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W M!lllllllillfllflllLl\flljlfll7llllllu6|fljllflll i This is to certifg that the thesis entitled l Evaluation of Alternative Solutions to the Food D1stribution Center Location Problem 1 presented by Donald John Bowersox has been accepted towards fulfillment of the requirements for _P_h._Q.___ degree in_BnS_ine_S_S Administra- tion Major ansfif Date 11-21-60 0—169 LIRRARY i M ich 1gan State University W ( i? b I. i. .142- 3:: N 1 2 [.00 S F E B 1920 05 U l, / k U 4 EVALUATION OF ALTERNATIVE SOLUTIONS TO THE FOOD DISTRIBUTION CENTER LOCATION PROB LEM BY Donald John Bowersox AN ABSTRACT Submitted to the School for Advanced Graduate Studies of Michigan State University in partial fulfillment of the requirements for the degree of DOC TOR OF PHILOSOPHY Department of Marketing and Transportation Administration 1960 Approved Donald John Bower sox ABSTRACT The topic of this research is that phase of distribution :center location referred to as the market area location problem. An estab- lished supermarket chain often encounters selection of a market area location for a distribution center. This necessitates from obsolescence of existing distribution warehouses and/ or market area expansion. When either or both of these situations occur, a potential savings exists in one market segment. A precise selection of indi- vidual distribution center locations is one way that the chain may in increase distribution efficiency. The specific products, and the quantity of each, required for a given supermarket vary extensively from one order to the next. The wide product line of each supermarket order limits the shipment of quantity lots from individual suppliers. To solve this problem, supermarket chains use the services of a distribution center to facilitate constant, rapid, and economical inventory replenishment. A food distribution center functions as a break-bulk and re- grouping point. Products are purchased in quantity, temporarily stored, and then shipped in assortments necessary for replenishing individual supermarket inventories. While food chains have accomplished outstanding technological innovations in distribution center operations, thus, far they have generally neglected problems related to distribution Donald John Bower sox center location. In 1959, firms in the industry operated over 200 distribution centers. Because of the potential economies embodied in the scientific study of location and the number of distribution centers operatedyin this industry, this research was devoted to an analysis of the theoretical and analytical considerations involved. The threefold research problem was to determine: (1) In what geographical market patterns a currently available mathematical technique would more precisely isolate least-cost locations than a non- mathematical technique; (2) What variations in distribution cost would result as different location measurements were used with the mathe- matical technique to select locations; and (3) Whether including the influence of delivery time in the location measure would produce a superior location solution. One mathematical and one non—mathematical technique were employed in the analysis. These techniques were held constant throughout the experiment. In the mathematical technique, the location measurement formulation was allowed to vary in a controlled manner. By solving for market area locations in a number of prescribed ways, solutions were derived for all measurements under analysis. Alternative locations were evaluated by comparing total distribution costs estimated from a standard cost model simulating a private truck fleet. From each location solution, secondary data were assembled. 4 Donald John Bowersox These secondary data served as inputs to the transportation cost model. The output was an estimated cost of distribution for each alternative location. A comparative analysis of these cost estimates provided the basis for drawing the following conclusions: (1) The mathematically determined locations were, in all cases, equal or lower cost solutions than those derived by the non—mathematical technique; (2) The greater the total disparity among the location factors of time, tons, and distance, the larger the variation in estimated costs among solutions determined by various location measurements; and (3) The formulation including the basic cost determinant of time, in addition to tons and miles, resulted in the lowest cost location among those tested. These conclusions are qualified by the research limitations, standing as valid scientific statements only within the study parameters. EVALUATION OF ALTERNATIVE SOLUTIONS TO THE FOOD DISTRIBUTION CENTER LOCATION PROB LE M By Donald John Bower sox A THESIS Submitted to the School for Advanced Graduate Studies of Michigan State University in partial fulfillment of the requirements for the degree of DOC TOR OF PHILOSOPHY Department of Marketing and Transportation Administration 1960 4 li/M' - é//I / is) Copyright by Donald John Bower sox 1961 -_*,_. iii ACKNOWLEDGEMENTS The author wishes to express his sincere appreciation and gratitude to the following individuals and organizations: Dr. Donald A. Taylor, Department of Marketing and Transportation Administration, under whose inspiring supervision and unselfish contribution of time and encouragement this research was com- pleted. The over—all development this candidate has received from Dr. Taylor extends far beyond this single work. Dr. Edward W. Smykay, Department of Marketing and Transportation Administration, who served as a thesis committee member. To Dr. Smykay is owed a great deal of appreciation for his over- all guidance in the field of physical distribution which already has begun to mold the future years. Dr. Edward A. Brand, Graduate School of Business Administration, who, in addition to being a constant source of guidance during doctoral studies, served as a thesis committee member. Dr. Thomas A. Staudt, Head, Department of Marketing and Trans- portation, who served as the chairman of the candidate's course work committee and who encouraged this research. iv. Mr. George A. Ramlose, who, through his generosity in establishing the George A. Ramlose Foundation at Michigan State University, made this research possible. Messrs. Edward E. Clark, Jewel Tea Co. , and Herbert M. Thornton, Colonial Stores, who provided operational statistics for use in this research. The contributions greatly increased the practical relevancy of the research. Miss Elsie Van Alstine, an extraordinary amanuensis, who provided her services in an unselfish manner to help meet the constant deadlines. Carol, Pat, Ed, and Barb for constantly providing inspiration and support EVALUATION OF ALTERNATIVE SOLUTIONS TO THE FOOD DISTRIBUTION CENTER LOCATION PROBLEM PART I - THEORY AND STRUCTURE CHAPTER I - INTRODUCTION ............................... Importance of Research Scope of Distribution Center Location Problem Problem Statement General Research Synopsis Limitations Order of Presentation CHAPTER II - DISTRIBUTION CENTER LOCATION THEORY AND STRATEG Y ......................................... Introduction Location and Firm Strategy Synthesis of Relevant Location Literature The Concept of Spatial Monopoly The Concept of Space Island An Economically Justified High Cost Location Derived Nature of Distribution Center Location Distribution Center Location Strategy with Non-differentiated Products 12 13 15 17 19 19 21 24 25 28 31 34 35 vi Page Distribution Center Location Strategy with Differentiated Products 38 Distribution Center Location Strategy with Multiple Products 40 Influence of Retail Location upon Distribution Center Location Strategy 41 Conclusion 45 Distribution Center Location Logic 46 Market—Positioned Distribution Centers 52 Production-Positioned Distribution Centers 54 Intermediately Positioned Distribution Centers 55 Conclusion 56 CHAPTER III - RESEARCH DESIGN .......................... 58 Introduction 58 General Research Design 59 Terminology 62 Analytical Techniques 64 Non-Mathematical Techniques 64 Mathematical Techniques 67 Measurement Device 72 Ton-Center Solution 73 Mile-Center Solution 75 Ton-Mile-Center Solution 77 Time-Ton-Mile-Center Solution 78 Location Models Transportation Cost Model Model Assumptions Cost Categories and Accounts Fixed Costs Variable Costs Assignment of Cost Account Values Basic Fixed Costs Overhead Fixed Costs Distance Variable Costs Time Variable Costs Overtime Variable Costs Account Valuations Summarized Costing Procedure Location Data Table Qualification of Inputs Quantification of Total Costs Conclusion- —Research Design CHAPTER IV - HYPOTHESES .......................... Introduction Statement of Hypotheses Intra-Model Hypotheses Hypothesis I-A vii Page 82 84 85 86 86 87 88 89 91 93 94 95 95 97 97 99 103 104 106 106 109 109 109 viii Page Hypothesis I-B 110 Hypothesis I—C 110 Inter-Model Hypotheses 110 Hypothesis II-A 110 Hypothesis II—B 110 Hypothesis II-C 110 PART II - RESULTS AND CONCLUSIONS CHAPTER V - EXPERIMENTAL RESULTS ................... 112 Introduction 112 Experimental Results - Model B 112 Primary Data 113 Distribution Center Location Solutions 116 Estimated Distribution Expense 118 Experimental Results — Model C 121 Primary Data 121 Distribution Center Location Solutions 124 Estimated Distribution Expense 126 Conclusion 127 CHAPTER VI - CONCLUSIONS ............................... 129 Introduc tion 129 Evaluation of Hypotheses 129 ix Page Intra-Model Hypotheses 129 Hypothesis I-A 129 Hypothesis I-B 130 Hypothesis I—C 132 Inter-Model Hypotheses 133 Hypothesis II-A 133 Hypothesis II-B 134 Hypothesis II-C 135 Problem Conclusions 136 Theoretical and Analytical Research Contributions 140 Suggested Areas for Additional Investigation 145 APPENDICES .............................................. 148 A - Computer Flow Charts 148 B - Literature Review 157 C - Primary Data 175 D - Estimated Distribution Costs 179 BIBLIOGRAPHY .......................................... 182 Chart 11. III. IV. VI. VII. VIII. IX. XI. XII. XIII. XIV. XV. XVI. XVII. LIST OF CHARTS Smithies' Diagram of Optimum Location of the Spatial Monopolist Modified ................................ Losch's Diagram of Spatial Monopoly ................. Space Islands Under Conditions of Spatial Monopoly . . . . Losch System of Locations .......................... Illustration of Economically Justified High Cost Location .......................................... Market Extension by Use of a Distribution Center ..... White's Conception of the Marketing Process ......... Carte sian Coordinate s .............................. Location of a Point in the Positive Plane of Cartesian Coordinates ....................................... Geographic Retail Market Area Models ............... Research Design ................................... Geographic Dispersion of Selected Variables-~Model B . Relative Distribution Center Locations--Model B ...... Geographic Dispersion of Select Variables--Model C . . . Relative Distribution Center Locations--Model C ..... Center of Tons Diagram ............................ Trial and Error Diagram ............................ Page 27 29 31 32 33 37 49 68 68 82 105 115 118 123 125 151 152 Xi LIST OF TABLES Table Page 1. Time Estimation Table .............................. 81 2. Annual Total Overhead Fixed Cost Schedules .......... 93 3. Breakdown of Variable Distance Cost Values .......... 94 4. Classification and Value of Cost Accounts ............ 96 5. Sample Location Data Table ......................... 98 6. Distribution Center Locations--Mode1 B .............. 117 7. Comparative Cost Determinants--Model B ............ 119 8. Comparative Estimated Distribution Costs--Model B . . . 120 9. Total Estimated Distribution Cost as a Per Cent of Initial Location Cost--Model B ...................... 