribution systems. Multi-Echeloned System Inventory Control Literature In broad terms, multi-echeloned system inventory theory is concerned with a variety Of inventory problems involving two or more interrelated stocking locations. A multi-echeloned inventory system can be portrayed as a directed network wherein the nodes represent the various activities or facilities in the system and the linkages represent flows Of goods. If the network has, at most, one incoming link for each node, and flows are acyclic (no lOOps to the network), it is called an "arborescence" or inverted tree structure.“3 Figure 2.8 48 depicts an arborescence. The various stages of the system are commonly identified as echelons and the problems investigated are defined as multi-echeloned. [ Manufacturer | ¢ 99 #1 maul x A A i l A Figure 2.8 An Arborescence. Two special kinds of arborescence structures are commonly used in the literature. As illustrated in Figure 2.9, these are (l) the series structure consisting Of two or more activities (stock locations) with each sup- plying only one other (lower echelon) activity, and (2) the parallel structure, consisting of a number of activities experiencing independent external demands. Two broad categories Of analysis dominate the multi- echeloned system inventory literature--Forma1 mathematical techniques such as Dynamic Programming, which is the most Often used mathematical technique, and simulation. The 49 [Source I ' D] Series Parallel - - W I I Figure 2.9 Series and Parallel Structured Multi-Echeloned Systems. H, ._J source ‘__al Structure I: literature in each category will be reviewed, with emphasis on the works that pertain tO this research. Mathematical Bessler and Veinott“” extended Veinott's "Dynamic Process Analysis Technique"5 to a multi-echeloned problem. The multi-echeloned structure used was an arborescence with n facilities each stocking a single product. Customer demand was satisfied by the stock at each location, but excess demand was successively passed up the channel to the next echelon until it was satisfied. Backlogging was allowed, but only at the top Of the channel, at the tOp echelon. Given these policies, the one period cost function was established from which Optimal stock levels were derived. 50 Then, the Optimum policy was Obtained by solving N n—dimensional minimization problems, where (N) was the number of periods and (n) was the number of stocking locations. Upper and lower bounds for Optimal stock levels were calculated for each stocking location. Finally, Bessler and Veinott presented an algorithm for computing approximations of the Optimal stock levels based on the values Obtained for the lower bound of the stock level. Since excess demand at all echelons (except the tOp one) was passed up the channel immediately, no safety stock policy was considered for these echelons. Since backlogging occurred at the top echelon, no safety stock was required. Service level was 100 percent over time. Clark and Scarf“‘ used a dynamic programming approach to solve the cost minimizing problem for a single product at an arbitrary number of stocking locations. The stocking locations were arranged in a series structure."7 Implied shortage costs were generated at each echelon and passed up the channel to become part Of the cost function Of the echelon above. Thus, the Optimal policy for inventory was first established at the lowest echelon. The shortage costs were obtained and passed on. The process was then repeated at the next echelon. This continued until all echelons had an Optimal policy. 51 One of the features Of this model was an allowance of backorders at all echelons. Service level was 100 percent in the long run. Safety stock policy was not considered. Hochstaedeter"8 extended the Clark-Scarf"9 formulation adOpting the same cost-demand structure. However, Hochstaedeter permitted fixed reorder costs at the lower echelons as well as at the tOp echelon. He established upper and lower bounds for Optimal system costs, with each set of bounds yielding (s, S) type ordering policies for each echelon. The calculation of shortage costs was similar to that of Clark and Scarf, and only the functional form was changed. fAs with Clark and Scarf, the backorder policy eliminated safety stock from consideration. Sherbroke,5° using the Stationary Process Approach 1 analyzed the multi-product pioneered by R. L. Love,s problem involving inventories of recoverable (repairable) items in a parallel structure. At each stocking location, Sherbroke attempted to establish stock objectives which would minimize the sum Of expected backorders on all recoverable items, given budget constraints. Investment dollars were allocated across product using a marginal analysis, and priority was given to those items which incrementally could have the largest reduction in system backorders. Safety stock was not considered. 52 Simon52 refined and extended portions of Sherbroke's model. As before, a parallel structure of bases supported by depots was considered, and where repair Of a failed item could occur at any stocking location. The model allowed system losses to occur at a specified rate. However, Simon had (S-l,S) or one-for-One replenishment policy for bases, and (3,5) or Optional replenishment policies for depots. Simon derived exact expressions for stationary distributions Of stock on hand, stock in repair and backlogged demand at each facility and indicated how these expressions could be used for Optimization of system backorders and/or costs. Safety stocks were not considered in this model. Tan derived Optimal policies for a multi-echeloned inventory problem with periodic ordering.53 A central warehouse supplied two facilities with a product. The warehouse could allocate the stock to the facilities in each period, but could reorder from an exogenous source only after every "T" period. Given this problem, Tan solved it for the Optimal allocation policy. Safety stocks were not considered. Simulations Aggerwal and Dhavale measured the performance Of a multi-product, multi-echeloned distribution system in terms of five important management criteria: average investmei average : costs, a levels 0 utilized Three si tion. T five man analysis percenta Caused b interact SYStem w to deman findings inVestme Were aff. the numb. prOVisio] l SimUIatic linked tc System. 56 53 investment in inventories, average shortage costs per year, average reorder costs, average annual inventory carrying costs, and the total number of reorders per year.5“ Three levels of demand, lead time, and inventory costs were utilized. There were 3ar3ar3==27 factor level combinations. Three simulations were run for each factor level combina- tion. This resulted in 3ar27==81 values for each of the five management criteria. Within cell variances were calculated by using an analysis of variance. Thus, the authors could examine the percentage of variance in the five performance measures caused by the factors (demand, lead time, costs, and their interactions). One finding was that annual shortage costs of the system were most sensitive to lead times, less sensitive to demand and least sensitive to cost factors.55 Additional findings were: mean demand significantly affected inventory investment in the same direction; inventory carrying costs were affected most by mean demand; as lead time increased, the number Of reorders decreased. The model made no provision for safety stock. Ballou's doctoral dissertation involved a computer Simulation Of an inventory system consisting of three firms linked together as a multi-echeloned physical distribution SiYStem.56 With this simulation, various inventory policies 54 were tested. The major effects of any particular inventory policy on the individual firm as well as the cost tradeoffs within the system were determined. Of the inventory models used, the comprehensive model was the most SOphisticated.57 Although the compre- hensive model was a deterministic inventory model, with backorder costs and quantity discounts, it did include a number Of stochastic variables. These variables included demand, lead time, and inventory level. The inventory level depended on stochastic demand, stochastic lead time, and back-order costs. Other less sophisticated inventory models also were utilized and compared with the comprehensive model. Research conclusions were: 1. When highly predictable conditions prevailed, a less sOphisticated model yielded the best profits. 2. Backorder cost was a significant factor, and for the highest profits to be achieved, the model selected had to include this factor. 3. A single stage model with backorder costs could be used effectively when backorder costs were high. 4. Transportation and inventory carrying costs had little affect on model selection within a reasonable range of values. 5. Higher profits could be achieved if the inventory problem was viewed from a total systems approach rather than a single firm approach. 55 Since there was an assumption that all orders eventually would be filled (100 percent backorders, with a fixed backorder cost), the service level was 100 percent. Safety stock was not considered in the design.58 Forrester developed a multiple stock location, multi-echeloned model to study repercussions from dis- turbances occurring primarily at the retail level.59 The model used one product and did not consider costs. Delays in the flow of information and of goods were used to char- acterize the dynamics of the model. Inventory was held at each stage Of the system and reorders were made to the echelon above, when necessary. Forrester succeeded in showing that small disturb- ances or changes occurring at the retail level are amplified by a multi-echeloned inventory and ordering structure. Forrester's work dramatically pointed out the temporal aspects of inventory. Safety stock policies were not a part Of this design. Gross and Soriano studied a military overseas resupply system, where air transport replaced the reductions in on-shelf inventory and safety stocks in a multi-echeloned distribution system.6° Curves depicting the relationship between safety stock level and various (demand and lead time combinations) were develOped. The results of the study were: first, the higher the initial service level, the greater the 56 safety stock reduction when mean lead time was reduced. Second, changes in system performance were more sensitive to changes in mean lead time and variation and less sensi- tive to variation in demand and distribution shape. The absolute value of the mean demand had no significant affect on inventory. Third, the standard deviation Of demand over lead time indicated what the reduced safety stock levels should be when lead time was reduced and also measured the effects on (on-shelf) inventory. The demand over lead time formula was: _ , 2 2 2 O/ux — y’utvx +ut Vt where: O/ux = combined variance; ut = mean lead time; Vx = coefficient of demand variation; and Vt = coefficient Of lead time variation. Fourth, safety stock and on-shelf inventory levels seemed to be insensitive to changes in the Operating inventory level (S-s). Fifth, changing the time between inventory reviews affects system performance. This research showed that mean lead time does significantly effect safety stocks in multi-echeloned systems. Discussion Of the actual techniques used to calculate safety stock was omitted. 57 Sims used a dynamic computer simulation model to measure the combined effects of demand and lead time uncertainty on the performance Of a physical distribution system.61 Sims analyzed performance under four time series forecasting techniques, in combination with various levels Of demand and lead time uncertainty. Performance measures were in terms Of sales, service, and cost. The total dis- crepancy between sales and demand was separated into two types Of errors: (a) forecasting error and (b) operating error. Sims found that increases in variation Of demand resulted in increased stockouts and reduced profit, regard- less Of the level of Operating uncertainty or forecast technique used. Also, increases in Operating uncertainty resulted in increased stockouts and reduced profit across all combinations Of forecast techniques and demand patterns, except one. In addition, variations in forecast accuracy lead to variations in channel performance across all demand and Operating uncertainty combinations; complexity Of tech- nique was inversely related to accuracy; and the effects Of increases in demand and Operating uncertainty tended to cancel each other. Two conclusions were cited: defining forecast error as the difference between sales and forecast is incorrect. Such a procedure generates future forecasts based on past 58 levels Of operating as well as forecast error. Therefore, more consistent system performance is achieved using simpler forecast techniques which are not affected as easily by Operating uncertainty. Safety stock was not considered in this research design, as it would have worked against the main purpose Of the research. Speh examined the performance of a multi-echeloned physical distribution system under various conditions of demand uncertainty. Performance measures were cost and customer service capability. The experimental factors were probability distribution, mean, and variance Of demand. Six probability distributions of daily demand, three levels Of demand variance, and two levels of average demand per day were used: Speh's major conclusions were: 1. Total cost was not measurably affected by various demand uncertainties, although demand uncertainties did cause significantly higher stockouts to occur. 2. Exponential and normal demand distributions created the greatest impact on system performance. 3. Demand uncertainty affected demand stocked out. 4. In general, the amount Of demand stocked out was more sensitive to demand uncertainty than total costs. Total cost did not vary with changes in variances or distribution. 5. The more symmetrical distributions, the lower demand variances, and the high average demand 59 level appeared to create cost and service impacts at the wholesaler and manufacturer levels of the system. The less symmetrical distributions, the higher variances and low average demand level led to a higher inci- dence Of stockouts at the retail level.62 Safety stocks were not carried at any level since demand per day and lead time were fixed. Thus, no safety stock technique was employed. Wagenheim examined the performance of a multi- echeloned physical distribution system under various con- ditions Of lead time uncertainty.63 Performance measures were cost and customer service capability. The probability distribution, average duration, and variance Of lead time were the experimental factors. Eighteen different combina- tions of the experimental factors were examined, with the aid of a dynamic simulation. Wagenheim concluded: "For all three experimental factors, uncertain lead time resulted in higher costs and lower service level than the determinis- tic lead time." In addition, all probability distributions had similar effects on the system, except exponential. The symmetrical distributions (normal and gamma) had the least effect on cost and service while the skewed distributions (exponential and erlang) had the greatest effect. A major finding was that higher variance and longer lead time impacts the system cost and services negatively. A tenta- tive conclusion was that lead time uncertainty is more 60 critical than demand uncertainty in the physical distribution system. NO safety stocks were employed in this research because the Objectives Of the research were such that daily demand and lead time are fixed.““ The literature review showed that many Of the factors affecting safety stock requirements determination have been studied and included in various statistical safety stock formulations. However, one aspect which has not been fully explored is the interdependent nature of the factors impacting on safety stock requirements. Since current safety stock formulations may not accurately replicate the interdependence impact Of factors upon safety stock requirements, their use in attaining a prescribed customer service is questionable. Additionally, the applicability of current statistical safety stock formulations to multi- echeloned physical distribution situations has not been examined. Table 2.2 illustrates the lack Of consideration of safety stock requirements determination in multi- echeloned systems. 