120 10. Distribution Center Locations--Mode1 C ............... 124 11. Comparative Cost Determinants--Model C ............ 126 12. Comparative Estimated Distribution Costs--Model C . . . 128 13. Total Estimated Distribution Cost as a Per Cent of Initial Location Cost--Model C ...................... 128 14. Primary Data--Model B ............................ 176 15. Primary Data--Model C ............................ 177 16. Estimated Distribution Cost (Dollars)--Model B ...... 180 17. Estimated Distribution Cost (Dollars)--Mode1 C ...... 181 PART I THEORY AND STRUCTURE CHAPTER I INTRODUCTION IMPORTANCE OF RESEARCH The supermarket industry,1 in comparison to other industries or even other segments of the grocery industry, faces a unique inventory replenishment problem. A modern supermarket typically has a con- stantly shifting product line consisting of three to five thousand different products. Each product has varying characteristics regarding geo- graphic procurement points, seasonality, perishability, physical form, unit value, and stability of consumer demand. Within a given super- market chain, depending upon economic, ethnic and social characteristics of ultimate consumers, particular stores may require substantially different product lines. Additionally, within the industry, each super- market competes with a large number of other supermarkets offering identical products at similar prices. Consequently, out-of-stock conditions among fast turnover products can result in the loss of For purposes of this research, the supermarket industry is defined as consisting of chains operating eleven or more supermarkets, each with a minimum annual sales volume of 500, 000 dollars. This definition is based upon the standard definitions for food chain and supermarket. See Staff Report to Federal Trade Commission, Economic Inquiry into Food Marketing, Part 1. Washington, D. C. : United States Government Printing Office, January, 1960, p. 101; and "The True Look of the Supermarket Industry 1959, " Super Market Merchandisig, May, 1960, p. 1 (Reprint). generally indifferent consumers' patronage. As a result of demand sensitivity, the wide assortment of heterogeneous products, and the high degree of competitive substituability, a basic distribution problem exists in supplying supermarkets. The specific products and the quantity of each required for inventory replenishment of a supermarket vary extensively from one replenishment to the next. The inventory requirements of each supermarket within a chain also vary. The individual supermarket cannot economically order in quantity lots for direct shipment from suppliers. To solve this problem, supermarket chains universally utilize the services of a distribution center in order to facilitate a constant, rapid, and economical inventory replenishment. A distribution center supplying a grOup of supermarkets functions as a break-bulk and regrouping point. Whenever possible, products are procured in quantities adaptable to consolidated shipment to the distribution center. An initial economy is achieved by transporting all shipments to one . 3 . . . . nodal p01nt. Products are temporarily stored at the distribution center For example, a recent study of consumer food shopping habits points out that 64 per cent of all supermarket shoppers purchase food in more than one store, the average consumer purchases being from 2. 3 stores. See "Shoppers Buy in Two Stores or More, " Super Market Merchandising, Vol. XXIII (February, 1958), p. 122; also, 1960 Greater Milwaukee Shopping Habits, The Journal Co. , 1960, p. 37. The transportation consolidation economy referred to repeatedly throughout this research is based upon the standard practice of granting lower per-unit rates on quantity lot shipments. For a complete dis- cussion, see Frank H. Mossman and Newton Morton. Principles of Transportation. New York: The Ronald Press Company, 1957. to await orders. Upon request, merchandise is accumulated and shipped in the assortment necessary for replenishing inventories. Food chains have accomplished outstanding technological advance- ments in distribution center operations. In the areas of design, layout, and material handling, food chains take advantage of many innovations. Advancements have been achieved in automatic data processing of orders and in distributive communications. In some chains, inventories are maintained at absolute minimums with many rapid-turnover products arriving at and departing from the warehouse during a single work day. In the area of automatic order selection, break—throughs have been accomplished. A great deal of this emphaSis upon internal distribution center operations culminated from the need for efficient inventory replenishment at minimum cost. For example, see, among others, any of the following publications of the U. S. Department of Agriculture, Washington, D. C. : "Methods of Increasing Productivity in Modern Grocery Warehouses, ” Marketing Research Report No. 94, June, 1955; ”Methods of Increasing Labor Pro- ductivity in Multistory and Small One-Floor Grocery Warehouses, " Marketing Research Report No. 142, November, 1956; "Grocery Ware- house Layout and Equipment for Maximum Productivity, " Marketing Research Report No. 348, July, 1959. For example, see a special edition of Cooperative Merchandiser, devoted entirely to a discussion of electronic data processing: "Data for Decisions, ” Cooperative Merchandiser, Vol. XXV (March, 1960); also, see ”Improved Methods Among Wholesale Food Distributors, ” Marketing Research Report No. 271, U. S. Department of Agriculture, Washington, D. C., September. 1958. 6 . . . . For example, the Wrigley-Abner Wolf distribution center located in Detroit has an automatic frozen food selector system capable of pro- cessing an order in 26 seconds. Thus far, chains have generally neglected the problems related to distribution center location. This neglect may be attributed, for the most part, to a managerial practice of attacking problems in sequence of operational importance. Given a rudimentary logistics system, attention was directed to the pressing problems related to economical inventory replenishment. Initially, greatest advancements evolved from the scientific study of internal operations. Management generally selected distribution center locations which logically fit the geographic complex of supermarkets to be replenished. The general assumption underlying location selection was that a distribution center positioned in close proximity to the largest group of supermarkets to be serviced would result in the most economical delivery. Today, the supermarket industry represents one of the largest business undertakings in the American economy. Total chain sales alone in 1959 were estimated at 19,475, 000, 000 dollars. 7 In 1959, there were 22, 523 supermarkets in the industry which collectively enjoyed 70 per cent of total grocery sales. 8 In order to perform the necessary logistics for these supermarkets, firms in the industry operate in excess of 200 distribution centers. 9 The number of distribution centers utilized by supermarket chains ranges from a high of 38 operated by the A & P Tea 7R. W. Mueller, ”1959 Grocery Sales up 4. 2% as Total Tops $50 Billion, " Progressive Grocer, April, 1960 (Reprint), p. 2. 8”The True Look of the Super Market Industry 1959, " 10(3- Cit- C)Estimated from data reported in 7th Biennial Grocery Study-- SupermarketingU.S.A., 1957, This Week Magazine (Special Report), 1957. Company to a low of one employed by smaller firms. 10 While some attention has been directed to distribution center location, the problem generally has not been subjected to scientific evaluation. Because of the potential economic advancements embodied in the scientific study of location and the magnitude of distribution centers operated by the supermarket industry, this research is devoted to an analysis of the theoretical and practical considerations involved. SCOPE OF DISTRIBUTION CENTER LOCATION PROBLEM A typical food distribution center is market-oriented. The following principle supports a market orientation. A location in close proximity to points of ultimate consumption affords maximum transportation economies from distant procurement points with relatively short move— ments in more costly local delivery. ‘ The basic goal in selecting a distribution center location is to achieve one-day delivery to each supermarket at the lowest possible distribution cost.1 Therefore, the optimum location solution is one which identifies that geographic point from which all supermarkets can be replenished at least cost. The critical costs stem from local delivery to supermarkets. For example, delivery cost has been estimated at 40 per cent of total warehouse and , ll . . . transportation expense. Depending upon geographic location, these 10Ibid. Charles Crossed and Martin Kriesberg. Procedures for Evaluating Delivery Operations of Wholesale Food Distribution (Preliminary Draft). U.S. Department of Agriculture, Washington, D.C., June, 1960, p. 1. costs can vary substantially. Inbound transportation costs are not major considerations in selecting individual distribution center locations. The spectrum of location alternatives covers a limited geographic area for a single distribution center. Within this area, little variation is found among inbound rates due to the wide use of delivered pricing, zone pricing, and the common carrier practice of grouping origin and destin- ation for rate-making purposes. Therefore, in selecting a least cost location, attention is directed to minimizing the critical expense of local delivery. In broader perspective, selecting locations for individual distribution centers, while probably the most important phase, constitutes only part of the total location problem. To achieve the objective of one-day replenishment at minimum cost. a supermarket chain must arrive at solutions concerning three distinct, but related, problems. First, the number of distribution centers required to render one-day inventory replenishment to each supermarket must be determined. Once the total number of distribution centers is ascertained, the individual market area to be served by each is roughly delineated. Second, within this market area, a location must be selected for a specific distribution center. This problem was noted above. Throughout this research, this problem is referred to as the market area location solution. Third, given a market area solution. a site providing all necessary facilities must be selected. Only when a supermarket chain has arrived at optimum solutions to these three problems will the most efficient system of locations be available for inventory replenishment. The first location problem-~determining the required number of distribution centers and their market areas--while possibly the most complex, is seldom confronted by a supermarket chain. Typically, a chain expands in an evolutionary manner by adding supermarkets disproportionately around the initial nucleus of the chain or by merging with an existing supermarket chain. Initially, a single distribution center is sufficient to replenish inventories. As the geographic market area expands, it becomes increasingly difficult to provide economic one—day replenishment to all supermarkets. For a limited time period, the chain may replenish inventories from one distribution center. However, as annual volumes increase, a second, third, and nth number 0f new centers may be economically justified. Expansion patterns vary extensively among chains. Once additional distribution centers are added, market areas serviced from each are marginally divided, utilizing location distribution cost. 12 Given this form of evolutionary expansion with related rigidities, an established firm seldom has an opportunity to optimize its total