61 Table 2.2 Summary of Safety Stock Factors in Multi-Echeloned Case Forecast Order Service Author Demand Lead-Time Method Quantity Costs R.o.P. Level Aggerwal t Independent Carrying (8.5) Dhavale‘s varied varied average (hi-med-low) (hi-med-low) shortage. mean mean average order investment Ballou“ Exogenous Exogenous Demand 30 day Order Fixed loos (Comprehen- normal normal forecast moving carrying sive Model) distribution distribution average transport level-hi-med- level--hi- backorder constant loos med-constant (fixed) backorder manufacturer one product Bessler- Exogenous Immediate Historical Minimise-- loos V'einott‘7 variable (zero) trend proportional (over backorder at order cost. time) top echelon storage, transport Clark- Independent Constant Shipping-- Low loos Scarf variable linear, echelons (over backorder-- holding-- (5-1.3), time) all echelons convex. top shortage-- echelons convex (s.S) Forrestern Stochastic Variable None generation constant Gross and Monte Carlo Monte Carlo Periodic various Soriano7° generated normal/ (s.S) poisson constant. or normal uniform/ "lump sum exponential withdrawal“ Hochstaed- Independent ' Integer Shipping-- (s.S) loos eter71 backorder multiples linear. (over all of review holding-- time) echelons periods linear, shortage-- linear Sherbroke"2 Bayesian Backorder Initial generation (8-1.8) poisson continuous distribution review. no reorders Simon” Independent Independent Backorder Base-- poisson Determi- (5-1.5) nistic Depot ‘.05) Sims,“ Increase lrlang l. Empo— lo Days of Handling 10 Days Not set and decrease distribution nential forecasted and (fixed) trend,normal level, sero- smoothing sales inventory distribution hi-low 2 . adaptive variable smoothing 3. ITO moving ave. 4. self- adaptive 5. perfect 62 Table 2.2--Continued Forecast Order Service Author Demand Lead-Time Method Quantity Costs R.O.P. Level Speh7s Distribution Fixed time EOQ Total cost Not set fixed negative and distance contribution binomial, 10 days margin exponential, thruput poisson, warehouse normal, inventory log normal, gamma, ”M’-25, 75' variance--.lO, .30, .50, coefficient Tan76 Stochastic Zero, no Holding, all backlogged trans- shortage, shipments convex, order, allocation, linear Wagenheim77 Deterministic Determinis- EOQ Total cost Perpetual Not set tic vs nor- CM. order mal, log transport inventory normal, inventory gamma, poisson exponential erlang, level 4, 7, coefficient of variation -.18. .375 Safety Stock Mathematical/ Deterministic/ Author Technique Simulation Static/Dynamic Stochastic Aggerwal” Not considered S S Ballou” Not considered 5 D 0/5 Bessler Veinott°° Not considered M S D Clark a Scarfu Not considered M S D li'orrester'2 Not considered S D 5 Cross 5 Various levels Soriano used (standard deviation of demand over lead-time) S D S Hochstaedeter.“ Mot considered M S D Sherbroke‘s Not considered M S D Simon“ Not considered a s 0 Sims.7 Mot considered S D s Speh" Not considered 8 D 5 Tan" Not considered M S D Maggenheim’° Not considered S D S FOOTNOTES-~CHAPTER II 1Donald J. Bowersox, Logistical Management (New York: Macmillan Publishing CO., Inc., 1974), pp. 197, 207. 2George W. Plossl and Oliver W. Wight, Production and Inventory Control: Principles and Techniques (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1967). P. 98. 3Robert H. Eagle and James W. Prichard, Modern Inventory Management (New York: John Wiley & Sons, 1965), p. 208. “Evert W. Welsh, Scientific Inventory Control (Greenwich, Conn.: Management Publishing CO., 1956), p. 124. 5For further reading on this tOpic, refer to Louis M. Killeen, Techniques of Inventory Management (New York: American Management AssociatiOn, 1970), p. 87. 6For a more detailed description, see Ben L. Schwartz, "Inventory Models in Which Stockouts Influence Subsequent Demand" (Ph.D. dissertation, Stanford University, 1965). 7Ben L. Schwartz, "Optimal Inventory Policies in Perterbed Demand Models," Management Science 16 (April 1970): 509. : 8Joseph Buchan and Ernest Koenigsberg, Scientific Inventory Management (New York: Prentice-Hall, Inc.,‘l963), p. 14. 9Bowersox, Logistical Management, p. 206. 1°Char1es E. Vinson, "The Cost Of Ignoring Lead-Time, Unreliability in Inventory Theory,” Decision Science 3 (April 1972): 87-105. 11Robert G. Brown, Statistical Forecastinggfor Inventory Control (New York: McGraw-Hill Book CO., Inc., 1959), p. 114. 63 64 12A. H. Packer, "Simulation and Adaptive Forecasting as Applied to Inventory Control," Operations Research 15 (July-August 1967): 660-679. 13Joseph Buchan and Ernest Koeingsberg, Scientific Inventory Management, p. 344. 1"F. W. Harris, Operations and Cost, Factory Manage- ment Series (Chicago: A. W. Shaw CO.,‘1915), pp. 48-52. lsBowersox, Logistical Management, p. 192. 16For a more detailed review, see Bernard J. LaLonde and Douglas M. Lambert, "Inventory Carrying Costs: Signif- icance, Components, Means, Functions," The International Journal of Physical Distribution 6:51-63? 17Refer to any text on Inventory Control, or Inventory Theory, such as George W. Plossl and Oliver W. Wight, Production and Inventory Control: Principles and Techniques (Englewood Cliffs, N.J.: ‘Prentice-Hall, Inc., 1967); or Louis M. Killeen, Techniques of Inventory Mana ement (New York: American Management Association, I970; 17 , 5 pp. 18Bowersox, Logistical Management, p. 191. 19See Richard J. Tersine, Materials Management and Inventory Systems (Amsterdam: North Holland Publishing CO., 1976), p. 241. 2°Ibid., p. 219. 21Vinson, "The Cost Of Ignoring Lead Time Unreliabil- ity in Inventory Theory," p. 96. 22Robert H. Eagle and James W. Prichard, Modern Inventory Management (New York: John Wiley & Sons, 1965), p. 185. 23Frank P. Buffa, "A Model for Allocating Limited Resources when Making Safety-Stock Decisions," Decision Sciences 8 (1977): 415-426. 2"Clay D. Whybark and Gordon Constable, "The Interaction of Transportation and Inventory Decisions," Decision Sciences 9 (1978): 688-699. 25For an in-depth discussion of reorder point systems, see Eagle and Prichard, Modern Inventory Management, Chapter 9. 65 26Elwood S. Buffa and Jeffrey G. Miller, Production Inventory Systems Planning and Control, 3rd ed. (Homewood, 111.: Richard D. Irwin, 1979), p. 170. 27Elwood S. Buffa, Production-Inventory Systems (Homewood, 111.: Richard D. Irwin, Inc., 1968). p. 98. 28James L. Heskett, Nicholas A. Glaskowsky, Jr., and Robert M. Ivie, Business Logistics (New York: The Ronald CO., 1973), p. 328. 29Robert Camp, "The Effect of Variable Lead-Times on Logistics Systems" (Ph.D. dissertation, Pennsylvania State University, 1973). 3°See Bowersox, Logistical Management, pp. 321-326. 31Stanley Larson, Inventory Systems and Controls Handbook (Englewood Cliffs, N.J.: Prentice-Hall, 1976). 32Plossl and Wight, Production and InventorprontrOl: Principles and Technigues, p. 123. 33Larson, Inventory Systems and Control Handbook. 3|'Welsh, Scientific Inventory Control, p. 138. 35Stephen Smith, "Optimal Inventories for An (S-l,S) System With NO Backorders," Management Science 23 (January 1977): 522-528. 37David Huntsberger and Patrick Billingsley, Elements of Statistical Inference, 4th ed. (Boston: Allyn and Bacon, T977) I p. 133s 38Brown, Statistical Forecasting for Inventory Control, p. 93. . 39Bowersox, Logistical Management, p. 210; or see Colin D. Lewis, Demand Analysis and Inventory Control (New York: Saxon House/Lexington Books, 1974), p. 129. “°Robert B. Fetter and Winston C. Dallek, Decision Models for Inventory Management (Homewood, 111.: Richard D. Irwin CO., 1961), p. 105. “‘Ibid., p. 106. 66 “zFor discussion, see Bowersox, Logistical Management, p. 211; Buchan and Koenigsberg, Scientific Inventory Management, pp. 13-14; and Martin Starr and David Miller, Inventory Control: Theory and Practice, p. 227. “3Andrew J. Clark, "An Informal Survey of Multi- Echelon Inventory Theory," Naval Research Logistics Quarterly, December 1972, p. 622. I"'S. A. Bessler and A. F. Veinott, Jr., "Optimal Policy for a Dynamic Multi-Echelon Inventory Model," Naval Research Logistics Quarterly 13 (1966): 355-389. “5C1ark, An Informal Survey Of Multi-Echelon Inventory Theory, p. 634. “5A. J. Clark and H. Scarf, "Optimal Policies for a Multi-Echelon Inventory," Management Science 6 (1960): 475-490. I"’See Geisler for discussion of D P Optimal Solution. Murray Geisler, "A Study Of Inventory Theory," Management Science 9 (April 1963): 495. ““Dietu Hochstaedeter, ”An Approximation Of the Cost Function for Multi-Echelon Inventory Model," Management Science 16 (July 1970): 716-727. “9C1ark, "Optimal Policies for a Multi-Echelon Inventory." 5°Sherbroke, "METHRIC: A Multi-Echelon Technique for Recoverable Item Control," Operations Research 19 (May 1971): 761-773. 51Love, R. F. ”A Two Station Stochastic Inventory Model with Exact Methods of Computing Optimal Policies," Naval Research Logistics Quarterly 14 (1967): 185-217. 52R. M. Simon, "Stationary Properties of a Two- Echelon Inventory Model for Low Demand Items," Operations Research 19 (May 1971): 761-773. 53Felipe K. Tan, "Optimal Policies for a Multi- Echelon Inventory Problem with Periodic Ordering," Management Science 20 (March 1974): 1104-1111. 5"S. C. Aggerwal and D. G. Dhavale, "Simulation Analysis Of a Multiproduct, Multiechelon, Inventory Distribution System," Academy of Manggement Journal 18 (March 1975): 41-54. 67 SSIbid. 56R. Ballou, "Multi-Echelon Inventory Control for Interrelated and Vertically Integrated Firms" (Ph.D. dissertation, Ohio State University, 1965). 57Ibid., p. 55. 58Ibid., p. 146. 59Jay Forrester, Industrial Dynamics (New York: John Wiley & Sons, Inc., 1961). 6°D. Gross and A. Soriano, "The Effect of Reducing Lead-Time on Inventory Levels--A Simulation Analysis," Management Science 16 (October 1969): 66-76. 61Jeffrey R. Sims, "Simulated Product Sales Fore- casting: An Analysis Of Forecasting and Operating Discrepancies in the Physical Distribution System" (Ph.D. dissertation, Michigan State University, 1978). 6213 Speh, "The Performance Of a Physical Dis- tribution Channel Under Various Conditions of Demand Uncertainty: A Simulated Experiment" (Ph.D. dissertation, Michigan State University, 1974). ' 63G. Wagenheim, "The Performance Of a Physical Distribution Channel Under Various Conditions of Lead- Time Uncertainty" (Ph.D. dissertation, Michigan State University, 1974). 5“Ibid., p. 36. 6SS. C. Aggerwal and D. G. Dhavale, "Simulation Analysis Of a Multiproduct, Multiechelon, Inventory Distribution System," Academy Of Management Journal 18 (March 1975): 41-54. - 66R. Ballou, "Multi-Echelon Inventory Control for Interrelated and Vertically Integrated Firms" (Ph.D. dissertation, Ohio State University, 1965). 67S. A. Bessler and A. F. Veinott, Jr., "Optimal Policy for a Dynamic Multi-Echelon Inventory Model," Naval Research ngistics Quarterly 13 (1966): 355-389. 58A- J. Clark and H. Scarf, "Optimal Policies for a Multi-Echelon Inventory," Management Science 6 (1960): 475-490. 68 69Jay Forrester, Industrial Dynamics (New York: John Wiley & Sons, Inc., 1961). 7°D. Gross and A. Soriano, "Effect Of Reducing Lead-Time on Inventory Levels--A Simulation Analysis," Management Science 16 (October 1969): 66-76. 71Dietu Hochstaedeter, "An Approximation of the Cost Function for Multi-Echelon Inventory Model," Management Science 16 (July 1970): 716-727. 72Sherbroke, "METHRIC: A Multi-Echelon Technique for Recoverable Item Control," pp. 761-773. 73R. M. Simon, ”Stationary Properties of a Two-Echelon Inventory Model for Low Demand Items," Operations Research 19 (May 1971): 761-773. 7"Sims, "Simulated Product Sales Forecasting: An Analysis Of Forecasting and Operating Discrepancies in the Physical Distribution System." 75Speh, "The Performance of a Physical Distribution Channel Under Various Conditions Of Demand Uncertainty: A Simulated Experiment." 76Tan, "Optimal Policies for a Multi-Echelon Inventory Problem with Periodic Ordering," pp. 1104-1111. 77Wagenheim, "The Performance of a Physical Distribution Channel Under Various Conditions Of Lead-Time Uncertainty." 78Aggerwal and Dhavale, "Simulation Analysis Of a Multiproduct, Multiechelon, Inventory Distribution System," pp. 41-54. 79Ballou, "Multi-Echelon Inventory Control for Interrelated and Vertically Integrated Firms," 1965. 8°Bessler and Veinott, "Optimal Policy for a Dynamic Multi-Echelon Inventory Model," pp. 355-389. °‘Clark and Scarf, "Optimal policies for a Multi- Echelon Inventory," pp. 475-490. 82Forrester, Industrial Dynamics, 1961. 83Gross and Soriano, "The Effect of Reducing Lead- Time on Inventory Levels--A Simulation Analysis," pp. 66-76. 69 8|‘Hochstaedeter, "An Approximation of the Cost Function for Multi-Echelon Inventory Model," pp. 716-727. 85Sherbroke, "METHRIC: A Multi-Echelon Technique for Recoverable Item Control," pp. 761-773. 86Simon, "Stationary Properties of a Two-Echelon Inventory Model for Low Demand Items," pp. 761-773. 87Sims, "Simulated Product Sales Forecasting: An Analysis of Forecasting and Operating Discrepancies in the Physical Distribution System." 88Speh, "The Performance Of a Physical Distribution Channel Under Various Conditions Of Demand Uncertainty: A Simulated Experiment." 89Tan, "Optimal Policies for a Multi-Echelon Inventory Problem with Periodic Ordering," pp. 1104-1111. 9°Wagenheim, "The Performance Of a Physical Distribution Channel Under Various Conditions of Lead-Time Uncertainty." CHAPTER III HYPOTHESES AND RESEARCH METHODOLOGY Introduction The Objective of this research is tO measure both the accuracy Of a statistical safety stock technique and the relative impact of alternative safety stock policies and uncertainty levels on customer service performance in single and multi-echeloned channel systems. This chapter identifies the specific hypotheses and outlines the research methodology required to investigate these issues. Chapter III is divided into three sections. The first and second sections present the hypotheses and research methodology dealing with the single and multi- echeloned problems, respectively. The third section describes the statistical analysis employed in this research. Problem I: Single Echelon Systems Hypotheses Part A. In a comparison Of customer service predicted by a statistical approach and Observed from a dynamic simulation, no difference exists: 70 71 1. Independent of the safety stock policy employed; 2. Independent of the uncertainty level experienced; 3. Independent of the combination Of safety stock policy employed and uncertainty level experienced. Part B. In a comparison among customer service performance observed from dynamic simulations, no signifi- cant difference exists: 1. Independent Of the safety stock level employed; 2. Independent Of the uncertainty level experienced; 3. Independent of the combination of safety stock level employed and uncertainty level experienced. Methodology The hypotheses for Part A and Part B Of Problem I were tested by using dynamic simulations Of single echelon channel systems. TO create these channel simulations, the Simulated Product Sales Forecasting (SPSF) Model was employed.1 A detailed description of the SPSF Model is provided in the Appendix. System configuration. The simulated system con- figuration consisted Of one echelon, containing a single retail facility, with inventory stocking capability. Figure 3.1 illustrates the system configuration. A single plant facility and retailer are linked by order communication and transportation. 72 Single Echelon I Plant] 1' 1‘ ‘- \ l I \ I I Retailer I — — Communication Links —— Transportation Links Figure 3.1 Representative Channel System Configuration: Problem I Ten identical products were handled simultaneously by this channel system. The products had identical physical and economic characteristics. The use of multiple products in each channel system simulation allowed more observations per simulation. Uncertainry. Channel system uncertainty was intro- duced through stochastic demand and lead time variables. The simulation Of channel systems with alternative uncer- tainty levels was accomplished by changing the standard deviation Of one or both variables while holding their mean values constant. 73 Demand was generated stochastically by the ORDGEN program, a part of the SPSF Demand module.2 Specifically, the ORDGEN program generated orders containing some or all of the ten products for each simulated day. Within a given channel system, the demand distribution Of each product had the same mean value and standard deviation, but they were generated on an independent basis. Throughout the research Of Problem I, the demand distribution and mean value were held constant. Demand was normally distributed with a mean value of daily sales equal to fifty units per day. Three demand patterns were utilized to represent low, medium, and high demand uncertainty. Specifically, the levels were defined as "low," "medium," and "high," and respectively correspond to a coefficient Of variation of .l, .3, and .6. The specific levels of the coefficient of variation were selected arbitrarily, but they were set so that differences that might exist due to variability in demand could be measured. Lead time, referred to as replenishment cycle duration, is the amount of time required from order place- ment to order fulfillment. The major time components are Operational in nature and include: order communication time, order processing time, and transit time. 74 Lead times for Problem I were generated stochastically from an erlang distribution. The erlang distribution is a special case of the gamma probability family. The density function, expected value, variance, and standard deviation of the erlang distribution are the same as for the gamma distribution.3 In choosing a lead time distribution for this research, several criteria had to be met.” First, the distribution chosen had to contribute to the generality of the research by being representative of actual lead time distributions. Second, the lead time distribution chosen had to be both limited to non-negative values greater than some arbitrary minimum, and skewed to the right, exhibiting a greater range Of possible values above the mean value than below it. The first Of these requirements results from the fact that there is some minimum amount of time which must elapse between the placement and the receipt of an order. Orders are not filled instantaneously. The second require- ment results from the fact that while there is some required minimum amount Of time which must elapse before the comple- tion Of the order cycle, there is not a maximum amount before which the cycle must be completed. Third, the distribution used had to be able to vary the size of the standard deviation about a single mean. 75 The normal distribution was not employed as the lead time distribution because it failed to satisfy the second criterion.‘ The distribution is not skewed to the right. In addition, the normal distribution would not be applicable when the distribution exhibited a high variability around a low mean value since some of the events, which would have to occur, would be negative. The poisson distribution was not utilized as the lead time distribution because it did not meet the third criterion. The mean value could not be held constant while the standard deviation varied. The erlang distribution was chosen because it met all three criteria. Specifically, the distribution can be very representative Of lead time distribution since it is applicable in situations where a series of service opera- tions such as order communications, order processing, and order shipment are present. The distribution can be skewed to the right, and applied only to non-negative random variables. Finally, the erlang distribution is flexible enough to assume several shapes. The mean value of the lead time distribution was held constant at ten days. Three patterns Of variability around the mean value were employed to represent "low," "medium," and "high" lead time uncertainty. The low, medium, and high variability were represented by 76 coefficients Of variation Of .l, .3, and .6, respectively. As with demand, the specific levels of coefficient of variation were selected arbitrarily, but were set so that differences that might exist due to variability in lead time, could be measured. Nine uncertainty levels were produced using the combinations Of three demand and three lead time patterns. Table 3.1 lists the uncertainty levels utilized in the research of Problem I. Table 3.1 Uncertainty Levels: Problem 1 Number of Uncertainty Uncertainty Level Lead Time Levels Abbreviation Level Demand Level 1 LlDl Low (.1)* Low (.1)* 2 L1D2 Low (.1) Medium (.3) 3 L1D3 Low (.1) High (.6) 4 L2Dl Medium (.3) Low (.1) 5 L2D2 Medium (.3) Medium (.3) 6 L2D3 Medium (.3) High (.6) 7 L3Dl High (.6) Low (.1) 8 L3D2 High (.6) Medium (.3) 9 L3D3 High (.6) High (.6) *Coefficient of variation. 77 Inventory pglicies. Demand for products was placed initially against the retailer in the form of daily orders from customers. These orders were filled with inventory held by the retailer. In the event that the order could not be filled in total, a partial shipment was sent to the customer exhausting retail supply. The unfilled part of the order was treated as demand permanently lost and recorded as a stockout. Thus, backorders were not a part of this research design. In fact, backordering would have worked directly against the Objective of this research. The retailers' source Of inventory replenishment was the plant which produced an infinite inventory. The retailers' reorder policy was a fixed order quantitypolicy.5 Thus, inventory level was reviewed daily and when the sum Of the on-hand and on-order inventory was less than the specified order point, a replenishment order was initiated. In accordance with this policy, the reorder point (ROP) was set at a quantity equal to the average demand at retail during the lead time between plant and retail locations, plus safety stocks. The reorder point varied depending on the safety stock policy employed. The order quantity was set at an amount equal to the average demand at retail during the replenishment cycle between the plant and retailer. Thus, order quantity was set at 500 units 78 (50 units per day average demand for ten days average lead time). Safety stock policy considerations for single echelon channel systems consist of setting a safety stock level. Three safety stock levels were chosen to examine Problem I of this research. Amounts of safety stock equal to 0, .5, and 1.0 combined standard deviations Of demand over lead time were utilized. These standard deviations were chosen arbitrarily, but were set so that differences which might result from safety stock policies could be measured. Safety stocks were held only by the retailer. Table 3.2 summarizes the inventory policies used to research Problem I. Table 3.2 Inventory Policies: Problem I Indirect System: All customer demand draws on the retailer Manufacturer: Production policy: Infinite inventory Inventory policy: NO stock maintained at plant Retailer: Replenishment policy: Source Plant replenishes retailer Reorder point 500 units plus safety stock Order quantity 500 units (constant) Review period each simulation day Safety stock policy: Stocking location: Retailer only Safety stock levels (combined standard deviations) 0, 0.5, 1.0 79 Simulations. In testing the hypotheses Of Parts A and B of Problem I, twenty-seven channel systems were simulated. Each simulation represented one of the possible combinations of the three safety stock policies and nine uncertainty levels. Table 3.3 displays these simulations. Table 3.3 Simulations: Problem I Safety Stock Policies l 2 3 Uncertainty -———- Levels (0) (0.5) (1.0) 1 L101 (1) (2) (3) 2 L102 (4) (5) (6) 3. L1D3 (7) (8) (9) 4 L2Dl (10) (ll) (12) 5 L202 (13) (14) (15) 6. L203 (16) (17) (18) 7. L301 (19) (20) (21) 8. L3D2 (22) (23) (24) 9. L303 (25) (26) (27) Each simulation was 500 days in length, with customer service levels for each of the ten products being generated every sixty days, after an initial twenty-day period. Of the nine periods, only the customer service results from periods six and eight were included in the sample to be analyzed. 80 Prior to performing the set of simulations, the stability of the simulation was tested. The test measure was customer service levels. A simulation was performed in which ten customer service levels were generated every sixty days for a 300 day period after an initial twenty-day period. The simulated channel system contained no safety stock and experienced the highest uncertainty level (L3D3) used in the research on Problem I. An analysis of variance was performed on the customer service results generated for periods three through six. The result was an F value Of 1.709. The significance level of the F value was .183. Thus, the customer service results of the four periods were not significantly different, even at a==.10. The choice Of sample periods was made arbitrarily from the stable periods. However, non-contiguous periods were selected to avoid interdependence within the sampling data. Thus, simulation output consisted of twenty sample Observations: one for each Of ten products Observed over two separate time periods. The total sample resulting from all simulations was 540 customer service levels. Table 3.4 details the output recorded. In addition to the simulated output, 540 predicted customer service levels were required to test the hypotheses for Part A of Problem I. These customer service levels were 81 Table 3.4 Simulation Output: Problem I Total sample size . . . . . . . . . . . . . 540 SimUJ-ations O O O O O O I O O O O O O O I O 27 Observations per simulation . . . . . . . . 20 Time periods sampled per simulation . . . . 2 Products per simulation . . . . . . . . . . 10 Response variable: (customer service level) . . . . . . . . . . . . . 1 predicted using the statistical approach detailed in Chapter I. The next section describes the hypotheses and methodology for Problem II. Problem II: Multi-Echeloned Systems Hypotheses Part A. In a comparison of customer service predicted by a statistical approach and observed from a dynamic simulation, no difference exists: 1. Independent of safety stock policy employed; 2. Independent of the uncertainty level experienced; 3. Independent Of the combination of safety stock policy employed and uncertainty level experienced. Part B. In a comparison among customer service performance Observed from dynamic simulations, no signif- icant difference exists: 82 1. Independent of safety stock level employed; 2. Independent Of safety stock positioning employed; 3. Independent Of safety stock policy employed; 4. Independent Of uncertainty level experienced; 5. Independent of safety stock policy employed and uncertainty level experienced. Methodology In testing the hypotheses for Parts A and B Of Problem II, dynamic simulations of multi-echeloned channel systems were required. As with Problem I, the Simulated Product Sales Forecasting (SPSF) Model was employed. System configuration. The simulated system configuration consisted of two echelons, each containing a single facility with inventory stocking capability. Figure 3.2 illustrates the system configuration. A single plant facility, distribution center, and retailer are linked by order communication and transportation. Ten identical products were handled simultaneously by this channel system. The products had identical physical and economic character- istics. As in Problem I, the use of multiple products in each simulation allowed more Observations per simulation. Uncertainty. The demand and lead time uncertainty levels employed in Problem II were identical to those utilized in Problem I. Specifically, the method Of generation, the distribution shapes, mean values, 83 Multi-Echeloned * I \ I I I ’-- I Retailer ' -— Communication Links — Transportation Links Figure 3.2 Representative Channel System Configuration: Problem II. 84 variability levels, and the reasons for these choices all remained the same. Thus, nine uncertainty levels were produced, using the combinations of three demand and three lead time patterns. Table 3.1, which illustrated the uncertainty levels utilized in the research of Problem I, is also applicable to Problem II. Inventory_policies. Initially, demand for products was placed against the retailer in the form of daily cus- tomer orders. These orders were filled with inventory held by the retailer. In the event that an order could not be filled in total, a partial shipment was sent to the customer exhausting retail supply. The unfilled part Of the order was treated as a stockout. The retailer's source of inventory replenishment was the distribution center. The retailer used a fixed order quantity reorder policy. Therefore, the reorder point was set at a quantity equal to the average demand at retail during the lead time between the distribution center and retailer plus safety stock. The order quantity was set at an amount equal to the average demand at retail during the replenishment cycle between the distribution center and retailer or 500 units. Demand placed against the distribution center was in the form of periodic orders from the retailer. As with the retailer, the distribution center filled orders with 85 its locational inventory. When an order could not be filled in total, a partial shipment was sent exhausting supply at the distribution center. The remainder Of the order was recorded as a stockout. Thus, backordering was not a part Of the research Of Problem II. The distribution center issued replenishment orders tO the plant periodically. The distribution center reorder policy and order quantity were the same as those of the retailer. All orders placed against the plant were filled from an "infinite" inventory. Safety stock policy considerations for multi- echeloned channel systems consisted Of setting a safety stock level and choosing echelon position. Three safety stock levels in each Of two echelon positions were chosen to examine Problem II of this research. Amounts Of safety stock equal to 0, .5, and 1.0 combined standard deviations Of demand over lead time uncertainty were utilized. These amounts were chosen arbitrarily, but were set so that differences that might result from safety stock policies could be measured. Safety stocks were held by the retailer and/or distribution center. Thus, nine possible combina- tions of safety stock level and echelon positioning existed. Table 3.5 summarizes the inventory policies used to research Problem II. 86 Table 3.5 Inventory Policies: Problem II Indirect System: Manufacturer: Production policy: Inventory policy: Distribution Center: Backorder policy: Replenishment policy: Safety stock policy: Retailer: Backorder policy: Replenishment policy: Safety stock policy: All customer demand draws on the retailer Infinite inventory NO stock maintained at plant No backorders Source Plant replenishes DC Reorder point 500 units plus safety stock Order quantity 500 units (constant) Review period each simulation day Safety stock levels (combined standard deviations) 0, 0.5, 1.0 NO backorders Source DC replenishes retailer Reorder point 500 units plus safety stock Order quantity 500 units (constant) Review period each simulation day Safety stock levels (combined standard deviations) 0, 0.5, 1.0 87 Simulations. In testing the hypotheses Of Parts A and B Of Problem II, eighty-one channel systems were simulated. Each simulation represented one of the possible combinations Of nine safety stock policies and nine uncer- tainty levels. Table 3.6 displays the simulations that were performed. Each simulation was 500 days in length, with customer service levels for each of ten products being generated every sixty days, after an initial twenty-day period. As with Problem I, only the customer service results from periods six and eight were included in the sample analyzed. Before the set of multi-echeloned channel simu- lations were performed, the stability Ofthe simulation was tested. Customer service levels were utilized as the test measure. A simulation was performed in which ten customer service levels were generated every sixty days for a 300 day period after an initial twenty-day period. The channel system simulated contained no safety stock and experienced the highest uncertainty level (L303) used in Problem II. An analysis Of variance was performed on the customer service results generated for periods three through six. The result was an F value Of 1.499 with a significance level Of .231. Thus, the periods were not significantly different. Non-contiguous periods were selected to avoid interdependence within the sampling data. 88 3m. 83 at $3 2.5 35 Amt 33 22; mama .m Ammo Aabv Aowv Amov Ammo Ahoy Aowv Ammo ovmv mama .m 33 ANS :8 83 Ammo Ammo 2.3 $3 Ammo Hand .5 33 Ammo Ammo 33 83 33 $3 :3 33 mama .m Amvv onv Amvv Amvv Ava onv Ammv Ammv Anny mama .m 33 $3 38 $3 3.3 :2 33 33 83 Hand .v Anny Ammo Ammo Avmv Ammo Ammo many Acme Away mafia .m Away ABHV Away Away Away AMHV ANHV «Hue Aoav Nada .m Ame Amy Amy Amy Ame Ave Ame Amy Adv HQHA .H AH.HV Am..Hv Ao.av AH.m.V Am..m.v Ao.m.v “H.0V Am..ov Ao.ov mam>oq mucfluuuoocb m m h m m e m m H mdeonaod xooum summmm HH anaonm ”wcoflumasfiflm o.m manna 89 Thus, simulation output consisted Of twenty sample Observations, one for each of ten products Observed over two separate time periods. The total sample which resulted from all simulations was 1,620 customer service levels. Table 3.7 details the output recorded from the simulations performed for Problem II. Table 3.7 Simulation Output: Problem 11 Total sample size . . . . . . . . . . . . 1,620 Simlations O O O O O O O O O O O O O O O 81 Observations per simulation . . . . . . . 20 Time periods sampled per simulation . . . 2 Products per simulation . . . . . . . . . 10 Response variable: (customer service levels) . . . . . . . . . . . . 1 Additionally, 1,620 predicted customer service levels were required to test the hypotheses in Part A of Problem II. These customer service levels were predicted using the statistical approach described in Chapter I of the research. The next section describes the statistical analysis employed in this research. 90 Statistical Analysis: Problems I and II In testing the hypotheses of this research, analysis Of variance techniques were employed. Specifically, the techniques were the F-test, Tukey's Method Of Multiple Comparisons and Scheffé's Multiple Comparison Method.6 Additionally, t-tests were employed. In Part A of Problems I and II, two-factor analysis. of variance was used to compare statistically, the customer service predicted by a statistical approach with that observed from dynamic simulation. The dependent variable was the difference in customer service levels. The two independent variables were safety stock policy and uncer- tainty. Table 3.8 summarizes the experimental factors, their levels, and the number of treatments utilized. The results of the two-factor analyses of variance (ANOVA) were reviewed in order to present the simultaneous impact of the two main effects on the response (dependent) vari- able. When a significant two-way interaction was indicated, inferences from the results of the two-way ANOVA were limited to interpretations Of the two-way interaction. This was required due to the fact that the calculations and corresponding F-tests made for all lower order interactions and main effects could be accomplished by collapsing the data over the one remaining independent variable. This would cause no difficulty in interpretation, 91 Table 3.8 ANOVA: Part A Two-Factor ANOVA: Problem I Factor A: Safety Stock Policy Factor B: Uncertainty Levels Levels 0 LlDl .5 LIDZ 1.0 L1D3 L2D1 L2D2 L2D3 L3D1 L3D2 L3D3 Treatments: (27) Full Factorial Design Two-Factor ANOVA: Problem II Factor A: Safety Stock Policy Factor B: Uncertainty Levels Levels (0.0) L101 (0,.5) L102 (0,1.0) L1D3 (.5,0) L2D1 (.5..5) L202 (.5,l.0) L203 (1.0,0) L301 (1.0..5) L302 (l.0,l.0) L3D3 Treatments: (81) Full Factorial Design 92 if the two-way interaction was insignificant, and it would signify that the effects of the two independent variables are additive. However, if the two-way interaction was significant, this would mean that the effects Of the one- way interactions were different across the levels of the second variable (over which the data were collapsed). Thus, each of the one-way interactions could only be interpreted by specifying a particular level Of the second variable. When one or more significant F-tests were found, Tukey's or Scheffé's multiple comparison techniques were used to identify the exact nature Of the difference. In Part B Of Problems I and II, two-factor analysis Of variance was used tO measure the relative impact Of safety stock policies employed and uncertainty levels experienced on customer service Observed from dynamic simulations. The dependent variable was customer service level. The independent variables, factor levels, and treatments were identical to those in Part A Of Problems I and II. The results of both two-factor (ANOVA's) were analyzed as those of Part A of Problems I and II had been analyzed. This chapter specified the hypotheses Of this research and the methodology employed to investigate each. It also reviewed the statistical analysis used to test the hypotheses. FOOTNOTES--CHAPTER III 1Donald J. Bowersox, David J. Closs, John T. Mentzer, Jr., and Jeffrey R. Sims, Simulated Product Sales Forecasting-Documentation (East Lan31ng, Mich.: Graduate School of Bus1ness Administration Research Bureau, Michigan State University, 1978). 