distribution system in the constantly changing geographic market. {1’1 ' . . . . . . . The market areas of indiVidual distribution centers are determined, basically, by locating a line of equal distribution cost for similar size shipments between the centers. For example, similar shipments are moved outbound from each distribution center until the point of equal cost from each center is determined. This point extended into a line of equal cost gives a first approximation of market areas. Adjustments are then necessary to satisfy other considerations peculiar to the firm in question. See: Edward W. Smykay, Donald J. Bowersox, and Frank H. Mossman. Physical Distribution Management. New York: Macmillan Company, Scheduled for publication, January, 1961, Ch. VIII. The third aspect of location--site selection--does not constitute a major problem in distribution center location. The selection of a specific site for any form of economic activity is essentially a matching process. The requirements that the site must provide are listed, and potential sites are filtered until the one adhering most closely to the specifications is identified. The specifications which sites must satisfy may be grouped as physical and non-physical. Physical features include natural endow— ments and economic developments of thesite. The non-physical features include such factors as competitive locations, traffic flows, and socio- economic characteristics of surrounding population. Depending upon whether the site is for a retail, wholesale, or manufacturing enterprise, the relative importance of physical and non-physical features varies extensively. For example, in selecting a retail location, both physical and non-physical features are equally important. Therefore, retail site selection is a complicated process. However, site selection for dis- tribution centers is relatively simple since physical features of the real estate receive primary emphasis. This research concentrates upon the second location problem--the market area location solution. Selection of a location for a single distribution center is a problem often experienced by an established 1 . . . 3For example, see the following check-lists to guide Site selection: Richard L. Nelson. The Selection of Retail Locations. New York: F. W. Dodge Corp., 1958; and/or Leonard C. Yaseen, Plant Location. New York: American Research Council, 1956. 10 supermarket chain. The market area location problem evolves from two situations: (1) Obsolescence of an existing distribution warehouse; (2) Market area expansion. When one of these situations occurs, the supermarket chain realizes a degree of flexibility in one market seg- ment seldom experienced for the chain in total. Thus, it is in the precise selection of individual distribution center locations that the supermarket chain can adjust toward more efficient distribution. Historically, market area locations have been selected without the aid of mathematical techniques. Selection of distribution center locations was based upon an assumed relation betWeen market density and least- cost location. The supermarkets replenished from the distribution center were plotted on a map. The distribution center was then located within the geographic area containing the largest cluster of supermarkets. In some special cases, locations were selected on the basis of tradition or managerial preference. For example, the location spectrum was initially limited to one city because the firm traditionally operated at such a geographic point, or because of a preference for that particular community. When using mathematical techniques, little attention was given to their capability for selecting superior locations. Quantifying necessary inputs and calculating solutions can represent substantial expense. In order to make sound decisions concerning the use of mathematical techniques, insight into the conditions under which they are superior to non-mathematical methods is required. 11 The location solutions determined by any given mathematical formulation may vary substantially depending upon the measurement device utilized. Little is found in current literature concerning the variation in distribution expense resulting from locations selected through different measurement devices. It is generally accepted that when a private trucking fleet is operated, time, distance, and tonnage influence the total distribution cost experienced from a given location. However, in the most sophisticated measurement device currently reported, an attempt is made to minimize ton-miles in selecting dis- . . . 14 . . . . . tribution center locations. The utilization of ton—miles has economic . . , l5 merit when common carriers are used for local delivery. Normally, chains in the supermarket industry use private carriers. Under such conditions, costs directly related to equipment-utilization time account . , l6 . . for apprOXimately one-half of local delivery expense. Little is currently available concerning the quantification of time in a location measurement device or regarding the superiority of distribution center locations accounting for the temporal influence. 4 . . "Warehouse Location Based on Trucking Costs, " Materials Hand- ling Manual No. 1, Boston Publishing Company, Inc. , 1955, pp. E84-E86. l . 5When common carriers are employed for local delivery, the expense to the firm is more closely a function of ton-miles. See: Explanation of the Development of Motor Carrier Costs with Statement as to Their Meaning and Significance, Washington, D. C. ; Interstate Com- merce Commission, Statement No. 4-59, August, 1959. 6Report of Study Dealing with the Cost of Transporting General Freight by Motor Vehicle Equipment in the State of California, Case No. 5432, Vol. II, Truckload Costs, San Francisco: State of California Public Utilities Commission, January 31, 1957. 12 Lastly, it is possible that the superiority of mathematically derived solutions and the variation in the usefulness of supplementary measurement devices are directly related to the geographic configuration of supermarkets serviced. Given certain geographic configurations, solutions utilizing different location measures and techniques may result in similar locations. On the other hand, there may be great variation in alternative solutions if supermarkets fit different geographic configurations. Consequently, the validity of different techniques and measurement devices cannot be substantiated until the relationship of supermarket configuration and derived location solutions is investigated. Until the problems introduced above are examined, little reliability can be placed upon various location techniques, and little validity can be placed upon any given location as representing a least-cost location. The market area location problem is commonly confronted by supermarket chains. Consequently, a complete investigation of these several problems is selected for research analysis. PROBLEM STATEMENT The concern of this study is threefold. Given the predominant geographical retail market patterns observable in the supermarket industry, the problem is to determine: (1) In what geographical market patterns the mathematical approach will more precisely isolate least- cost market area locations; (2) What variation in distribution expense will result as a function of the measurement device employed; (3) 13 Whether including the influence of delivery time in the location measure will produce a superior location solution. GENERAL RESEARCH SYNOPSIS17 The specific task is to evaluate alternative techniques and measures for selecting market area locations for food distribution centers. In the supermarket industry, three geographic market con- figurations stand out as representative of normal spatial relationship among supermarkets. In two of these geographic retail market areas, considerable variation in distribution expense may result depending upon distribution center location. For research purposes, location models representing these two geographic retail market areas are simulated. By utilizing models, alternative locations can be selected and tested under simulated conditions. Physical and operating data from two established supermarket chains, each distributing to a configuration of supermarkets representing one of the location models simulated, are utilized for experimental inputs. While in structure the research findings are limited to case studies, the simulation of location models provides a basis for generalizing study conclusions. One mathematical and one non-mathematical technique are selected for analysis. These techniques are held constant throughout the experimentation. In the mathematical formulations, the location A complete discussion of research procedure is presented in Ch. 111, ”Research Design. " l4 measurement device is allowed to vary in a controlled manner. Among the array of measurement devices tested, one includes the quantification of delivery time. By solving for market area location several times for each location model, solutions are derived from all measurement devices under analysis. A desk size analog computer is used to calculate all mathemati- cally derived location solutions. 18 The use of a digital computer was considered. In order to complete the necessary computations two custom programs would have been required. The digital computer was rejected in favor of the analog due to the quantity of programming required in comparison to the magnitude of the problem. Flow diagrams developed to help make this decision are presented in Appendix A. To evaluate alternative distribution center locations, total dis- tribution costs are compared. Given the mathematically and non- mathematically derived location solutions, total distribution cost is estimated via a standard transportation cost model. The transportation cost model simulates the cost structure of a private carrier fleet and contains cost accounts with representative dollar values. From each location solution, secondary data are assembled for a given time period. These secondary data serve as inputs to the transportation model. The output is an estimated cost of distribution for each alternative location 18For a comparison of analog and digital computers see: Edward L. Brink, "A Simplified Solution for the Location of Marketing Outlets Using an Analog Computer, " Marketing's Role in Scientific Management, Chicago: American Marketing Association, 1957, pp. 468-75. 15 solution. A comparative analysis of these estimated costs provides the basis for drawing conclusions concerning the threefold problem as stated above. LIMITATIONS The limitations Of this research are as follows: 1. The research concentrates upon one phase of the three-stage distribution center location problem in order to completely develop all aspects of this phase. This creates a limitation since important interrelations between stages of distribution center location may be overlooked. 2. The research is limited to the supermarket industry, and the results are directly applicable to only this industry. While in- sights of significance to other industries evolve, generalizations cannot be scientifically justified. A fundamental limitation to generalization is the assumption of insignificant inbound transpor- tation cost. While justified for the particular problem under analysis, such an assumption is not generally applicable to location problems. 