2Ibid., p. 170, Appendix Of this research. 3E. Martin Basic, "DevelOpment and Application of a Gamma Based Inventory Management Theory" (Ph.D. disser- tation, Michigan State University, 1965). “G. Wagenheim, "The Performance of a Physical Distribution Channel Under Various Conditions of Lead-Time Uncertainty" (Ph.D. dissertation, Michigan State University, 1974), p. 83. 5Elwood S. Buffa, Production-InventorySSystems (Homewood, 111.: Richard D. Irwin, Inc., 1968), p. 161. 6John Neter and William Wasserman, Applied Linear Statistical Models (Homewood, 111.: Richard D. Irwin, Inc., 1974). 93 CHAPTER IV RESULTS OF ANALYSIS Introduction This chapter presents the research results. Specifically, it shOws the results of both Problems I and II. The analyses Of variance performed on the simu- lation results are discussed. The post hoc tests, results, and analyses are presented. Table 4.1 lists the additional abbreviations employed tO present the results. The abbreviations were employed to simplify and clarify the results. This chapter is divided into two sections, each containing two parts. Section one reports the results Of Parts A and B Of Problem I. Section two reports the results Of Parts A and B of Problem II. Results: Problem I Part A The general hypothesis is that in a comparison of customer service, predicted by a statistical approach and that Observed from a dynamic simulation, no difference exists. The response variable was the mean difference 94 95 Table 4.1 Abbreviations Safety Stock Poligy Abbreviations: Policy Distribution Center . . . . . . . . Retailer 0 .5 1.0 combined combined combined standard deviations standard deviations standard deviations Safety Stock Level Abbreviations: real. 0 1 l. 2 OU'IOU) combined combined combined combined combined standard deviations standard deviations standard deviations standard deviations standard deviations Of of of of Of safety safety safety safety safety Safety Stock Positioning Policy Abbreviations: Positioning Policy All safety stock held at distribution center All safety stock held at retailer . stock stock stock stock stock Some safety stock held at both distribution center and retailer Abbreviation DC WNl-‘w Abbreviation SSL-O SSL-.5 SSL—1.0 SSL-1.5 SSL-2.0 Abbreviation (DC) (R) (DC-R) 96 in customer service level recorded as a quantity fill rate. Table 4.2 presents the mean differences in customer service level resulting from comparisons Of the predicted and simulated mean values of customer service levels for each treatment. A positive mean difference indicated that the simulated mean value of customer service was higher than predicted. A negative mean difference indicated the reverse. The grand mean difference for the 540 pairs was 3.02 percentage points. A t-test resulted in a t-value Of 9.41, which was significant at a value of o==.001. Thus, the simulated customer service levels were significantly higher than predicted. T-tests performed on the treat- ment mean differences in Table 4.2 resulted in significant differences at a = .05 for seventeen Of the twenty-seven treatments. As shown, twelve Of the significant mean differences were positive values and five were negative. Individually, the simulated mean values Of customer service level were significantly higher than predicted at high uncertainty levels. Conversely, the simulated mean values of customer service level that were significantly lower than predicted occurred at low uncertainty levels. Figures 4.1 through 4.3 illustrate these differences graphically. 97 Table 4.2 Mean Differences in Simulated and Predicted Customer Service Levels Safety Stock Policy Uncertainty Level R1 R2 R3 LlDl -2.0* -0.3 -l.l* L1D2 -5.6* -1.0 -l.6* L1D3 -1.6 -0.6 -0.7 L2Dl -5.6* -0.7 0.4 L2D2 2.6 2.3* 1.4* L2D3 -0.1 2.4* 1.6 L3Dl 13.6* 11.0* 5.7* L3D2 14.4* 8.7* 7.4* L3D3 13.7* 9.9* 7.4* *Significant difference. The two-way analysis of variance performed on the mean differences is presented in Table 4.3. The two factors were safety stock policy (A) and uncertainty (B), and the response variable was the mean difference in customer service levels. The two-way interaction was significant. Thus, the combined impact Of the factors on the response variable was significant. Since the significance Of a two-way interaction bars direct inter- pretation Of factor effects, Tukey's and Scheffé's tests were used to investigate each Of the remaining hypotheses in Part A Of Problem I. 98 Uncertainty Level j; LlDl r Increasing Uncertainty L1D2 i L1D3 P L2D1“ L2D2 —' L2D3 )- L3D2 L3Dl . r 3 :' J L3D3 l J j a I a j 94 96 98 100% a 11 a 76 78 80 82 84 86 88 90 92 Customer Service Level I 1 J .—'—‘ Simulated ." "‘ " " . Predicted Figure 4.1 Mean Values of Simulated and Predicted Customer Service Levels for Safety Stock Policy Rl Under All Uncertainty Levels. 99 uncertainty Level LlDli- Increasing L1D2 _ Uncertainty L103 - p L201 22 L2D2 b L203 b e L3Dl )- f’ L3D2 - I L... . J l s l s a . I l s a _l 76 78 80 82 84 86 88 90 92 94 96 Customer Service Level O-—-—0 Simulated ..— -- --0 Predicted Figure 4.2 Mean values Of Simulated and Predicted Customer Service Levels for Safety Stock Policy R2 Under All Uncertainty Levels. 100 Uncertainty Level LlDl r Increasing Uncertainty LlDZ I- R3 L1D3 e L2Dl m L2D2 p L2D3 e I . L3D1 O L3D2 ‘ L3D3 O J l J 4 I J_ 1 L a A j J a 76 78 80 82 84 86 88 90 92 94 96 98 100% Customer Service Level ‘----0 Simulated .—. - -0 Predicted Figure 4.3 Mean Values Of Simulated and Predicted Customer Service Levels for Safety Stock Policy R3 Under All Uncertainty Levels. 101 Table 4.3 Analysis Of Variance: Mean Difference in Simulated and Predicted Customer Service Levels Degrees Source Of of Mean Critical Variation Freedom Square F F a==.05 Main Effects: A 2 .008 3.244* 3.00 B 8 .187 75.901* 1.94 Two-Way Interaction: AB 16 .014 5.668* 1.67 Residual 513 .002 Total 539 .006 *Significant. Hypothesis 1: In a comparison Of customer service predicted by a statistical approach and Observed from dynamic simulation, no difference exists: independent of the safety stock policy employed. Figure 4.4 displays the mean difference in customer service level for each safety stock policy employed (R1, R2, R3) under all uncertainty levels. Tukey's multiple compar- ison technique was used for comparisons Of the mean differ- ences in customer service between safety stock policies at each uncertainty level. The critical value at a = .05 was 5.81. Of the twenty-seven comparisons made, four resulted in significant differences. Comparisons of the mean 102 Uncertainty Level LlDl r L1D2 " L1D3 . . \ L202 r \‘r Increasing Uncertainty L2D3 - L3Dl p L3D2 r L3D3 )— 4 I j l l m a l l l a -8 -4 0 4 8 12 Mean Difference (Simulated-Predicted) Critical Value a.05= 5.81 Figure 4.4 Mean Difference in Customer Service for Each Safety Stock Policy Under All Uncertainty Levels. 103 differences in customer service for safety stock policies R1 and R3 resulted in significant differences at uncertainty levels L2D1, L3Dl, L3D2, and L3D3. NO other significant differences were found. Thus, Hypothesis 1 was rejected. The safety stock policy employed had an impact on the difference between simulated and predicted customer service levels in a single echelon channel system. Spe- cifically, a safety stock increase from 0 to 1.0 standard deviations significantly reduced the mean difference at high uncertainty levels. However, the simulated mean difference still was significantly higher than predicted at these high uncertainty levels. Hypothesis 2: In a comparison Of customer service predicted by a statistical approach and Observed from a dynamic simulation, no difference exists: independent of the uncertainty level experienced. Figure 4.5 illustrates the mean difference in customer service level for each uncertainty level expe- rienced under all safety stock policies. Tukey's multiple comparison technique was used for comparisons of the mean differences in customer service between uncertainty levels under each safety stock policy. The critical value at o==.05 was 5.81. Comparisons of the mean differences in customer service between each of the three highest uncer- tainty levels and each Of the other uncertainty levels 104 Safety Stock Policy R3 )- L102F 1 ‘ L301 L3D3 2D3 L201 L202 R2 b L101 L302 103 R1 - . l I s I J I a L s a #1 e -8 -4 o 4 8 12 16 Mean Difference (Simulated-Predicted) Critical value a.05 = 5.81 Figure 4.5 Mean Difference in Customer Service for Each Uncertainty Level Under All Safety Stock Policies. 105 resulted in significant differences under safety stock policy R1. In addition, comparisons Of the mean differ- ences of L202, with L2Dl and L1D2 resulted in significant differences. Comparisons Of the mean differences in customer service between each Of the three highest uncertainty levels and each Of the other uncertainty levels resulted in significant differences under safety stock policy R2. NO other significant differences were found. Comparisons of the mean differences in customer service between the two highest uncertainty levels and each of the lowest six uncertainty levels resulted in significant differences under safety stock policy R3. Additionally, comparisons Of the mean difference in customer service between L3Dl and the three lowest uncertainty levels resulted in significant differences. Thus, Hypothesis 2 was rejected. The uncertainty level had a significant impact on the mean difference between simulated and predicted customer service in a single echelon system. Two findings stand out. First, as uncertainty level increased, the simulated customer service level moved from being lower than predicted to higher than predicted. Second, at very high uncertainty levels, the mean difference was signifi- cantly different from lower uncertainty levels. Uncertainty 106 level had a significant impact on the nature Of the mean difference (positive or negative) and on the degree of difference. Hypothesis 3: In a comparison Of customer service predicted by a statistical approach and Observed from a dynamic simulation, no difference exists: independent of the combination of safety stock policy employed and uncertainty level experienced. Table 4.2 displayed the treatment mean differences Of simulated and predicted mean values Of customer service levels. The range was from -5.64 to 14.42. The analysis of variance confirmed that the two-way interaction was significant at a level Of a==.001. Accordingly, Hypothesis 3 was rejected. The combined impact Of safety stock policy employed and uncertainty level experienced had a significant impact on the mean difference between simulated and predicted customer service in a single echelon system. The uncer- tainty level experienced had a relatively greater impact than did the safety stock policy employed. When no safety stock was in the system, the statistical approach over- estimated customer service, at low uncertainty levels and underestimated customer service at high uncertainty levels. The pattern was the same when safety stock was introduced into the system. However, the degree Of error in predicting customer service was reduced relatively, 107 although the error remains significant at low and high uncertainty levels. Part B The general hypothesis is that in a comparison among customer service performance observed from dynamic simulations, no significant difference exists. The response variable representing customer service performance is customer service level. Table 4.4 presents mean values of the customer service levels resulting from the set Of simulations. The two-way analysis of variance performed on the simulation results is presented in Table 4.5. The factors were safety stock level (A) and uncertainty (B), and the reSpOnse variable was customer service level. The two-way interaction was highly significant. Thus, the combined impact Of the factors on the response variable was sig- nificant. The F values in Table 4.5 are all significant at a level of a=:.005. Since the significance of a two-way interaction bars direct interpretation Of factor effects, Tukey's and Scheffé's tests were used to investigate each of the remaining hypotheses in Part B Of Problem I. Hypothesis 1: In a comparison among customer service performance Observed from dynamic simulations, no significant difference exists: independent of safety stock level employed. 108 Table 4.4 Mean Values Of Simulated Customer Service Levels Safety Stock Levels uncertainty Levels (0) (.5) (1.0) l LlDl 93.8* 97.7 98.1 2 L1D2 89.0 96.4 97.0 3 L1D3 90.0 94.8 97.3 4 L2D1 82.4 93.2 97.0 5 L2D2 90.0 95.7 97.8 6 L2D3 85.5 94.8 97.2 7 L3Dl 90.0 97.6 98.1 8 L3D2 90.8 95.3 99.2 9 L3D3 88.7 95.9 99.6 *Rounded to one decimal place. Table 4.5 Analysis of Variance: Simulated Product Customer Service Levels Degrees Source of of Mean Critical Variation Freedom Square F F a==.05 Main Effects: A 2 .397 160.825* 3.00 B 8 .016 6.679* 1.94 Two-Way Interaction: AB 16 .054 2.176* 1.67 Residual 513 .002 Total 539 .004 *Significant. 109 Figure 4.6 displays the mean values Of customer service levels for each safety stock level employed (SSL-O, SSL-.5, SSL-l.0) under all uncertainty levels. Tukey's multiple comparison technique was used for safety stock level comparisons at each uncertainty level. The critical value at a==.05 was 5.81. Of the twenty-seven comparisons made, thirteen resulted in significant differences. Comparisons of customer service levels for safety stock levels SSL-O and SSL-l.0 resulted in significant differences at all uncertainty levels except the lowest level, LlDl. The customer service level under SSL-O was lower in each instance. Comparisons of customer service levels for safety stock level SSL-O and SSL-.5 resulted in five significant differences and three differences which were close to the critical value. In each instance, the cus- tomer service level under SSL-O was lower than that under SSL-.5. NO significant difference was found at the lowest uncertainty level. Comparisons of customer service levels for safety stock levels SSL-.5 and SSL-1.0 resulted in no significant differences. The largest difference was 3.9 percentage points. Thus, Hypothesis 1 was rejected. Safety stock level had a significant impact on customer service performance. Specifically, customer service levels increased as safety stock level increased, but at a decreasing rate. The customer service level 110 Uncertainty Level LlDl L1D2 L1D3 SSL-l.0 L2D1 L2D2 e L2D3 e L301 p L3D2 p L3D3 l l, s s I s a a l _1 a is S: 76 78 80 82 84 86 88 90 92 94 96 98 100% Customer Service Level Critical Value a.05 = 5.81 Figure 4.6 Mean values Of Customer Service Level for Each Safety Stock Level Under All Uncertainty Levels. 111 difference between SSL-O and SSL-.5 was greater than that between SSL-.5 and SSL-l.0 at all uncertainty levels. Additionally, nine Of the fourteen non-significant findings had differences of between 3.6 and 5.7 percentage points. Although these differences were not large enough to be statistically significant, they could have managerial significance. Sypothesis 2: In a comparison among customer service performance Observed from dynamic simulations, no significant difference exists: independent of uncertainty level experienced. Figure 4.7 presents the mean values of customer service levels for each uncertainty level experienced under all safety stock levels. Tukey's multiple comparison tech- nique was used for uncertainty level comparisons at each safety stock level. The critical value at a==.05 was 5.81. Of the 108 pairwise comparisons made, nine resulted in significant differences. All of the significant differ- ences were at safety stock level SSL-O. The customer service level under L2D1 was significantly lower than that under all other uncertainty levels except L2D3. The customer service level under L2D3 was significantly lower than under LlDl. At higher safety stock levels, no sig- nificant differences were found by changing uncertainty levels. Thus, Hypothesis 2 was rejected. 112 .mouuaHOL xOOum muouem flat aspen Ho>oa mucueuuooco zoom ecu ~o>oa oo«>uom unsounso no neoue> can: h.v vacuum «m.m I m.5 esum> Aeouuuuo dosed soa>uem nelouaso coed mm no no 00 no em no No «m cm mm no um mm mm v0 no mm m u q\( q . u «x a J\.- a (a d e Onamm annN\\\Lu““uuuw\uuuu\\\\\\ s m.namm Mona ., a .3... «and Haste gooum seamen 113 The uncertainty level experienced did impact customer service performance in a single echelon system. Specifically, the impact was significant when there was no safety stock in the system. The impact Of uncertainty level on customer service performance decreased as safety stock level increased. Additionally, increasing the vari- ations in combined uncertainties of demand over lead time did not always result in decreasing customer service levels as shown in Table 4.4. This is due to the random interac— tions of demand and lead time over many contiguous order cycles. Hypothesis 3: In a comparison among customer service performance Observed from dynamic simulations, nO significant difference exists: independent of the combinations of safety stock level employed and uncertainty level experienced. The analysis of variance revealed that the main effects Of both factors and the two-way interaction were highly significant. The mean values of customer service varied from a minimum of 82.4 percent to a maximum Of 99.6 percent across all treatments. Thus, Hypothesis 3 was rejected. The combined impact of safety stock level and uncertainty level on customer service performance was significant. 