3. Only one mathematical and one non-mathematical technique for locating distribution centers are employed in the research. The basic assumption is that alternative techniques are equally capable. It is assumed that the measurement device and the geographic market patterns are the significant variables altering location solutions. l6 Experimentation is limited to the study of two supermarket chains. Thus, in final analysis, the research findings are limited to generalizations concerning only these two case studies. This is the typical problem of time and budget. To some extent, this limitation is compensated by the application of case studies to more general location models. However, all generalizations con- cerning simulation models must be qualified by reference to the number of cases studied. Both case studies of the experiment represent vertically integrated regional supermarket chains. It is assumed that each chain owns and operates a private carrier fleet to satisfy local delivery. No cooperative or independent operations are analyzed. No consideration is given to other forms of local delivery. Consequently, the findings are biased in some undetermined manner toward chains fitting the above characteristics. All research findings must be accepted with an understanding that better measurement devices for quantification of location forces capable of rendering superior locations may exist or may be developed in the future. This all—encompassing limitation acknow- ledges the fact that the least-cost location determined by this research may be inferior to those obtained by continued analysis. While this general limitation applies to all research, it is parti- cularly significant in the current study. In the research conclusions, alternative solutions are ranked in order of superiority, however, 17 no proof is presented concerning the absolute superiority of the superior locations among all other potential solutions. 7. Finally, a qualification concerning the exact nature of the superior location solution is required. The superior least—cost location of the distribution center, as isolated by this research, represents a scientifically determined point within a configuration of super- markets. Given this supermarket configuration and the determined distribution center location, the chain has determined a structure of location points within which efficient distribution may be accomplished. Additional economies may be achieved by expert programming of local delivery and by utilizing managerial initiative in establishing efficient procedure, for example, the utilization of back-hauling, multiple store deliveries, etc. However, the potential attainment of such economies depends upon local conditions somewhat beyond the parameters of the specific location problem under analysis. ORDER OF PRESENTATION The research is reported in two major parts. Part 1, “Theory and Structure, " contains four chapters. The first chapter is an introduction to the entire work. Chapter 11, "Distribution Center Location Theory and Strategy, " contains a partial evaluation of location literature offering theoretical insights relevant to the research. A complete review of literature is presented in Appendix B. In Chapter III, the research design 18 is developed in detail. Chapter IV includes a statement of hypotheses. Part II, "Results and Conclusions, " contains two chapters. Chapter V presents the research findings for each location model simulated. In Chapter VI, research conclusions are reported with analytical support. The hypotheses under observation are evaluated, and, on the basis of research results, the threefold problem is examined in detail. 19 CHAPTER II DISTRIBUTION CENTER LOCATION THEORY AND STRATEGY INTRODUCTION The field of economic space theory, or location theory, has historically received only intermittent attention in the literature of English-speaking countries. This Anglo-Saxon bias can be traced, in part, to the general acceptance of Ricardo's differential rent theory on ' 1 as opposed to von Thunen's location theory. Throughout the years, most theorists have been content to analyze economic problems with the implicit assumption that all firms have identical locations. With problems so stated, attention focused upon identifying firm behavior, given various competitive markets. Major emphasis was placed upon . . 2 the resultant divergence from maXimum welfare standards. Recently, new and refreshing advancements, based upon the reality of variable location, have evolved in the areas of both micro and macro economics. In macro economics, new approaches to the study of regionalism have resulted in a renewed interest in general equilibrium analysis. 1Philip C. Newman. The Development of Economic Thought. Englewood Cliffs, N. J. : Prentice Hall, Inc. , 1952, p. 127. 2‘For example, see: Melvin W. Reder. Studies in the Theory of Welfare Economics. New York: Columbia University Press, 1947; and Tibor Scitovsky. Welfare and Competition. Chicago: Richard D. Irwin, Inc.,1951. 3 See: Walter Isard, ”Interregional and Regional Input-Output Analysis: A Model of Space Economy, " Review of Economics and Statistics, 20 Advancements in micro—economics have clearly identified location selection as one of the strategic variables controlled by the firm. From this second development, insights regarding the logic of distribution center location have evolved. The purpose of this chapter is to review theoretical insights relevant to distribution center location strategy. Contributions in micro—location theory and practice may be grouped into the categories of industrial, retail, and wholesale location. Contributions relating most directly to the logic of distribution center location have the lowest frequency of appearance in location literature. Consequently, the task is to evaluate contributions in all areas and to construct a synthesis relevant to the problems under analysis. Steps in this synthesis include: (1) Directing attention to the overall importance of location in the strategy of the firm; (2) Investi- gating some major ideas found in location literature relevant to under- standing distribution center location; (3) Developing a theoretical frame- work based upon current literature capable of explaining the derived nature of distribution center location; and (4) Developing a logical system for classifying distribution center location. Vol. XXXIII (1955), pp. 318-28; Walter Isard. Location and Space Economy. New York: John Wiley 8: Sons, 1956; and Walter Isard, 3t a_1_. Methods of Regional Analysis. New York: John Wiley 8: Sons, 1960. 4 See: Edward H. Chamberlin. The Theory of Monopolistic Com- petition, 7th ed. Cambridge: Harvard University Press, 1956; Smykay, loc. cit. ; and John F. Magee, "The Logistics of Distribution, " Harvard Business Review, Vol. XXXVIII, No. 4 (July-August, 1960), pp. 89-101. 21 In total, the chapter is devoted to developing a theoretical frame- work for the experimental research which follows. A complete review of location literature is contained in Appendix B. LOCATION AND FIRM STRATEGY Acceptance of the fact that management has considerable latitude in locating physical facilities introduces an interesting new dimension in the theory of the firm. 5 By virtue of superior location, a firm can often gain a competitive advantage in a geographic market segment. The strategic positioning of production plants, distribution centers, and retail outlets allows the development of distribution systems capable of providing high levels of customer service at lowest possible cost. In order to fully understand the importance of location, it is useful to build upon the principles of traditional economic models. Economists classify industries along a continuum ranging from pure competition to pure monopoly. The practicality of these polar forms is readily accepted by the economist as providing reference points for contrasting and explaining various market configurations which fall between these extrem— ities. Industry configurations found between pure competition and pure 6 monopoly are broadly defined as imperfect competition. This basically 5See: John A. Howard. Marketing Management, Ch. XV. Homewood, Illinois: Richard D. Irwin, Inc. , 1957; and/or Wroe Alderson. Marketing Behavior and Executive Action, pp. 336—44. Homewood, Illinois: Richard D. Irwin, Inc., 1957. In a technical sense, pure monopoly is a form of imperfect compe- tition. However, the significant forms of imperfect competition for under- standing location as a strategic factor exclude pure monopoly. 22 includes the models of monopolistic, oligopolistic, and duopolistic competition. The underlying assumptions of models of imperfect competition basically culminate in an acknowledgment of an interdependence among the action of all firms in the industry. The fundamental difference among the various constraints of imperfect competition is the number of firms in the industry and the resultant degree of interdependence. The synapse of imperfect competition is the struggle among firms to gain a real or apparent differential advantage among consumers. A differential or competitive advantage may be obtained under conditions of imperfect competition because demand in all models is assumed to be somewhat elastic and sensitive to the individual firm's market offer. This advantage is traditionally assumed to evolve from product differ- entiation, advertising, sales promotion, and/ or pricing. To the degree that a given firm is able to gain a differential advantage, consumer loyalty is enjoyed. The firm possessing a differential advantage holds a temporal monopoly over a market segment. The normal reaction of other firms is to adjust their market offers to overcome this differential advantage. Shifting to a new industry equilibrium has been labeled neutralization. Within this framework of competition for differential advantage, location strategy gains eminence in the theory of the firm. Dropping the traditional assumptions of concentrated location, the firm may geographically 7Alderson, op. cit., p. 108. 23 adjust to market demand and competitive market offerings. Thus, a new method of gaining a differential advantage via spatial adjustments becomes a part of competitive strategy. The differential advantage achieved by astute location strategy has been referred to as spatial monopoly. To fully understand the implications of spatial competition, it is necessary to think of consumer demand in terms of geographic area. The concept of market area emphasizes the fact that population density and economic capability are geographically variable. In a sense, con- tinental United States represents a multitude of sub-markets having substantial variation in demand potential. The cost and competitive aspects of location, added to geographic demand variation, complete the picture. Each firm selects locations which allow maximum demand penetration at the lowest possible total cost. To the degree that a firm achieves control over a geographic market segment, its market position is entrenched by virtue of a spatial monopoly. It makes little difference whether the location spectrum is a city in terms of retail location, a more general market area in the case of wholesale location, or the entire United States when considering industrial location. The fact remains that each firm can enhance its market position by seeking that location offering the greatest differential advantage. Competitive superiority by virtue of location is distinctly different from other methods of gaining differential advantage, the fundamental 8Chamberlin, op. cit., p. 62. 