114 Results: Problem II Part A The general hypothesis is that in a comparison of customer service, predicted by a statistical approach and that Observed from a dynamic simulation, no difference exists. The response variable was the mean difference in service level recorded as a quantity fill rate. Table 4.6 presents the mean differences in customer service resulting from comparisons Of the predicted and simulated mean values of customer service levels for each treatment. A positive mean difference indicated that the simulated mean value Of customer service was higher than predicted. A negative mean difference indicated the reverse. The grand mean difference for the 1,620 pairs Of comparisons was 1.20 percentage points. A t-test resulted in a t-value of 5.36, which was significant at a value of a==.001. Thus, the simulated product customer service levels were signif- icantly higher than predicted. T-tests performed on the treatment mean differences in Table 4.6 resulted in sig- nificant differences at o= .05 for sixty Of the eighty-one treatments. As shown, thirty-three of the significant mean differences were positive values and twenty-nine were nega- tive. Specifically, the simulated mean values Of customer service level were significantly higher than predicted at high uncertainty levels, regardless of the safety stock 115 .ooconowmwo amusemwcmwm« «0.0 «0.NH «g.ma «0.0 «0.NH «v.ma «0.0 «0.NH «v.0H momn 0 «0.5 «H.0 «5.HH «0.5 «H.0 «5.HH «0.5 «H.0 «5.NH N0mq m «0.0 «0.0 «0.0 «0.0 «0.0 «0.0 «0.0 «0.0 «H.0H H0m0 5 m.0! 0.0 5.0! m.0! 0.0 5.0! «0.5! 0.0! «0.0a! momq 0 «0.H a0.N m.H! «0.H «m.N m.H! «H.0I «5.0! «0.0! NDNA m 0.0 0.0! «H.v 0.0 0.0 «H.v «v.m! «5.0! «0.5! H000 v 0.0 0.0 «N.m! 0.0 0.0 «N.M! «m.m! «N.m! «m.m! moan m m.0 0.0! «0.0! m.0 0.0! 0.0! «5.5! «0.0! «0.5! NDHA N «0.0! «0.H! «m.m! «N.N! «0.H! m.MI «0.vH! «5.0! «0.0H! HOHA H 2000 .9300 .9300 2000 00000 H0000 9:00 «”300 2.80 H950 aucflnuuooca mOfiHom xOoum wuomom mao>oq oow>nom Hoeoumso ooMOfloonm 0cm owuoHsEHm cw uneconommwa com: 0.v mHQMB 116 policy employed. Conversely, the simulated mean values of customer service level were significantly lower than predicted at lower levels of uncertainty. Figures 4.8 through 4.10 illustrate these differences graphically. The two-way analysis of variance performed on the mean differences is presented in Table 4.7. The two factors were safety stock policy (A) and uncertainty (B), and the response variable was the mean difference in customer service levels. The two—way interaction was significant. Thus, the combined impact of the factors on the response variable was significant. Since the significance Of the two-way interaction bars direct interpretation of factor effects, Tukey's and Scheffé's tests were used to investigate each Of the remaining hypotheses in Part A of Problem II. Table 4.7 Analysis Of Variance: Mean Difference in Simulated and Predicted Customer Service Levels Degrees Source Of of Mean Critical Variation Freedom Square F F a==.05 Main Effects: A 8 .105 28.990* 1.94 B 8 .693 190.525* 1.94 Two-Way Interaction AB 64 .016 4.480* 1.30 Residual 1,539 .004 Total 1,619 .008 *Significant. 117 Uncertainty Level DCZRl LlDl )- , DClRl . I Increasing DC3R1 1 L D2 - Uncertainty \ /’ L1D3 . L202 # L2D3 «- , 3. ’ / L3Dl .- r " ’ L3D2 - 1 \ . ' \ L3D3 p I J J J I I l J A l l L A __I 76 78 80 82 84 86 88 90 92 94 96 98 100% Customer Service Level tr *3 Simulated .- -— -'0 Predicted Figure 4.8 Simulated and Predicted Mean Values of Customer Service Level for Safety Stock Policies With R1. 118 Uncertainty Level .161 . f I . m \ , ncreasing DC2R2 LlD2 _ Uncertainty I; \\ L103 I I DC2R3 L2D1 . f ' \ L2D2 I- ’ a I L203 - J L3Dl - r L3D2 .. ’ ' . L3D3 . J J I l l L l I j e a e a l 76 78 80 82 84 86 88 9O 92 94 95 93 100% Customer Service Level O————-O Simulated ‘— — --0 Predicted Figure 4.9 Simulated and Predicted Mean Values Of Customer Service Level for Safety Stock Policies With R2. 119 Uncertainty Level L1 1 D P . DC1R3 DC2R3 \, Increa51ng Uncertainty LlD2 P \ ’/ L103 . / :2: $\ ./ L2D3 .. f ’ DC3R3 L3Dl . ~ "/ L3D2 P L303 L a s a I j I J I s s I J I 76 78 80 82 84 86 88 90 92 94 96 98 100% Customer Service Level .—-—. Simulated 0'- — -—0 Predicted Figure 4.10 Simulated and Predicted Mean Values of Customer Service Level for Safety Stock Policies With R3. 120 Hypothesis 1: In a comparison Of customer service predicted by a statistical approach and observed from a dynamic simulation, no difference exists: independent of safety stock policy employed. Figure 4.11 displays the mean difference in customer service level for each safety stock policy employed under all uncertainty levels. Scheffé's multiple comparison techniques (a==.05) were used for comparisons of the mean differences in customer service between safety stock pol- icies at each uncertainty level. Comparisons of the mean difference in customer service between safety stock policies at each uncertainty level resulted in the following signif- icant differences: DClRl and DC1R3 were different from the rest of the safety stock policies at uncertainty level LlDl; DClRl, DC1R2, and DC1R3 were different from DC2R3 and DC3R3 at uncertainty level LlD2; DClRl and DC1R2 were different from the rest Of the safety stock policies except DC1R3, at uncertainty level L2Dl; DC1R1 and DC1R3 were different from the rest of the safety stock policies at uncertainty level L2D2; DClRl and DC1R3 were different from the rest of the safety stock policies at uncertainty level L2D3. NO significant differences were found at uncertainty levels L1D3, L3Dl, L3D2, or L3D3. Thus, Hypothesis 1 was rejected. The safety stock policy employed did impact the difference between simulated and predicted customer service levels in a multi-echeloned channel system. Specifically, 121 .m00>o0 aucfiuunooca 00¢ Mecca 000000 xooum muommw zoom How Hm>o0 moa>uom muscumoo :0 oocouommwo coo: 00.v ousmfim 00 NH Acou00ooum!vouu0:fifimv mucoH00000 one: 0 V! 0! NH! 00! 0 v * — 1 J a 1 e a a aucwmuuooca 4 0c0meonoc0 l 0000 N000 H000 0000 NON0 H000 0000 N000 0000 093 Ammuueaod endow aummmm. wucflmuuoocs 122 safety stock policies having an (R) retailer positioning policy (DClRl, DClR2, DC1R3) and employed at low uncer- tainty levels resulted in significantly larger negative differences than safety stock policies having a (DC-R) positioning policy. Safety stock policies having an (R) retailer positioning policy and employed at intermediate uncertainty levels resulted in significantly larger nega- tive differences than all other safety stock policies. The safety stock policy employed at high uncertainty levels did not have a significant impact on the mean differences. However, using safety stock policies having a (DC) distri- bution center positioning policy resulted in larger (seven percentage points) positive differences than safety stock policies using 1.0 standard deviations of safety stock at retail. Hypothesis 2: In a comparison Of customer service predicted by a statistical approach and Observed from a dynamic simulation, no difference exists: independent of uncertainty level experienced. Figure 4.12 illustrates the mean difference in customer service level for each uncertainty level expe- rienced under all safety stock policies. Scheffé's multiple comparison procedures were used (a==.05) for comparisons of the mean difference in customer service between uncertainty levels under each safety stock policy. Comparisons of the mean difference in customer service 123 .mmeoaaod sooum >ummmm 00¢ Home: Ho>o0 hucHnuumoco 0000 now 00>o0 oow>uom Museumsu :0 coconowwH0 one: 00.v ou9000 AvoUOHUoum!oou00:E0mv muconommwn cum: 0H NH 0 v 0 V! m! 0H! 0H! . f. u an . . a . _ q . ax . a (a . I I H00 CN0H0 0000 H000 0000 N000 HOH0 L HOH00 00H00 00H00 H0000 H0000 00000 00000 00000 00000 moaaom xooum acumen 124 between uncertainty levels under each safety stock policy resulted in the following significant differences: the three highest uncertainty levels were significantly dif— ferent from the other six uncertainty levels under safety stock policies DClRl, DClR2, DC1R3, DC2R2, and DC3R2. Additionally, the three highest uncertainty levels were different from all other uncertainty levels, except L2Dl, under safety stock policies DCZRl and DC3R1. The three highest uncertainty levels were different from only uncertainty level LlDl under safety stock policies DC2R3 and DC3R3. Uncertainty level LlDl was different from L1D3 under safety stock policies DClRl and DC1R3. Thus, Hypothesis 2 was rejected. The uncertainty level had a significant impact on the mean difference between simulated and predicted customer service in a multi-echeloned channel system. Specifically, at low uncertainty levels, simulated customer service levels were significantly lower than predicted. At high uncertainty levels, simulated customer service levels were significantly higher than predicted. Thus, the uncertainty level experienced had a significant impact on whether the statistical approach over or underestimated customer service. 125 Hypothesis 3: In a comparison of customer service predicted by a statistical approach and observed from a dynamic simulation, no difference exists: independent of the safety stock policy employed and the uncertainty level experienced. Table 4.6 displayed the treatment mean differences of simulated and predicted mean values of customer service. The range was from -l4.92 to 13.36. The analysis of vari- ance confirmed that the two-way interaction was significant at a level of a==.001. Thus, Hypothesis 3 was rejected. The combined impact of safety stock policy employed and uncertainty level experienced had a significant impact on the mean difference between simulated and predicted customer service in a multi-echeloned channel system. The statistical approach overestimated customer service at low uncertainty levels, and particularly when the safety stock policy employed had no safety stock at the distribution center. The statistical approach under- estimated customer service at high uncertainty levels across all safety stock policies. The underestimation was partic- ularly high when the safety stock policy employed had no safety stock at the retail stage. Part B The general hypothesis is that in a comparison among customer service performance observed from dynamic simulations, no significant difference exists. The 126 response variable which represents customer service performance is customer service level. Table 4.8 presents mean values of the customer service levels resulting from the set of simulations performed for Problem II. The two-way analysis of variance performed on the simulation results is presented in Table 4.9. The factors were safety stock policy (level and positioning) (A) and uncertainty (B). A review of the fifth column of Table 4.9 indicated that the two-way interaction was highly significant. The F value of 4.259 clearly exceeded the critical F value (.95, 64,1539) of 1.320. The two-way interaction was confirmed graphically in Figure 4.13. The lines were not parallel and therefore the two factors A and B were not additive. Since the significance of a two-way inter- action bars any direct interpretation of the factors, Tukey's and Scheffé's tests were used to investigate each of the remaining hypotheses in Part B of Problem II. Hypothesis 1: In a comparison among customer service performance observed from dynamic simulations, no significant difference exists: independent of safety stock level employed. The impact of safety stock level on customer service performance was isolated by holding constant both the safety stock positioning policy and uncertainty level. 127 .momHm Hafifiomo oco ou vmocdomt >.mm o.mm v.mm >.mm o.mm v.wm o.mm o.mm v.mw mama m m.mm n.mm H.mm «.mm h.mm wam m.mm h.mm H.mm damn m v.mm m.mm m.mm v.mm m.mm m.mw m.mm m.mm m.om Hand 5 m.mm o.mm m.vm m.mm o.mm m.vw m.mw m.mm o.mh mama m m.mm m.om o.mm m.mm ~.mm w.mw m.mm h.mm m.hh NQNA m m.hm m.¢m H.~m m.hm m.vm H.~m «.mm H.mm m.om Hana v m.mm no.wm v.wm m.mm 0.9m v.mw h.Nm ~.om H.mm mafia m m.mm m.wm H.mm m.mm 0.0m H.mm 0.0m 0.0m b.0w moan N 0.5m H.0m m.mm 0.5m H.mm m.mm m.¢w m.mm «m.~m HQHA H mumoo mmmoa ammoo mamoa mmmoa ammuo mmaua mmaoa HmHUQ Hm>wq aucwmuuoocb mowaom xooum aummmm mam>oq moa>umm uoEoumso nonmassflm mo mosam> coo: m.v manna 128 Table 4.9 Analysis of Variance: Simulated Customer Service Levels Degrees Source of of Mean Critical Variation Freedom Square F F d==.05 Main Effects: ‘ A 8 .463 127.213* 1.940 B 8 .066 18.016* 1.940 Two-Way Interactions: AB 64 .015 4.259* 1.320 Residual 1,539 .004 Total 1,619 .007 *Significant. Figures 4.14 through 4.16 diSplay the mean values of customer service levels for the safety stock levels employed under each combination of safety stock positioning policy and uncertainty level. Tukey's multiple comparison tech- nique was used for safety stock level comparisons under each set of conditions. The critical value at a==.05 was 7.99. Figure 4.14 presents the mean values of customer service levels for each safety stock level employed (SSL-O, SSL-.5, SSL-l.0) under a distribution center safety stock positioning policy. Comparisons of customer service levels for safety stock levels SSL-O and SSL-.5 resulted in sig- nificant differences at four of the nine uncertainty levels: LlDl, L2Dl, L2D2, and L2D3. The customer service level for 129 Uncertainty Level L191 . DClRl DCIRJ nczni DC2RZ \ DC2R3 DC ' DC3R2 \ - 3113 Increasing uncertainty DClRZ \\ \\\ L102 b L103 b L2D1 . L2D2 r L203 . L3D1 # '\ L302 p L3D3 .. ‘ n 41 1, A n 41 1, 1 e e e 41L 1 76 78 80 82 84 86 88 90 92 94 96 98 100\ Gusto-er Service Level Figure 4.13 Mean values of Cuetceer Service novel for Each Sefety Stock Policy Under All Uncertainty Levels. Uncertainty Level LlDl L1D2 L1D3 L2D1 L2D2 L2D3 L3D1 L3D2 L3D3 F 130 SSL-O SSL-.5 _‘ SSL-1.0 Increasing ////// Uncer ainty J \ j n l I All I 4; 411 I, n 1 j 76 78 80 82 84 86 88 90 92 94 96 98 100% Customer Service Level Critical Value a.05 = 7.99 Figure 4.14 Mean Values of Customer Service Levels for Each Safety Stock Level Under a Distribution Center Safety Stock Positioning Policy. 131 Uncertainty Level L1D1 P Increasing Uncertainty L1D2 P L1D3 <- LZDl L L2D2 L. L2D3 . L3D1 - L3D2 - L3D3 p l n J, .1 I 4L n l l j I I. 41 76 78 80 82 84 86 88 90 92 94 96 98 100% Customer Service Level Critical Value 0 .05 = 7.99 Figure 4.15 Mean Values of Customer Service Levels for Each Safety Stock Level Under a Retailer Safety Stock Positioning Policy. 132 Uncertainty Level Sfi?'°5 LlDl 'P Increasing Uncertainty L1D2 ’ L1D3 p L2D1 P SSL-O SSL-1.0 L2D2 P L2D3 - L3Dl - L3D2 L L303 - 14, 44, 1 l _1 L j_ I l l n 4~1____[ 76 78 80 82 84 86 88 90 92 94 96 98 100% Customer Service Level Critial Value a.05 = 7.99 Figure 4.16 Mean Values of Customer Service Levels for Each Safety Stock Level Under a Distribution Center—Retailer Safety Stock Positioning Policy. 133 safety stock SSL-O was lower in each instance. The same results appear when comparisons were made between safety stock levels SSL-O and SSL-l.0. No differences were found in comparing customer service levels for safety stock levels SSL-.5 and SSL-l.0. Figure 4.15 presents the mean values of customer service levels for each safety stock level employed (SSL-O, SSL—.5, SSL-l.0) under a retailer safety stock positioning policy. Comparisons of customer service levels for safety stock levels SSL-O and SSL-.5 resulted in significant dif- ferences at all uncertainty levels except L1D2 and L1D3. The customer service levels for safety stock level SSL-O were lower in each instance. Comparisons between safety stock levels SSL-O and SSL-l.0 yielded the same results. Comparisons of customer service levels for safety stock levels SSL-.5 and SSL-l.0 resulted in only one significant difference. The customer service level under safety stock level SSL-.5 was significantly lower than that under SSL-l.0 at uncertainty level LlDl. Figure 4.16 shows the mean values of customer service levels for each safety stock level employed (SSL-1.0, SSL-l.5, SSL-2.0) under a distribution center-retailer safety stock positioning policy. Comparisons between the customer service levels of the three safety stock levels resulted in no significant differences. 134 Hypothesis 1 was rejected. The safety stock level employed had a significant impact on customer service per- formance in multi-echeloned channel systems. Table 4.10 summarizes the significant differences. Twenty-two of the twenty-three significant differences result from comparing a safety stock level of zero with that of .5 or 1.0 standard deviations. At safety stock levels of SSL-.5 and higher, increases in safety stock equaling .5 or 1.0 standard deviations had no significant impact on customer service levels, regardless of the safety stock positioning policy employed and/or the uncertainty level experienced. Thus, customer service level increased as safety stock level increased, but at a decreasing rate. Increases in safety stock level from .5 to 1.0 standard deviations resulted in customer service level increases ranging from zero to four percentage points. Increases in safety stock level from 1.0 to 2.0 standard deviations resulted in cus- tomer service level increases ranging from one to three percentage points. In most instances, the larger increases (3 to 4 percent) occurred at higher uncertainty levels. 135 .ucmoflcncoww. .. .. .. .. 