24 difference being the time duration of a location advantage. Once a firm commits resources to a given system of locations, a great deal of flexibility is sacrificed. Only rarely can a firm adjust locations. Capabilities for adjustment are highest in retail location and lowest in industrial plant location. Thus, the location strategy of a firm is fundamentally important. Having gained a spatial advantage, the firm reacts differently to competition. Adjustments are more analagous to a chess game than to the normal ping-pong-like reaction associated with other competitive tactics. In summary, location problems are found at all levels of product distribution. Under conditions of imperfect competition, astute location provides the firm with an advantage which is difficult for competitive firms to neutralize. Therefore, the area of location strategy provides a new vista of action for firms operating in imperfectly competitive markets. SYNTHESIS OF RELEVANT LOCATION LITERATURE As noted in the introduction to this chapter, current literature contains a limited number of location strategy writings. The contributions available fall into three categories: industrial, retail, and wholesale location. The current purpose is to single out specific contributions which are relevant to an understanding of the logic underlying distribution center location. 25 THE CONCEPT OF SPATIAL MONOPOLY The spatial monopoly concept is of fundamental importance to understanding all forms of economic location since it embodies the aspired goal of each firm. The case of the spatial monopolist can be traced to Chamberlin9 and a group of writers who may collectively be referred to as the spatial duopolists.10 While these writers built upon the foundation of the German location school, it is interesting to note that the refinement of spatial monopoly models probably represents the first major contribution of English-speaking countries. Chamberlin's classical work is apparently one of the earliest works including an attempt to identify the strategy and advantages of superior location. Treated almost as a secondary thought, Chamberlin viewed a superior location as a temporary spatial advantage--one aspect of the businessman's attempt to gain competitive superiority. Unfortunately, Chamberlin was concerned with introducing the vast confines of monopolistic competition. Consequently, little detail was devoted to location. 9Ibid. 1 . . . 0The spatial duopolists include: Harold Hotelling, "Stability in Competition, " The Economic Journal, Vol. XXXIX (1929), pp. 41-57; Arthur Smithies, ”Optimum Location in Spatial Competition, " The Journal of Political Economy, Vol. XLIX (1941), pp. 423—39; A. P. Lerner and H. W. Singer, ”Some Notes on Duopoly and Spatial Competition, " The Journal of Political Economy, Vol. XLV (1937), p. 145; and Arthur Smithies and L. J. Sovage, "A Dynamic Problem in Duopoly, " Econo- metrica, April, 1940, p. 130. 26 . . 11 . . . . Smithies, representing the last major writer in the duopoly group concerned with spatial competition, summarized most of the earlier writings. While the main stream of economists tended to neglect location as an important variable, the duopolists did not. This may be attributed to the fundamental simplicity inherent in approaching the study of location when only two firms are engaged in the strategy. Utilizing a linear market assumption and a price structure based upon f. o. b. mill, Smithies argued the optimum strategy of two firms assumed capable of instantaneously adjusting location. The bi—product was a clear statement of the actions of a spatial monopolist. He sum— marized and improved upon the work of earlier economists by clearly pointing out that location is indifferent to the monopolist if freight rates 12 , . . are neglected. Once freight enters the analySis, the monopolist faces problems related to the inability to change uniform prices throughout the market area and the need to make some decision concerning freight absorption. These problems necessitate selecting a location which minimizes the freight burden and thereby allows profit maximization. Smithies logically defends a market center location for the spatial . l3 . . . . . monopolist. His solution is diagrammed in Chart 1, where MM' re represents a linear market, L1 represents the monopolist's location, ll . . . Smithies, ”Optimum Location in Spatial Competition, " Ibid. 12Ibid. , p. 429. l3lbid. 27 CHART I SMITHIES' DIAGRAM OF OPTIMUM LOCATION OF THE SPATIAL MONOPOLIST MODIFIED I! P1 is the net mill price, and AP and/or EP represents the delivered price level at which the product is offered to consumers located at various points in the market. A minor modification of Smithies' diagram is the inclusion of a consumer price indifference line, labeled II'. The assumption is that consumers uniformly will reject the mono- polist's product if the total delivered price exceeds the level indicated by 11'. At the level of II', the consumer is generally indifferent to the purchase of the product since he can obtain a higher degree of satis- faction by utilizing his income in alternative ways. Utilizing a price indifference line more simply illustrates the exact market area served by the monopolist. 28 In Chart I, the monopolist is able to select a profit maximization location since no adjustments to competitive location are necessary. Thus, the monopolist seeks the location which affords highest total revenue at lowest possible total cost. The monopolist sells an equal distance in all directions until he equates revenue and cost on the margins. This is assumed to occur at a uniform point in all directions; consequently, the total market area served is circular. The fundamental importance of spatial monopoly is that partial attainment of market control by superior location is the motive underlying location strategy. Rarely will only one firm be found in an industry as assumed above. The more normal case of imperfect competition is a number of firms seeking to select superior locations. However, the magnitude of numbers does not diminish the importance of theoretical goals motivating firms to scientifically engage in spatial competition. From the theory of spatial monopoly, insights into the strategy of dis- tribution center location are formulated. THE CONCEPT OF SPACE ISLAND 14 Building upon the theoretical insights of spatial monopoly, Losch developed the first model of spatial competition capable of explaining the strategies of a large number of firms engaged in an imperfect market. Losch presented a model of the spatial monopolist which he referred to 4Stefan Valavanis, "Losch on Location, " American Economic Review, Vol. XLV (1955), pp. 637—44. Z9 15 . . . . . . as a demand-cone. He pOinted out that initially the spatial monopolist will sell in all directions to the point of consumer indifference to product price. The interesting improvement offered by Losch in discussing the spatial monopolist was a clear presentation of demand intensity throughout the market area. Due to price elasticity of demand, sales intensity was assumed highest surrounding the monopolist's location, decreasing in magnitude as a product was sold further into the hinterlands. This demand-cone presentation is diagrammed in Chart II, where L1 represents the spatial monopolist's location, the circle represents total market area, and the height of the cone represents the intensity of consumer demand. The circumference of the market circle is limited by product price (mill net plus transportation) and the consumer indifference level for the product CHART II LoSCH's DIAGRAM or SPATIAL MONOPOLY 15 Ibid., p. 639. 30 More important, concerning distribution center location, is Losch's generalization from this model. Losch concluded that the market area which a monopolist could profitably serve from a given location was limited by price elasticity of demand for his product. Thus, the more general case is a series of monopolists located in the total industry market. Each firm selling under these conditions will serve circular market areas. The number of such monopolists initially will be limited to areas offering the highest demand potential, and all firms engaged in the industry will select the least—cost locations from which profits may be maximized. The net result is a series of space islands between the market areas serviced by each of the spatial monopolists. These space islands occur as pockets in which monopolists are unable to sell at acceptable profits. Chart III illustrates the concept of space islands. The area ABCD is assumed to represent the total industry market. Circles, appropriately labeled, represent the market areas of individual monopolists. In the long run, Losch generalizes that all such space islands will be filled by small—scale firms operating from high cost locations. Theoretically, it is defensible that the size of the market area would depend on the product classification in the consumer's mind as an inferior, normal, or superior good. This would influence the consumer's willingness to purchase the product as total delivered price increased. Thus, in final analysis, the price elasticity of demand associated with a given product identifies the price level at which the consumer becomes indifferent to the purchase of a given product. This may result in larger or smaller market area independent of the influence of transportation rates. 31 CHART III SPACE ISLANDS UNDER CONDITIONS OF SPATIAL MONOPOLY A B AN ECONOMICALLY JUSTIFIED HIGH COST LOCATION The high cost location is generally associated with a space island. The small-scale firm is characterized by high cost curves. While the cost of production is somewhat higher than those of the spatial monopolist, the high cost producer is able to take advantage Of demand intensity in the market area immediately adjacent to his plant. This, coupled with the fact that the spatial monopolist experiences a reduction in sales as he sells in distant markets, provides the economic foundation for justifying high-cost production. Accounting for the entry Of high-cost firms, LOsch logically generalizes that the total market area will finally be served by a number Of firms selling in hexagonal market areas. A simplified presentation Of two such firms of the LOsch system is shown in Chart IV. CHART IV LOSCH SYSTEM OF LOCATIONS \/ Reflecting upon Smithies' illustration Of the spatial monoplist, LOsch accomplished an improvement concerning the location of high cost firms. Chart V once again presents, with modifications, the Smithies diagram Of the spatial monopolist. In Chart V, the concept Of high cost location has been added. Originally, the spatial monopolist selected a location at L1 and sold in the MM' market segment labeled BD. The high cost producer selected a location at point L‘2 in the hinterlands Of the spatial monopolist. This high cost producer is located in a space island from which he can realize substantial profit regardless Of higher production costs. He finds economic justification since he can satisfy the heretofore untapped demand Of market area TB at a total price less than the spatial monopolist can Offer. The high cost producer is also able to capture a 32 33 segment Of the monopolist's original market labeled BS because his total landed price as far into the monopolist's market area S is less than that Of the monopolist. Additionally, the high cost producer can sell at a price lower than the consumer indifference level as far as C into the monopolist's market. Likewise, the monopolist can Offer the product at less than the indifference price over his entire original market area, BD. In the market segment labeled BC, both firms can sell under indifference levels. Therefore, this area represents demand most vulnerable tO other forms Of non-price competition. On a line indicated by RS, total product prices are equated between the firms. This point Of price equality is expressed in LOSCh‘S explanations as one side Of the hexagon division Of market areas. CHART V ILLUSTRATION OF ECONOMICALLY JUSTIFIED HIGH COST LOCATION \ 34 These rather abstract principles Of location theory contribute considerable insight into the logic of manufacturing and retailing location patterns. Very little is found in current location literature concerning the theoretical foundations Of distribution center location. This deficiency may be traced to an insufficient understanding Of the derived nature Of distribution center location. Distribution centers, per se, represent only a segment Of the firm's total strategy for creating time and place utility. Therefore, an investigation of manufacturing and retailing location patterns is necessary for a clear understanding Of the logic Of distribution center location. Building upon the contribution Of spatial economics, the derived nature of distribution center location is examined in the next section. DERIVED NATURE OF DISTRIBUTION CENTER LOCATION In Order to understand the lOgic Of distribution center location, it is fundamentally important tO visualize its dependence upon manu— facturing and retailing locations. Distribution centers enter a logistics System only when a degree of differential advantage results from their inclusion. This advantage may take the form Of increased speed or decreased cost in inventory replenishment from manufacturers tO retailers or consumers. For purposes Of understanding distribution center location, consumer location is assumed constant. Therefore, the relevant location spectrum IS one confined by retail and production locations. Potential distribution center locations fall between these extremes. 