4 4 .. .. .. mama m .. .. .. .. 4 4 .. .. .. mama m .. .. .. .. 4 4 .. .. .. Hana h .. .. .. .. 4 4 .. 4 4 mama o .. .. .. .. 4 4 .. 4 4 NQNA m .. .. .. .. 4 4 .. 4 4 HQNA v .. .. .. .. .. .. .. .. .. moan m .. .. .. .. .. .. .. .. .. «can N . . . . . . 4 4 4 . . 4 4 HDHA H o.mlm.a o.mlo.H m.Hlo.H o.HIm. OHIO m.lo o.HIm. o.HIo m.uo Hm>0n hucwmuuooca qmm Amm Amm >0Haom OGHGOwuamom xoflaom unacOMawmom unfiaom mcacofluwmom $705 9: 8n: mGOmHHmmEoo Hm>oq xooum aummmm mo mumEEsm oa.¢ manna 136 Hypothesis 2: In a comparison among customer service performance observed from dynamic simulations, no significant difference exists: independent of safety stock positioning employed. The impact of safety stock positioning on customer service performance was isolated by holding constant both the safety stock level and the uncertainty level. Figures 4.17 and 4.18 display the mean values of customer service levels for the safety stock positioning policy employed under each combination of safety stock level and uncertainty level. Tukey's multiple comparison technique was used for safety stock positioning comparisons under each set of con- ditions. The critical value at a==.05 was 7.99. Figure 4.17 presents the mean values of customer service levels for each safety stock positioning policy employed [(DC), (R)] under safety stock level SSL-.5. Comparisons of customer service levels for safety stock positioning policies (DC) and (R) resulted in significant differences at the three highest uncertainty levels, L3Dl, L3D2, and L3D3. In each instance, the customer service level under safety stock positioning policy (R) was higher than that under safety stock positioning policy (DC). The average significant difference was 9.9 percentage points. Figure 4.18 presents the mean values of customer service levels for each safety stock positioning policy employed [(DC), (R), (DC-R)] under safety stock level Uncertainty Level L1D1 L1D2 L1D3 L2D1 L2D2 L2D3 L3D1 L3D2 L3D3 I 76 137 Increasing Uncertainty (DC) (R) l I .I I I l I I I I I J 78 80 82 84 86 88 90 92 94 96 98 100% Customer Service Level Critical Value 0!. .05 = 7.99 Figure 4.17 Mean Values of Customer Service Levels for the Safety Stock Positioning Policies Under Safety Stock Level SSL-es e Uncertainty Level LlDl L1D2 L1D3 L2Dl L2D2 L203 L3D1 L3D2 L3D3 138 (93 (nah we) (a) (DC-R) Increasing Uncertainty I 76 I I I I I I I I I I II I 78 80 82 84 86 88 90 92 94 96 98 100% Customer Service Level Critical Value on .05 = 7.99 Figure 4.18 Mean values of Customer Service Levels for the Safety Stock Positioning Policies Under Safety Stock Level SSk100. 139 SSL-l.0. Comparisons of customer service levels for safety stock positioning policies (DC) and (R) resulted in significant differences at the lowest (LlDl) and three highest uncertainty levels, L3Dl, L3D2, and L3D3. At uncertainty level LlDl, the customer service level under safety stock positioning policy (R) was significantly lower than that under safety stock positioning policy (DC). At the three highest uncertainty levels, the customer service level under safety stock positioning policy (R) was significantly higher than that under safety stock positioning policy (DC). The average significant difference was 12.6 percentage points. Comparisons of customer service levels for safety stock positioning policies (DC) and (DC-R) resulted in significant differences at all uncertainty levels except L1Dl and L2Dl. In each instance, the customer service level under safety stock positioning policy (DC-R) was significantly higher than that under safety stock posi- tioning policy (DC). The average significant difference was 9.2 percentage points. Comparisons of customer service levels for safety stock positioning policies (R) and (DC-R) resulted in significant differences at uncertainty levels of LlDl, L2D2, and L2D3. The difference at uncertainty level L1D2 was close to the critical value. In each instance, the 140 customer service level under safety stock positioning policy (DC-R) was significantly higher than that under safety stock positioning policy (R). Thus, Hypothesis 2 was rejected. The safety stock positioning policy employed significantly impacts customer service performance in multi-echeloned channel systems. Specifically posi- tioning a safety stock level of .5 standard deviations at the retailer rather than the distribution center, resulted in significantly higher customer service levels when employed under conditions of high uncertainty. When positioning a safety stock level of 1.0 standard deviations in a multi-echeloned system experiencing low or intermediate uncertainty levels, a safety stock positioning policy where the stock is equally divided between distribution center and retailer resulted in significantly higher customer service than those that concentrated the full amount of safety stock at either the distribution center or retailer. At higher uncertainty levels, positioning the full amount of safety stock at the retailer, resulted in customer service levels of one to four percentage points higher than a positioning policy that divided the stock between distribution center and retailer. However, either of these safety stock positioning policies resulted in significantly higher customer service levels than a 141 policy of concentrating the full amount of safety stock at the distribution center. Hypothesis 3: In a comparison among customer service performance observed from dynamic simulations, no significant differences exist: independent of safety stock policy employed. The safety stock policy in a multi-echeloned channel system consists of setting a safety stock level and position. It has been determined that both safety stock level and position (independently) impact customer service performance significantly. A determination of the impact of safety stock policy on customer service level requires an examination of the combined impact of safety stock level and position on customer service. Figures 4.19 through 4.21 present the mean values of customer service levels resulting from safety stock policies employed at each uncertainty level. These figures illustrate the impact of different combinations of safety stock level and positioning on customer service. As shown, the safety stock policy employed did significantly effect customer service at all uncertainty levels. The nine safety stock policies employed in Problem II resulted in a wide range of customer service levels. Within a given uncertainty level, the minimum range of customer service levels was ten percentage points. 142 SSL 2.0 I- 1.5 "' (DC-R) 1.0 - (R) (DC) .5 p 0 I I L I I I I I I I I L I 76 78 80 82 84 86 88 90 92 94 96 98 100‘ customer Service Level SSL 2.0 I- 1'5 " (DC-R) 1.0 I- (DC) (R) .5 .- 0 I I I J I I I I I I I I I 76 78 80 82 84 86 88 90 92 94 96 98 100\ Customer Service Level SSL 2.0 I' 1-5 - (DC-R) 1.0 p (001 (R) .5 P O I I J I I I I I J I I l I 76 78 80 82 84 86 88 90 92 94 96 98 100\ Customer Service Level Figure 4.19 Cuetaaer Service of Safety Stock Policies Under Low Uncertainty Levels LlDl. 1.102, L103. 143 SSL 2e0- 1.5 - (DC—R) 1.0 . (R) (DC) .5 b O I I I J I I I I I _I L 4g 76 78 80 82 84 86 88 9O 92 94 96 98 100‘ customer Service Level SSL 2.0 . 1.5 *- (DC-R) 1.0 .- (DC) (R) .5 P O l l I _L J I J J I J I I 4 76 78 80 82 84 86 88 90 92 94 96 98 1004 Customer Service Level SSL 2.0 .. 1.5 -- (DC-R) 1.0 " (DC) (R) .5 I- 0 J I I 1 I I I I I J I I #I 76 78 80 82 84 86 88 90 92 94 96 98 1004 Customer Service level Figure 4.20 Customer Service of Safety Stock Policies Under Intermediate Uncertainty levels, L201. L202, L203. SSL 2.0 1.5 1.0 .5 SSL 2.0 1.0 .5 SSL 2.0 1.5 1.0 .5 144 ['1 (DC-R) (no) (R) I I L I I I I I I L I I J 76 78 80 82 84 86 88 90 92 94 96 98 100‘ Customer Service Level H (W‘R) (R) (DC) I I I I I I I I I I I I 76 78 80 82 84 86 88 90 92 94 96 98 Tom Customer Service level (DC-R) (DC) (R) I I I I I I J I I I I I I 76 78 80 82 84 87 88 90 92 94 96 98 100s Customer Service level Figure 4.21 anteater Service of Safety Stock Policies Under High Uncertainty levels, L3Dl. L302, L3D3. 145 Two findings stand out. First, safety stock positioning had a greater influence on the resulting customer service levels than did the safety stock level. The significant differences in positioning policy were much larger than those for safety stock level. Second, in gen- eral, the safety stock positioning policies can be ordered, from the highest customer service to the lowest, as follows: (DC-R) followed by (R) followed by (DC). An exception to this order occurs at very high uncertainty levels, where (R) and (DC-R) may change places. In effect, this shows that more safety stock at retail locations results in higher customer service levels when high uncertainty levels are experienced. Accordingly, Hypothesis 3 was rejected. The safety stock employed had a significant impact on customer service performance in a multi-echeloned channel system. Hypothesis 4: In a comparison among customer service performance observed from dynamic simulations, no significant difference exists: independent of uncertainty level experienced. Figure 4.22 shows the mean values of customer service level for each uncertainty level experienced across all safety stock policies. Tukey's multiple comparison technique was used for uncertainty level comparisons. The critical value of F at a==.05 was 7.99. As illustrated in Figure 4.22, the uncertainty level experienced under safety 146 Safety Stock . Policy (Uncertainty Levels) DC3R3 DC2R3 '- DC3R2 - mm L DC1R3 ' DC1R2 ' DC3R1 P DC2R1 ' DC1R1 ’ I II II I I I I, I It I I :L___‘ 76 78 80 82 84 86 88 90 92 94 96 98 100% Customer Service Level Critical Value a.05==7.99 Figure 4.22 Mean values of Customer Service Level for Each Uncertainty Level Across All Safety Stock Policies. 147 stock policies, D2R2, D3R2, D2R3, and D3R3, did not significantly impact customer service levels. These four safety stock policies were those which employed safety stocks at both the distribution center and retailer. Comparisons of uncertainty levels under each of the other safety stock policies resulted in significant differences. Thus, Hypothesis 4 was rejected. The uncertainty level experienced had a significant impact on customer service performance in a multi-echeloned channel system. The analysis of variance (Table 4.9) con- firmed this conclusion. The main effect of factor (B) was significant. The F value was significant at a level of 0L= .001. Two findings were especially significant. First, the impact of the uncertainty level on customer service performance diminished as the system safety stock level increased. Specifically, the range of the customer service levels was fourteen percentage points at SSL-0; twelve and nine percentage points at SSL-.5; sixteen, nine, and five percentage points at SSL-1.0; five and four percentage points at SSL-1.5; and four percentage points at SSL-2.0. Second, an increase in uncertaintly level did not always result in a decrease in customer service level. While the basic relationship between uncertainty level and customer service level was inverse, 37 percent of the increases in 148 uncertainty level resulted in increases in customer service. Although these increases were not statistically significant, they were increases, not decreases. In addition, 5 percent of the increases in uncertainty level resulted in signif- icant increases in customer service. Thus, the direction customer service would take was not fully predictable. Hypothesis 5: In a comparison among customer service performance observed from simulations, no significant difference exists: independent of the combinations of safety stock policy employed and uncertainty level experienced. Table 4.8 shows the wide range of customer service levels resulting from combinations of safety stock policy employed and uncertainty level experienced. The values range from 75 percent to 99.6 percent. The analysis of variance confirmed that the two-way interaction was significant at a==.001. Thus, Hypothesis 5 was rejected. The combined impact of safety stock policy employed and uncertainty level experienced on customer service performance in a multi-echeloned channel system was significant. CHAPTER V CONCLUSIONS Introduction This chapter presents the research conclusions, relates the conclusions to the present body of knowledge for distribution inventory planning and suggests areas for future research. The first section of the chapter discusses the conclusions derived from the hypotheses in Parts A and B of both research problems. The second section acknowledges the research limitations and offers areas for future research. Conclusions for Safety Stock Planning and Control The objective of this research was to measure both the accuracy of a statistical approach and the relative impact of alternative safety stock policies and uncertainty levels on customer service performance in single and multi- echeloned channel systems. The measures are discussed first for single echelon channel systems followed by a discussion of the conclusions drawn for multi-echeloned channel systems. 149 150 Problem I: Conclusions Safety stock policy effects. Safety stock policy has a significant effect on the difference between predicted and simulated customer service. Specifically, higher safety stocks decrease the difference between predicted and simu- lated customer service. This behavior can be explained by examining the safety stock policy-customer service relationship. Safety stock policy has a significant effect on customer service. A safety stock increase results in a customer service increase, but at a decreasing rate.1 Specifically, the introduction of safety stocks into the channel system resulted in an average customer service increase of seven percentage points, while an addition to safety stocks, equal in size to the introductory amount, resulted in an average customer service increase of only two percentage points. Thus, given the safety stock policy- customer service relationship and the fact that customer service has an upper limit, the potential margin for error in predicting customer service diminishes as the upper limit is approached. So, managers should not use the statistical approach unless the desired customer service is close to the upper limit. Uncertainty effects. Uncertainty has a significant effect on the difference between predicted and simulated 151 customer service. Specifically, higher uncertainty increases the absolute difference between predicted and simulated customer service. At high uncertainty levels, the differences were never below six percentage points. Thus, managers should not use the statistical approach in channel systems experiencing high uncertainty levels. A second conclusion relating to uncertainty effects is that of the two types of uncertainty, lead time had the greatest effect on the difference between predicted and simulated customer service. The effect was in terms of degree of difference and direction of difference. Predicted customer service was higher than simulated customer service when low lead time variances were experienced and lower than simulated customer service when high lead time variances were experienced. Thus, managers who use the statistical approach under low lead time variance conditions, will fall short of their desired customer service goal. This may be a significant problem for managers who are facing highly competitive market situations where high customer service goals must be attained. Under market conditions such as this, managers would not want to fall short of their planned customer service goal since stockout costs are high compared to inventory carrying costs. So, use of the statistical approach under low lead time variance conditions is not recommended when managers must attain a desired customer service goal. 152 Since the statistical approach underestimates uncertainty effects on customer service at low uncertainty levels and overestimates uncertainty effects on customer service at high uncertainty levels, this seems to imply that the statistical approach is overreacting to changes in uncertainty level. It is possible that within the statistical approach, the effect of lead time variance on customer service has been misrepresented. In addition, part of the difference may be explained by examining the relationship between uncertainty and customer service. Uncertainty has a significant effect on customer service. Specifically, increasing uncertainty generally resulted in decreasing customer service. Although this was expected, the change in customer service was lower than expected based on tables compiled by T. A. Burgin and A. R. Wild from Pearson's Tables on the Incomplete 2 This may be explained, in part, by the Gamma Function. interaction of demand and lead time variabilities. Because demand and lead time variabilities are not additive, a sort of "cancellation effect" may cause customer service to be higher than expected.3 For example, demand variability may cause the average daily demand to exceed the expected or mean value of daily demand over a specific lead time. How- ever, at the same time, lead time variability may result in this specific lead time being shorter than the mean value of 153 lead time. Therefore, the shortened lead time "cancels" some or all of the negative effects that excess demand might have had on customer service. The implication is that the statistical approach does not accurately replicate the uncertainty-customer service relationship because, in part, it does not replicate demand—lead time interactions. Safety stock policy and uncertainty effects (com- biped). Safety stock policy and uncertainty have a signif- icant combined effect on the difference between predicted and simulated customer service. Figure 5.1 shows the fea- sibility of using the statistical approach under alternative combinations of safety stock policy and uncertainty in a single echelon channel system. The conditions under which the statistical approach can be accurately used are repre- sented in Figure 5.1 by blank squares. It should be noted that in the two blank squares where uncertainty is low, use of the statistical approach results in customer service that falls short of the prescribed customer service. Thus, man— agers who face highly competitive market situations may find the statistical approach unusable under these conditions as well. It is apparent that the statistical approach, for the most part, does not accurately predict customer service in single echelon channel systems and should, therefore, not be used. 154 I Decreasing Accuracy Safety Stock Policy Uncertainty Low Medium High Medium Decreasing Accuracy High Figure 5.1 Statistical Approach-Application in Single Echelon Channel Systems. 