35 The exact location selected for a distribution center is properly viewed as part of the logistics strategy of the firm. Distribution center location strategy culminates from the firm's desire to gain a cost and/or service advantage in a market segment. The nature Of this strategy depends a great deal upon the degree of product differentiation, product line width, competitive structure, and the basic mission Of the distribution center. The purpose Of this section is to illustrate the dependence Of distribution center location upon other location decisions of the firm and its competitors. Through economic principles, a few business conditions are examined to illustrate the derived nature Of distribution center location strategy. DISTRIBUTION CENTER LOCATION STRATEGY WITH NON-DIFFERENTIATED PRODUCTS In the case Of an industry characterized by near-identical products, little consumer loyalty is commanded by individual firms. The industry demand curve is relatively elastic. Fundamentally, individual firms can differentiate their products by location dispersion. Under these conditions, LOsch's hexagon and generalizations concerning location patterns are likely to be experienced. The major firms in the market will seek locations in prime sub-markets under the principles Of spatial monopoly. Smaller high cost firms will normally find economic justification by selecting locations in marginal markets contained in Space islands. It is equally possible that spatial monopolists located in the market may follow the practice Of utilizing distribution centers as a means Of servicing marginal 36 markets. By locating distribution centers in space islands, major producers may extend their effective market coverage. Attaining entry barriers to the location of high cost producers in space islands is the net result of this type of market extension. Consolidating shipments is a basic economic principle underlying the utilization Of distribution centers tO extend market areas. The spatial. monopolist initially sells f. O. b. mill over his entire market area. Each customer is shipped products directly from the production point by some method of less-than-quantity shipment. By consolidating product shipments to a distribution center, transportation expense is substantially reduced. Thus, the monopolist is able to move large quantities Of his product into market areas heretofore beyond his reach at a total cost considerably below the consumer's price acceptance level. Products may then be distributed f. O. b. distribution center in all directions to a point where total product price reaches the level Of consumer indifference. The net result is a considerable expansion Of markets into hinterlands previously beyond the reach Of the spatial monopolist. Chart VI contains an example Of market expansion by utilizing a distribution center. 17 The case of the spatial monopolist is illustrated only in one direction in the linear market. Under conditions Of direct 1 7Chart V1 is adopted from a chart presented by John H. Frederick: John H. Frederick. Using Public Warehouses. Philadelphia: Chilton Company, 1957, p. 81. 37 shipment, the monopolist is able to sell only as far into the market as point D. At the line ED, the total cost Of his product reaches the consumer indifference price level. By placing a distribution center at some point in the market beyond D, the monopolist is able to make consolidated shipments to the distribution center at a landed cost below the consumer indifference price level. Shipments are then returned toward the production point and further out into the market area until total price once more becomes prohibitive tO the consumer. The total market expansion achieved by utilizing a distribution center is expressed in the linear diagram by the area DC. CHART VI MARKET EXTENSION BY USE OF A DISTRIBUTION CENTER LCL I E l3 I' W%/CL ,,// P M M. L D WL C 38 To generalize a step further, locating a number Of such distribution centers around the total market area initially served by the spatial monopolist will once more result in a system of LOsch hexagons. The fundamental difference is that marginal markets are now served by distribution centers controlled by the spatial monopolist rather than by competitive high cost producers. Thus, one function of distribution centers is to extend prime markets under conditions Of non-differentiated products. DISTRIBUTION CENTER LOCATION STRATEGY WITH DIFFERENTIATED PRODUCTS Distribution centers Often play a vital role in the expansion of firms engaged in nation-wide sales of differentiated products. Since products Offered by all firms are differentiated in the consumer's eyes, the neat theories Of spatial monopoly break down. Each firm is forced to sell over a larger total market area in order to realize sales volumes sufficient for survival. Under these conditions, it is likely that large producers will initially be forced to concentrate product plants in the geographic area having low production costs and a substantial proportion Of industry demand. This is necessary Since no individual sub—market demands a firm's total production. From such concentrated locations, each firm 18 may be characterized as playing a waiting game. Each is able to meet Basically, this type of location strategy represents a game in which each player possesses perfect information concerning opponents' ex-post moves. Consequently, each player is content to maintain status quo until a location alternative Offering a definite payoff is discovered. 39 the service capabilities of competitors, and all confront near—similar transportation costs. Under these conditions, the industry initially settles down to conventional tactics of non—price competition in order to achieve differential advantage. An excellent example is the geographic concentration Of the auto industry prior to World War II. The dynamics Of spatial competition enter the industry when differentiated products begin tO gain acceptance in distant markets. The firm finds it desirable to decentralize physical facilities when sales volumes become sufficient in sub-markets to justify, first, distribution centers and, second, branch plants. The transportation principle justifying the use of distribution centers is the same as in geographically dispersed industries. When total demand in a given market segment becomes substantial enough to consolidate shipments, the resultant economies may be sufficient to justify a distribution center. Thus, a second economic force leading tO the use Of distribution centers is the normal expansion Of firms selling differentiated products on a nation-wide basis. Once a major producer Obtains sufficient volumes to support a distribution center in a market segment, the waiting game which earlier characterized such a concentrated industry is abandoned. In addition tO transportation economies, firms operating distribution centers also gain For a discussion Of the logic Of game theory in competition, see: Martin Shubik. Strategy and Market Structure. New York: John Wiley 8: Sons, 1959, Pp. 3-18. 40 a service advantage in these market segments. These select firms are than able to replenish consumer inventories in less time than major competitors. For customers this means faster special order handling and an overall reduction in basic inventories. ‘IThus, the firm capable of supporting distribution centers is availed one more method Of gaining a differential advantage. The counter-strategy is for all major firms to neutralize this location advantage by developing a competitive system Of distribution points when sufficient sales volumes are Obtained. DISTRIBUTION CENTER LOCATION STRATEGY WITH MULTIPLE PRODUCTS Distribution centers may also provide an economic function for many firms engaged in the production and marketing Of a broad line Of highly differentiated products. Industrial location theory points out that plants producing a particular type Of product are Often highly restricted to locating near geographic points which provide required inputs. While for reasons Of production economy firms may be faced with the need for geographically decentralized production plants, for purposes Of marketing control, they may prefer to utilize a convergent marketing plan for the multiple product line. l . . . 9Melvin L. Greenhut. Plant Location. Chapel Hill: UniverSIty Of North Carolina Press, 1956, p. 113. 0Thomas A. Staudt, ”Program for Product Diversification, ” Harvard Business Review, Vol. XXXII, NO. 6 (November-December, 1954), p. 125. 41 Under conditions of joint marketing, a distribution center may be operated as a collection point for various products produced at decen- tralized locations. By centralizing all products, it becomes possible to sell mixed carloads. 21 Mixed carloads allow customers tO realize economies related to consolidated shipment as well as faster replenish- ment of all products which are normally purchased only in quantity lots. In addition to gaining a competitive advantage on the basis Of Offering these additional services, the firm Offering mixed carloads may sell slow-moving products mixed with faster movers and, thereby, Offer the total product line at consolidated transportation rates. Thus, a third economic justification for distribution centers is the need to en- gage in joint marketing Of a multiple product line manufactured at decentralized locations. INFLUENCE OF RETAIL LOCATION UPON DISTRIBUTION CENTER LOCATION STRATEGY The basic principles discussed above also apply, in a more limited way, to the spectrum Of retail location. To a degree, retail store location may be theoretically explained by the concepts Of space islands and spatial monopoly. The small retailer generally faces somewhat high cost curves resulting from his inability to purchase in quantity lots. Consequently, he is confronted with the need tO charge 21 . . . . A mixed carload is defined as a quantity rail shipment mOVIng under consolidated economies and containing various amounts of dif- ferent products shipped from the same origin. The same general definition applies to mixed truckloads. 42 higher prices in order to realize sufficient profit margins. Assuming that the small scale retailer sells identical products as his larger scale competitors, he must find some way to induce consumer purchase at his administered price structure. This is normally accomplished by providing maximum location convenience as part Of his total market Offer. While little empirical research is available concerning the impact of location convenience upon the acceptability Of higher product prices, a few generalizations can be scientifically supported. *First, a con- sumer will travel a considerable distance when purchasing an item which constitutes a major portion Of his annual budget. 