155 Currently, there are no similar alternative statistical techniques available for managers to use in setting safety stocks. Thus, either a new statistical approach must be devised or the original statistical approach must be modified. In either case, a better understanding of the effects of safety stock policy and uncertainty on customer service performance will be useful. Safety stock policy and uncertainty have a signif- icant combined effect on customer service. Safety stock policy changes have a greater effect than uncertainty changes on customer service. The first safety stocks placed in the channel system have the largest effect on customer service, regardless of the uncertainty level. A partial explanation for the significant effects of safety stocks on customer service, even at low uncertainty levels, is that the placement of the safety stocks is at retail. Because the safety stock is at the point of demand, it can be fully used, if needed. Managers, who attempt to devise a new statistical approach or modify the existing statistical approach, may want to consider this combined effect as well as the independent effects of safety stock policy and uncertainty on customer service. Problem 11: Conclusions Safety stock policy effects. Safety stock posi— tioning policies have a significant effect on the difference between predicted and simulated customer service in a 156 multi-echeloned channel system. The use of a distribution center-retailer positioning policy rather than a distribu- tion center or retailer positioning policy results in a significant decrease in the difference between predicted and simulated customer service. Specifically, a distri- bution center-retailer positioning policy under low or intermediate uncertainty conditions results in a minor difference between predicted and simulated customer service, while distribution center or retailer policies under the same conditions results in simulated customer service that is significantly lower than predicted. The average differ— ence is five percentage points. Thus, managers can use the statistical approach when safety stocks are positioned at both echelons, except at high uncertainty levels. However, managers should not use the statistical approach when all safety stocks are positioned at only one of the two eche— lons. To further understand why the statistical approach should not be used under absolute postponement or absolute speculation positioning policies, the relationship between safety stock policy and customer service was examined. Safety stock policy has a significant effect on customer service in a multi-echeloned channel system. Both safety stock positioning and safety stock level have significant effects on customer service, but safety stock positioning effects are greater. A distribution 157 center-retailer positioning policy results in significantly higher customer service than a retailer positioning policy, except at high uncertainty levels where this changes. The distribution center-retailer positioning policy was six percentage points higher at low and intermediate uncer- tainty levels and three percentage points higher overall. Thus, the principle of postponement is verified.” The reason that this partial postponement positioning policy results in higher customer service than absolute speculation is that safety stocks are held at both the distribution center and retailer. This is important because inventory performance at sequential locations is interrelated. Total system performance is dependent, in part, on the inventory performance at all stocking locations. Thus, inventory performance at retail depends on the inventory performance at the distribution center and the lead time characteristics between the distribution center and retailer. The amount of safety stock at the distribution center directly affects the ability of the distribution center to fill retail replenish- ment orders, which, in turn, affects the retailers' inven- tory performance and ultimately customer service performance. Thus, managers can use partial postponement to increase cus- tomer service significantly in multi-echeloned channel systems, except at very high uncertainty levels. 158 A related conclusion is that a distribution center-retailer positioning policy results in significantly higher customer service than a distribution center posi- tioning policy. The average difference is eight percentage points. Thus, absolute postponement suffers from the same limitation as absolute speculation in that one echelon will have poor inventory performance which will affect total system performance negatively. Thus, managers can attain higher customer service by positioning safety stocks at all interrelated stocking locations in the channel rather than positioning safety stocks at one location. The exception is the placement of all safety stock at retail, when the channel is experiencing high uncertainty levels. In more complex channel systems, where a distribu- tion center supplies multiple retail locations, a comparison of the distribution center-retailer positioning policy and retailer positioning policy would result in an even higher difference in customer service. In this situation, post- ponement of some retail safety stock to the distribution center by each retailer improves distribution center inven- tory performance which, in turn, impacts total system per— formance. An additional benefit is that the distribution center can combine retail variations in demand which, in effect, reduces uncertainty. The effect of safety stock postponement on customer service would be higher in channels 159 where multiple retail locations were supplied by a distribution center. The previous point reemphasizes the importance of a total channel concept. Employment of a channel-wide inventory policy rather than independent wholesaler and retailer inventory policies can result in increased channel system customer service performance. Safety stocks introduced at retail result in significantly higher customer service than if placed at the distribution center. This difference increases as uncertainty increases. Thus, the best single location for introducing safety stocks in the channel is at retail. Additional safety stocks, at retail, will increase customer service slowly, while additional safety stocks at the distribution center become useless quickly. Thus, managers who have safety stocks at both echelons and want to increase customer service, should place the additional safety stock at retail. The examination of the safety stock policy-customer service relationship clearly identifies why the statistical approach failed in channels with absolute postponement or absolute speculation positioning policies. Simulated cus- tomer service was significantly lower than predicted because the statistical approach did not account for the inter- related inventory performance of sequential stocking 160 locations. Thus, managers employing absolute speculation or postponement safety stock positioning policies should not use the statistical approach. Uncertainty effects. The uncertainty level has a significant effect on the difference between predicted and simulated customer service. Specifically, at low uncertainty levels, the simulated customer service is significantly lower than predicted, while at high uncer- tainty levels the simulated customer service is signifi- cantly higher than predicted. At high uncertainty levels, the statistical approach error averages nine percentage points. To explain these conclusions, the uncertainty- customer service relationship was examined. Uncertainty has a significant effect on customer service. In general, an increase in uncertainty level resulted in a decrease in customer service. However, in many instances, an increase in uncertainty resulted in customer service that was higher or lower than expected. This may be explained by the interaction of demand and lead time variabilities and the interaction of uncertainties at sequential echelons. Thus, the statistical approach does not accurately represent the uncertainty-customer service relationship because, in part, it fails to consider the interaction of uncertainties of sequential echelons. 161 Safety stock policy and uncertainty effects (combined). Safety stock policy and uncertainty have a significant combined effect on the difference between predicted and simulated customer service. Figure 5.2 shows the feasibility of using the statistical approach under alternative combinations of safety stock policy and uncer- tainty in a multi-echeloned channel system. The condition under which the statistical approach can be accurately used is represented in Figure 5.2 by a blank square. It is apparent that the statistical approach does not accurately predict customer service in multi-echeloned channel systems, and, for the most part, should not be used. There are no alternative statistical safety stock techniques that con- sider the effects of interaction of sequential echelons. Thus, managers can either devise a new statistical approach or attempt to modify the existing statistical approach. In either case, a better understanding of the effects of safety stock policy and uncertainty on customer service performance in a multi-echeloned channel system will be beneficial. Safety stock policy and uncertainty have a signif- icant combined effect on customer service. Safety stock positioning policy changes have a greater impact than uncertainty changes on customer service. Customer service under the distribution center-retailer positioning policy remained stable as uncertainty increased. This occurred, Decreasing Accuracy 162 Decreasing Accuracy ‘ Safety Stock Policy Medium High Figure 5.2 Statistical Approach-Application in Multi-Echeloned Channel Systems. 163 in part, because safety stocks were held at each echelon to act as a buffer against uncertainty. Thus, inventory performance at all sequential locations was adequate. The implication is that managers can achieve relative stability in customer service if safety stocks are held at all echelons. This positioning policy can be beneficial to managers who face rapid and/or substantial changes in demand or lead time uncertainties. Customer service under the retailer positioning policy increased as uncertainty increased, while customer service under the distribution center positioning policy decreased as uncertainty increased. When all of the safety stock is placed at retail, it can be fully utilized to fill excess orders because it is at the point where excess demand will occur. However, when all of the system safety stock is at the distribution center, the probability that a retail replenishment order is filled increases, but whether or not the replenishment order reaches the retailer when needed, depends on the lead time characteristics between the distribution center and retailer. As uncertainty increases, fewer of the filled replenishment orders reach the retailer when required. Thus, as uncertainty increases, the effect on customer service of a retail positioning policy versus a distribution center positioning policy widens. A retailer positioning policy is more desirable at high uncertainty levels. 164 Managers who devise new statistical approaches or modify the existing statistical approach for use in multi- echeloned channel systems, should consider the effects of safety stock positioning on customer service performance. Because inventory performance at sequential locations is interrelated, the safety stock policy—customer service relationship of single and multi—echeloned channel systems differs. Thus, identical statistical approaches should not be used to set safety stocks for both single and multi- echeloned channel systems. Summary The statistical approach, for the most part, should not be used for setting safety stocks in either single or multi-echeloned channel systems. New statistical approaches should be devised or the existing statistical approach modified so that the relationship between the combined factors and customer service are more closely replicated. Using identical statistical approaches for setting safety stocks in single and multi-echeloned channel systems should be avoided because the safety stock policy-customer service relationship in single and multi-echeloned channel systems differs and safety stock policy effects on customer service are significant. Safety stock policy has a more significant effect than uncertainty on customer service in both single and 165 multi-echeloned channel systems. In single echelon systems, introductory amounts of channel system safety stock are the most effective in increasing customer service. In multi- echeloned systems, higher customer service can be achieved by positioning some of a given amount of safety stock at each echelon rather than by positioning all of the safety stock at one echelon. Partial postponement results in higher customer service than either absolute speculation or absolute postponement because inventory performance at sequential locations is interrelated. Therefore, a total channel approach to setting safety stock requirements increases customer service. Research Considerations This section discusses the research limitations and suggests areas for future research. The section con- tains two parts. The first part states research limitations and the second part discusses future research endeavors which might be undertaken. Research Limitations As is typical of all simulation studies, the gen- eralizability of this research is constrained to the extent that the model employed replicates actual distribution systems. However, the SPSF testing environment, which was used in this research, has been subjected to extensive evaluation.s 166 The research was limited as to the types of network designs employed. Only a parallel structure of both single and multi-echeloned distribution systems was used, so cross— shipments were not accommodated in the network design, and any interactions of the inventory performance between multi- ple locations at the same echelon were omitted. Although many channel systems have cross-shipment capability, an examination of this added complexity was beyond the scope of this research effort. An additional limitation was the number of levels employed for each of the independent factors. Ideally, numerous demand, lead time, and safety stock policies would be employed. However, cost and time constraints made this impractical. A further constraint upon the research was that several other factors which have an effect on inventory policy decisions in channel systems either were held con- stant or assumed to be constant. Thus, reorder policies such as reorder system and order quantity were held con- stant. Again, cost and time constraints made the addition of these considerations impractical. Future Research The statistical approach did not accurately predict customer service in single echelon or multi—echeloned chan- nel systems. This occurred because the statistical approach 167 did not accurately reflect the relationship between the combined factor effects and customer service. Thus, an area for future research would involve the reformulation of the statistical approach for use in both single and multi-echeloned channel systems. Factors which have an effect on safety stock policy and ultimately customer service performance were not consid- ered by this research. These factors were held constant to allow measurement of the impact of the experimental factors. Such factors, including order quantity, might be allowed to vary, to measure their relative effect on the accuracy of the statistical approach and customer service. Answering such questions represents research areas which would more fully explain the relationship between safety stock policies and channel system performance. Another path that must be followed in the future is the expansion of the research to include inventory policies outside of physical distribution that may impact channel system effectiveness and efficiency. For example, the inventory policies of vendors who supply manufacturers in the channel as well as the raw material or in-process inventory policies of manufacturers could be included in the research design. System effectiveness and efficiency could be compared, through consideration of alternate safety stock policies, such as the form in which safety stocks are 168 held, as raw material, in—process inventory, or as finished goods. This wider view is consistent with the systems concept and should be explored if a desired channel system effectiveness and efficiency is to be attained. FOOTNOTES--CHAPTER V 1This relationship is described in many current production control and logistics textbooks. 2T. A. Burgin and A. R. Wild, "Stock Control- Experience and Usable Theory," Operational Research Quarterly 18 ( ): 48-49. 