22 Second, consumers will travel a greater distance if a number Of purchases can be made at one location. This contributes a great deal to the market area pull enjoyed by regional Shopping centers. 23 Third, it appears that as the importance Of a given purchase, expressed as a percentage Of a consumer's total budget, decreases, his willingness to travel sub- stantial distances decreases. This generalization, supported by research concerning the distance consumers are willing to travel for single- 2 2 Alan M. Voorhees, Gordon B. Shorpe, and J. T. Stegmaier. Shopping Habits and Travel Patterns, Urban Land Institute, Technical Bulletin NO. 24, Washington, D. C. , March, 1955. However, it is interesting to note this generalization is somewhat reversed when the product being purchased is a luxury. In such cases, consumers may travel considerable distances for a relatively small purchase. See: Gregory P. Stone and William H. Form. The Local Community Clothing Market, Michigan State University Agricultural Experiment Station, Technical Bulletin 262, East Lansing, November, 1957, p. 29. 23Nelson, op. cit., Chs. XVII and XIX. 43 purpose purchases, partially explains the dispersed location pattern Of retail drug stores. 24 Lastly, the larger the number Of retailers offering identical product-price structures, the shorter the distance the consumer is willing to travel. While almost tautological, this last generalization is vividly supported by research which points out that major food chains make 73 per cent of sales to consumers living within two miles of the store location. These generalizations concerning consumer purchase habits formulate the foundation for understanding the economic justification supporting high cost retail location. Small retailers attempt to select locations which will afford consumers maximum convenience in fitting normal purchase patterns. They accept the fact that each purchase has a convenience cost as well as a product cost. 26 Therefore, they select locations which minimize convenience cost, develop a product line characterized by high convenience purchase, and charge a higher price to compensate for Offering maximum convenience. Many of these locations are in fringe areas along main traffic arteries and in close proximity to Z4tWilliam L. Garrison, et al., Studies Of Highway Development and Geographic Change. Seattle? University Of Washington Press, 1959 pp. 197-226. 25"Super Value Study, “ Progressive Grocer, August, 1958, P- S-ll (Reprint). 26Eugene J. Kelley, "The Importance Of Convenience in Consumer Purchasing, " Journal Of Marketing, Vol. XXII (July, 1958), pp. 32-38. 44 major population clusters. 27 Large scale retailers are attracted to business and shopping areas for maximum benefits Of agglomeration. These locations represent spatial monopolies. Space islands attract small scale retailers. An example of small scale convenience location is the recent development of miniature grocery stores on the fringes of large cities. Such high cost operations find economic justification on the basis of increased convenience. The typical bantam grocery operates from 7:00 a. m. to 11:00 p. m. , thereby combining time and location convenience. Thus, in many ways, the principles Of economic industrial location are also applicable to retail location patterns. Somewhat different in the case Of retail location is the economic justification supporting the employment Of distribution centers. ‘The average retail store, whether large or small scale, does not have sufficient demand to order inventory in consolidated quantities directly from manufacturers. Retail product lines are usually extensive, being manufactured or processed at widely 27For a discussion Of profitable fringe locations for small food stores, see: Ray O. Harb, ”Why Three Out Of Four Stores Should Con- sider a New Location, " Progressive Grocer, Vol. XXXII (August, 1953), pp. 48-52; and/ or Robert w. Muller, "What's the Best Location for Today‘s New Store 7" Progressive Grocer, Vol. XXXII (February, 1953), p. 50; and/ or Lew Milkovics, "Convenient Food Mart Sets 2000 Drive- In Goal by 1965, ” Progressive Grocer, Vol. XXXVII (December, 1959), pp. 67-71. Agglomeration is a term employed by Weber to describe the process of firms attracting to adjacent locations in order to enjoy benefits Of concentration. Carl J. Friedrich (trans. ). Alfred Wever's Theory of Industries. Chicago: The University of Chicago Press, 1929, Ch. III. Alderson referred to this tendency as ”systasy. " Nelson, in the case Of retail location, referred to this tendency as the "Theory Of Cumulative Attraction“; see; Alderson, op. cit. , p. 326 and Nelson, op. cit. , pp. 58-64. 45 scattered geographic points. In order to Obtain rapid inventory replenish- ment Of this heterogeneous product line, the retailer normally utilizes some form of Off distribution center. Distribution centers directly servicing retail outlets have widely varied ownership arrangements. Some are owned and operated by large retail chains which serve their stores exclusively. This form Of vertical integration is common in the supermarket industry. The location of such distribution centers is the major concern Of this research. Other distribution centers are owned and operated by independent wholesalers whose prime business is the replenishment of retail inventories. Still others are owned by independent retail cooperatives. Whatever the ownership arrangements, the basic purpose of the distribution center is tO consolidate purchase from distant procurement points and replenish inventory to retail outlets. A distribution center strategically located tO provide a cost-and—service benefit to retail stores is best located near the outlets it serves. This allows maximum advantages Of consolidated shipment with relatively short local delivery. Therefore, retail store location determines the alternatives available in selecting a location for this particular type Of distribution center. CONCLUSION These few illustrations serve to emphasize the dependent nature Of distribution center location upon the characteristics Of the industry and the manufacturing and retailing location decisions made by each firm. 46 It also points out the applicability Of economic location theory to an understanding Of distribution center location strategy. Upon this foundation, it is possible tO summarize the logic underlying distribution center location. DISTRIBUTION CENTER LOCATION LOGIC A dichotomy appears in historical marketing literature concerning the role Of traditional warehousing and the function of product distribution. In early literature, the warehouse is considered a static unit for satis- . . . Z9 fying the marketing function Of product storage. The warehouse was viewed as a unit for product storage until demand became sufficient tO support distribution. The creation-Of-time—utility principle was used to . . . . , , 30 . _ justify this type Of economic activ1ty. Throughout the majority Of early writings, storage is viewed as an ancillary function merely to match supply with erratic demand. This tendency tO consider storage as merely a required facilitating function generally resulted in criticism Of efficiency with little appreciation or consideration Of the broader distribution spectrum Of which storage played a vital role. A few early writers did attempt tO generalize the physical distribution function, namely, lngersoll, Cherington, Clark, and White. 2 - . 9Hugh B. Killough, The Economics Of Marketing. New York: Harper and Brothers, 1933, p. 101. 30H. H, Maynard, T Beckman, and W. Davidson Principles Of Marketing, p. 473. New York Ronald Press Company, 1957. 47‘ In 1919, Wilber Ingersoll directly attacked the question of distribution inefficiency by stressing the importance of distribution systems. 31 He illustrated the economic reasons why several marketing steps were inevitable in distributing goods produced in large quantities at a factory or farm. He stated that distribution systems were necessary to satisfy consumer demand and concluded that only a limited number Of commercial points--called trade parlance--could justify wholesale centers. He also pointed out the need to disseminate products to tributary territories from each Of these commercial centers. His fundamental argument was that countless economic enterprises Of various sizes were required to distribute products. These would be located in various areas, depending upon demand, with the scale Of the enterprise being proportionate with the intensity Of demand--surprisingly similar tO the theoretical con- tentions Of spatial economists. Paul Cherington in 1921, broadened the perspective Of storage and transportation by acknowledging the necessity for adjustments in place. He clearly separated the flow Of paper and the flow Of physical products 34 . from production tO consumption. With a System Of Circles to represent 1 3 W. H. lngersoll, National Civic Federation Review, June 5, 1919. 2 3 Ibid., p. 3. 33 Paul T. Cherington. The Elements Of Marketing. New York: The Macmillan CO., 1921. 34Ibid.. p. 93. 48 market demand, Cherington illustrated the attraction Of distribution facilities to the points Of demand concentration. Unfortunately, he spent little time considering the nature of distribution systems and the relative importance Of product storage. Fred Clark, in both of his basic marketing books, was probably the first writer to purposely utilize the term ”physical distribution" in discussing the process of market logistics. In his principles book, he included such facilitating functions as transportation, materials handling, and storage as fundamental in distributing products. In the readings book, the subjects discussed under physical distribution were expanded to include more detail on the warehouse operation. 36 This reader was left with the impression that Clark gained Significant insights into the basic forces influencing distribution systems; however, he was unable to clearly orientate this to the marketing strategy Of the firm. Percival White, in 1927, made considerable advancement in 37 integrating basic marketing functions into a system Of market action. Writing probably the first book on managerial marketing, White 35Fred E. Clark. Principles of Marketing, pp. 293-324. New York: The Macmillan CO., 1923. 36Fred E. Clark. Readings in Marketing, p. 481. New York: The Macmillan CO. , 1924. 7Percival White. Scientific Marketing Management. New York: Harper and Brothers, 1927. 49 visualized traditional marketing functions as sequential steps in the broader process Of product concentration and dispersion. 38 His general thesis was that marketing is normally concerned only with the process of broadcasting commodities, while in reality it deals with commodity reception as well as transmission. White's classification Of marketing functions included three main categories: (1) concentration; (2) dispersion, and (3) facilitation. Concentration was assumed to include the traditional functions of assembling and grading. Dispersion included demand creation and merchandising. Facilitation functions included storage, communication, transportation, and financing. White's conception of marketing is contained in Chart VII. CHART VII WHITE'S CONCEPTION OF THE MARKETING PROCESS39 Concentration Disper sion 8 .5. '3 D d . . r 3 Assembly Grading Storing cfgflirfig MerchandiSIng % Po . g > ——> —-——> ———> > a C‘. mw\ 8 Also Communicating Transporting Financing 38Ibid., p. 72. 3 91bid., p. 73. 