3George D. Wagenheim, "The Performance of a Physical Distribution Channel System Under Various Conditions of Lead Time Uncertainty: A Simulated Experiment" (Ph.D. dissertation, Michigan State University, 1974). I‘Wroe Alderson, Marketing‘Behavior and Executive Action (Homewood, 111.: Richard D. Irwin, Inc., 1957), p. 425. 5David Joseph Closs, "Simulated Product Sales Forecasting: Mathematical Model, Computer Implementation, and Validation" (Ph.D. dissertation, Michigan State Univer- sity, 1978). 169 APPENDIX APPENDIX SPSF MODEL This appendix provides an overview of the Simulated Product Sales Forecasting Model and its analytical capabil- ities. Specifically, the Appendix contains a brief overview of the model; a discussion of the general model design: and a detailed review of the four model modules. SPSF Model SPSF is a computer simulation model that provides a forecast testing environment by combining the attributes of market area demand simulation, dynamic operational simula- tion, and statistical sales forecasting. The SPSF model is capable of rendering a sales forecast while simultaneously creating customer orders and replicating the physical dis- tribution process of providing timely inventory to satisfy customer order requirements. Thus, through the combined capabilities of two types of simulation and a statistical forecasting package, a complete time-sequenced picture of events leading to forecast deficiency is captured and fully documented. Such a documentation provides the basis for subsequent sensitivity analysis. A prime feature of the 170 171 SPSF model is that it provides a testing environment for controlled experimentation. SPSF Model Design The SPSF testing environment consists of four sep— arate modules which are capable of being used simultaneously or independently. The four modules are: (1) Demand Module, (2) Forecast Module, (3) Operations Simulator Module, and (4) Analysis Module. Each module is reviewed briefly in terms of its function within the overall SPSF model. The first module is the Demand Module which provides a methodology for creating potential sales. The purpose of this module is to produce synthetic orders from a geograph- ical market area. Thus, the Demand Module is employed to quantify pattern, level, and disPersion of product orders over a time period. The design approach of this module is important to the SPSF testing environment as it provides the primary data for forecasting. Four alternative demand generating procedures are included in the Demand Module. The second module is the Forecast Module in which various forecasting techniques may be used to forecast the demand generated by the Demand Module. Sales forecasts are used to establish inventory levels. Thus, the Forecast Module provides the interface between the firm's operations and its environment. 172 The demand and forecast, generated by their resPective modules, are fed into an Operations Module which replicates a specific physical distribution system. The Operations Module is capable of replicating inventory availability and movements based upon a variety of different replenishment policies. It replicates the performance of the test Operating system across the time horizon of the forecast period. The Operations simulator is designed as a generalized stochastic model capable of simulating the performance of a distribution system with either a single or multi-echeloned network structure. To obtain maximum realism, it is designed on a dynamic basis wherein the state of the model at any given point in time is dependent upon the performance of the system in preceding periods and, in addition, forms the basis for operating performance in future periods. For example, the Operations Module adjusts inventory levels on a time dependent basis to replicate both receipts and shipments over time. Thus, the Operations Module can explore management problems in areas such as operation policy, network structure design, and inventory policy. The fourth module is the Analysis Module which is primarily concerned with the reporting of the interactive effects of the Demand, Forecast, and Operation Modules. The module provides management status, system activity, and cost computation reports. 173 Figure A.l provides an overview of the SPSF Testing Environment general design and the foundation for a more detailed discussion of the four modules. As a matter of terminology, the term "simulator" is used to refer to the combined use of the Operations, Forecast, and Demand Modules. The term SPSF Testing Environment" is used to refer to the above defined simulator plus the Analysis Module. SPSF Module Review Demand Module The Demand Module generates customer orders on a daily basis. Through this module, various types of demand environments can be created to facilitate observations of system performance. Three alternatives are available for demand genera- tion in the SPSF Testing Environment: (1) the direct input of actual orders from sales history; (2) the use of Monte Carlo processes or probability distributions to create individual orders; and (3) determination of an aggregate sales figure, such as the industry sales for a market area which is reduced to individual product orders. The first method of demand generation, directly inputing product orders is termed Procedure One in the Demand Module. The use of orders as sales history is the ‘most realistic and simple method of demand replication. 174 09mm: PRODUCTS PRODUCTS ABC DE HANU‘ACTURERS DISTRIBUTION APCDE CENTERS -e~ ———————————— 4 I I I I I J -\ 7 ABCDE ABCDE ABCDE RETAILERS r— I I -.nT-I ——-——— I r— --.r- ..-.4 I I I I ~"‘ capo-o4 I I o {4 I I I I I I I I I I ?- SIHULATED SALES HISTORY BASE I FORECAST _ -FORECAST run—m... PROCEDURE SALES - . ....... , DATA BASE v I I .._ SI'IIJLATED- DEMANr L-w DEMAND GENERATION d L--——-—--I I.-'-—"-"— 086.3: and L--- -—---- - 1 u I l I l l I I I cams no u I I ‘ ‘ OUTPUT ANALYSIS 7T " HANABEHEVT [ L """" ‘I'" REPORTS TOTAL ---------—————-—dp-—--_ p--——J ERROR _..___.__..__ 1........] l I I I I I I l I I I I I I I I I l I. ANALYSIS HODULE Figure A.l SPSF Testing Environment--General Design. 175 However, this procedure has the shortcomings of requiring more data than alternative methods of demand generation and an inability to create experimental test conditions. Procedure Two employs statistical procedures such as normal, log-normal, erlang, and poisson distributions to generate total daily sales. Although easy to implement, this approach offers the researcher no assured approximation to market reality. Even if the probability distribution IA used is statistically fitted according to historical sales, the parameters of the model are static. Once the periodic sales level is identified, it is reduced to daily orders for use by the Operations Module. The general procedure is to select orders randomly from a predetermined sample order file until daily demand is com- plete. Pseudo orders can be constructed to permit experi- mental conditions or to replicate events such as new product introduction. Procedure Three utilizes the correlation between historical demand and other economic indicators to generate an estimate for the periodic sales level. There are numer- ous economic indices which can be correlated to sales. Indices which may be considered include pOpulation, Gross National Product, net income, and new housing starts. The choice of indices depends on the specific situation. In Procedure Three, firm sales is determined using multiple 176 linear regression. The effect of various factors upon firm sales is measured using the method of least squares. Given a number of factors as independent variables, a linear regression equation is used to arrive at firm sales for a particular month. Daily sales are generated by multiplying F this monthly sales level by a daily sales factor based on ' an expected mean and variance for the month in question. Procedure Four uses an alternate correlation pro— cedure. In Procedure Four, industry demand is generated within the market area by inputing independent variables into a correlation equation of the general form: X +...+bX IS=a+bX+be+b33 nn 1 1 2 where: IS = industry sales for the period in question; a = the vertical axis intercept; X1_ = the independent variable influencing n industry sales; and bl-n = the respective factors of the independent variables. This form of generalized equation permits inclusion of any independent variables deemed relevant to the deter- mination of market area industry sales. In addition, it allows specification of different variables for different product situations. 177 The regression formulation provides an estimate of industry demand which is decomposed to monthly estimates. Next, specific market share is determined using the approach proposed by Kotler.1 This method uses a ratio of the firm's "market effort" to the industry "marketing effort" to arrive at specific market share. The result of the regression analysis for Procedures Three and Four is a monthly or weekly sales estimate. Given this figure, daily sales are determined from a normal dis— tribution using the expected mean and variance of daily sales for the month under analysis. Given a value for daily sales, Procedure Two is used to arrive at individual product orders. Use one of the four procedures in the Demand Module allows the modeler to simulate the demand environment desired. The generated daily orders become a part of the input into the Operations Module. Forecast Module The Forecast Module provides the firm's interface between the demand environment and the operationalization of its policies and actions.2 Incorporation of the fore- cast into the simulation is accomplished in the following manner. Given a product, the first forecasting Option is to generate independent forecasts for each location in the 178 operation structure. Each forecast is generated from an analysis of historical sales patterns (throughput) at each location. The second Option generates forecasts at the echelon level serving the final customer. A forecast is made for several periods in advance. This forecast is then exploded back to the source locations which replenish the customer 1L service location. Upper echelon forecasts depend on the I estimated lead time from the location in question to the I market. The estimates are computed for all products in an event subroutine. The SPSF Model is equipped with four forecasting techniques for time series analysis. The techniques are: l. Brown's Simple Exponential Smoothing Model; 2. Trigg and Leach's Adaptive Smoothing Model; 3. P. R. Winters' Exponentially Weighted Moving Averages; and 4. Robert's and Reed's Self-Adaptive Forecasting Technique. Brown's Simple Exponential Smoothing Model is the most basic technique provided in the module.3 This technique applies a static smoothing constant (a) to the previous period's sales and forecast by the formula: Forecast1 = a(Saleso) + (l-a)(Forecasto). 179 It is easy to use, but contains no forecast error adaptability or specific trend, cyclical or seasonal elements which limits its capability. Trigg and Leach's Adaptive Smoothing Model is adaptive.“ The technique Operates with a smoothing constant (a) set equal to the absolute value of a tracking signal. The tracking signal is a measure relating the degree of forecast error during the most recent period to that in the preceding periods. When error becomes large, the tracking signal approaches a value of one. As the value of the tracking signal increases so does the corresponding value of a, allowing the forecast to adapt more quickly to changes in demand. As this adaptation leads to decreases in the error, the tracking signal and the value of a will decline. P. R. Winters' Exponentially Weighted Moving Average incorporates trend and seasonality.s This technique uti- lizes a smoothing constant and smoothed estimates of trend and seasonality. The combination Of these factors yields a sales forecast. Since the Winters' technique incorporates trend and seasonal variations, it represents a more sophisticated approach than either Brown's or Trigg and Leach's technique. Winters' technique has the deficiency of not adapting smoothing constants to changes in the level of forecast error. 180 Robert's and Reed's Self-Adaptive Forecasting Technique is the most complex technique furnished by the Forecast Module.6 Level, trend, and seasonal factors are all considered by the adjustment of smoothing constant values. I The techniques of the Forecast Module are used by the modeler in an attempt to forecast the demand generated by the Demand Module. The forecasts generated by the Fore- cast Module become a part of the input to the Operations Module. Operations Module The Operations Module is a dynamic simulator that integrates input from the Demand and Forecast Modules. This permits both time and function-dependent Observations to be replicated and Observed. The simulator models the individual activities of physical distribution process which might include order processing, order shipping, production, transportation, and inventory management. The dynamic characteristic of actual Operations is achieved through activity interaction. In the linkage of events, dynamic realism is achieved through the inclusion of probabilistic time variables. Typical components requiring probability variables are communication, order processing, and transit time. 181 The design of the Operations Module provides substantial flexibility in permitting multiple plants, distribution centers, echelons, and products. The Operations Module has the capability to simulate physical distribution systems with up to fifteen locations and ten individual products or product groups. In addition, the location may be arranged in any number of echelons from manufacturing plants to final customers. These capabilities allow the Operations Module to replicate the typical phys- ical distribution configuration used to replenish inventory to a specific market area. Figures A.2 and A.3 illustrate the structural flexibility of the Operations Module. .Figure A.2 presents a simplified distribution structure consisting of inventory stocking locations at manufacturer, distribution center, and retailer. The product flows from manufacturing plant to a distribution center and then to the customer. Policies capable of alternative testing are illustrated on the right side of Figure A.2. Figure A.3 illustrates a more complex example of a physical distribution structure consisting of four echelons and twelve locations. The complexity of the network exists because of the multiple source destinations. These examples illustrate only two of the many system structures which can be designed using the Operations Module. The specific network design employed in this research is developed in Chapter III. Location Products Description Stocked Manufacturer l ABCDE' Distribution l l Center ABCDE Retailer ABCDE Customer 182 Alternative Policies Production Policies Inventory Policies Order Processing Times Available Transit Modes Speed And Consistency 0f Communication And Transit Times 'lbrecasting Methodology Inventory And Stocking Policies Order Processing Times Review Periods Demand Draw-Off Emctions Replenishment Order Factoring Methods Available Transit "I odes Speed And Consistency 0f Communication And Transit Times Inventory And Stocking Policies Review Periods Replenishment Order Factoring Methods Ibrecasti ng *1 ethodology Demand Level And hriability Figure A.2 Example of Simplified Distribution Structure. 183 Location Description Products Stocked Wholesaler - Distribution Center ABCDE W O o o O a Figure A.3 Example of Complex Distribution Structure. 184 Analysis Module The Analysis Module of the SPSF testing environment calculates the levels of cost and service variables for each simulation. It consists of two distinct routines, the Cost Generator and the Report Generator. The Cost Generator computes the costs incurred by simulated distribution Operations. Cost elements include transportation, warehousing, storage, inventory, ordering, and backorder costs. The Report Generator prepares reports on system performance. The reports may be divided into four cate- gories. The categories of reports are sales and physical levels, costs, service, and error. In addition, run summary reports are provided. Each category is divided into records which can be selected independently. The categories and their records are listed in Table A.l. These reports provide a means of analyzing operations and correcting them.7 Table A.1 Category Sales and physical 0 levels costs 0 Service 0 Error 0 Managerial summary 0 I85 Report Categories and Records Records System customer sales System shipments System receipts System inventory report Replenishment sales Replenishment sales and in-transit inventory Replenishment volume: weight shipped Product inventory report Product sales report (units) System bleeding report Product bleeding report System cost Replenishment volume: cost of shipping System service measure System percentage of orders by quantity met System backorder recovery and thousands of dollars filled within days System backorder recovery: tens of units filled within days Replenishment order cycle time summary Operating error report Forecast error report Run summary: sales Run summary: service Run summary: inventory and backorders Run sumary : costs FOOTNOTES--APPENDIX 1Philip Kotler, Marketing Degision Making: A Model Building Approach (New York: Holt, Rinehart & Winston, 1971). 2David Joseph Closs, "Simulated Product Sales Forecasting: Mathematical Model, Computer Implementation, and Validation" (Ph.D. dissertation, Michigan State University, 1978). 3R. 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