50 Following White's basic diagram, marketing is concerned with the process Of product flow from production to consumption. Of particular interest is the central position occupied by storage. NO longer is storage considered a necessary evil, rather it assumes para- mount importance in the marketing process. White saw the storage function in its broader perspective. Storing occupies a position midway between the functions Of concentration and those of dispersion. It helps to take care Of the inevitable lack Of coordination between production and consumption. It will include not only the control Of finished stores at the factory, but also the provision Of suitable stocks, properly warehoused, at strategic points throughout the market territory. White's major Objective was to illustrate that managerial marketing embraced considerably more than merely advertising and selling, which he felt received undue emphasis tO the detriment of other vital functions. As a by-product, he made considerable improvement upon the role Of physical supply in the marketing process. Subsequent events have somewhat resolved the dichotomy between static storage and the dynamics Of product distribution. White came closer tO explaining the true role Of physical distribution but, unfortunately, did not carry his discussions Of storage tO the logical conclusion. If the diameter Of the storage circle had been assumed variable, his diagram would have been more nearly correct. If the storage circle is free to vary with the magnitude Of products held in storage, then it follows that 40%. , p. 75 (underscoring added by author). 51 the nearer supply and demand are matched, the smaller the circle will become. This reduction in product storage with its related economies is precisely what is achieved by the operation Of modern distribution centers. A modern distribution center is designed with primary emphasis upon product flow. As noted earlier, the desired Objective is to have pro- ducts arrive at and depart from the distribution center in a single work day. Modern philosophy clearly places the traditional dichotomy in proper perspective. Those like White who viewed product distribution and storage as basic marketing functions more closely approximated the nature Of modern physical distribution systems. The meaning Of storage, as used by these earlier writers, has been redefined as a result Of modern technological advancements. Based upon improved sales forecasting and production scheduling, storage has become a temporary function. Other writers who concentrated upon storage, per se, without reference to more encompassing distribution systems, succeeded in explaining a mere secondary and relatively unimportant part Of modern distribution--namely, permanent storage. Due tO special conditions, it may be necessary to retain products in a warehouse longer than the normal inventory replenishment cycle. Such permanent storage may result from seasonal production, product conditioning, and/or the realization Of special quantity discounts. In the philosophy 52 underlying modern distribution, such permanent storage is considered the exception rather than the rule. This evolution of marketing thought, coupled with the various economic justifications supporting distribution centers, helps explain the logic of such distribution points. The distribution center is viewed as a vital link in the dynamics of market logistics rendering a service and/ or cost advantage to a firm in a given market segment. The geographic location confines Of a distribution center are controlled by production locations and markets to be penetrated. Logically, three types Of distribution structures evolve when a distribution center is adopted. Under Hoover's plant location classification, these may be identified and summarized as: (1) market positioned, (2) production 41 positioned, and (3) intermediately positioned. MARKET - POSITIONED DISTRIBUTION CENTERS A market-oriented distribution center serves the basic function Of inventory replenishment tO retail stores and delivery Of merchandise to consumers. The distribution center, by being located in close proximity to ultimate product consumption, affords maximum consolidation economies from distant shipping points and has relatively Short movements in local delivery. The geographic market area served from a market- oriented distribution center is dependent upon the required speed Of inventory replenishment to customers. The lower the service standard 1Edgar M. Hoover. Location Of Economic Activity. New York: McGraw-Hill Book CO., 1948, p. 35. 53 in terms of replenishment time, the greater the market area served. Market-oriented distribution centers may be retailer, manu- facturer, or independently-pwned. The mission of the distribution center will vary depending upon the ownership arrangement. Retailer- owned distribution centers are designed to serve as break-bulk points for a wide variety Of products purchased from different sources. Since the width Of product line processed through retailer owned distribution centers is extremely wide, the magnitude Of demand for a given product need not be a substantial proportion Of the center's total volume. The market-oriented, manufacture owned distribution center may represent an extension into sub-markets when the industry is characterized by differentiated products. Under these conditions, the manufacturer must enjoy sufficient sales volume in the market to operate a distribution center. In the case of an industry selling non- differentiated products, a market-oriented distribution center may serve as a means for extending sales territories into marginal markets. Under these conditions, volumes need not be as extensive as in the case Of differentiated products; however, they must be sufficient to realize consolidation economies and cover the cost Of distribution center operations. The volumes required under both cases of manufacture owned distribution centers may be substantially reduced by utilizing public warehousing. Such forms Of distribution reduce necessary 54 tonnages, but they also result in a system readily duplicated by major competitors. The independently owned, market-oriented distribution center may function primarily to replenish retail inventory or to act as distribution points for manufacturers. When the primary function is retail inventory replenishment, the distribution center is normally owned and operated as an independentiholesale establishment. Such business enterprises take ownership as well as physical possession Of products and assume full responsibility for the sales effort. When independently owned distribution centers primarily act as distribution points for manufacturers, they are commonly referred to as public warehouses. The typical pattern of operation is for public warehouses to take physical possession of products while assuming no responsibility for sales. The ownership Of such products is retained by the manufacturer or a middleman. This description Of the various forms of market-oriented distribution centers represents only a few combinations Of physical movement. The basic point is the logic underlying their location in close proximity to the market served. This can be attributed tO the need for rapid customer inventory replenishment and the desire tO achieve product distribution at lowest possible cost. PRODUCTION - POSITIONED DISTRIBUTION CENTERS A production-oriented distribution center is located in close proximity to production plants in order tO act as a collection point for 55 a large number Of products manufactured at different plants. The fundamental reason for using production-oriented distribution centers is the manufacturer's desire to provide maximum service to customers. Quantities Of products produced at each plant are shipped tO the collection center from which customer orders are filled. Upon order receipt, merchandise is loaded in the mixture necessary to satisfy consumer requirements. Location near manufacturing plants allows such mixed carloads to move under consolidated trans- portation rates. Under carload conditions, a customized order may be shipped to a customer in a shorter period Of time than smaller quantities, thereby allowing rapid replenishment and lower basic inventories. This mixed carload service stimulates purchase of products which normally move under less-than-carload rates. Therefore, the advantage of a production-oriented distribution center is its ability to furnish a high degree Of service across the total product line Offered by a firm. TO the degree a manufacturer is able tO Offer all products in customized quantities at consolidated transportation rates, a differential advantage is Obtained in servicing customers. INTERMEDIATELY POSITIONED DISTRIBUTION CENTERS Distribution centers located some distance between customer locations and production locations are referred tO as intermediately positioned. Such distribution centers find economic justification on the basis of increased service similar tO production-oriented centers. 56 They serve as mixing points for manufacturers engaged in the production and marketing of a multiple product line. In the earlier discussion Of the derived nature of distribution center locations, it was pointed out that manufacturing facilities Often must be decentralized due to the nature of inputs required for production. Under these conditions, it is likely that firms engaged in the manufacture of disparate products will have manufacturing locations spread over a large geographic area. Conse- quently, the most economical grouping point may be a centralized distribution center location. From a distribution location which minimizes inbound transportation cost from all plants, the firm can most economically provide mixed-carload service to customers. CONCLUSION Traditional location theory and the historical development Of modern marketing distribution have been examined in order tO uncover some theoretical insights regarding distribution center location. All forms Of location were established as important strategic elements in a firm's total marketing plan. Differential advantage, by virtue Of astute location, is basically different from the advantage Obtained by other marketing tactics because Of the temporal element. Once a firm is committed tO a location, its ability to maintain flexibility is limited. On the other hand, it gains an advantage difficult to neutralize. Thus, a firm must move cautiously in selecting locations because of the fixity of such decisions. Once superior locations are Obtained, a firm enjoys a differential advantage difficult tO duplicate. 57 This research is concerned with the exact location Of a market- positioned distribution center. In the supermarket industry, distribution centers are attracted to the retail stores in order to give maximum service at minimum cost. Full recognition is rendered the fact that retail store locations determine precisely at what point a food distri— bution center should be located. The overall Objective is to study the nature of the market area food distribution center location problem in detail. 58 CHAPTER III RESEARCH DESIGN INTRODUCTION Chapter III is devoted to a detailed treatment Of the research design employed in this study. Research design represents the structure within which data are organized and correlated to arrive at defensible conclusions concerning the research problem. Evaluation Of problem hypotheses requires a controlled blending Of raw data, analytical techniques, location measures, and a costing procedure. This blending is accomplished within the structure Of the research design. Therefore, the research design provides the foundation for all problem-solving. In this chapter, the objective is to introduce the various elements Of the research design and to blueprint the structure for fitting them to the problem. The order of development is as follows: (1) TO present an overview Of the research structure indicating the general plan of attack, reemphasizing the problems under analysis, and defining terminology; (2) To explain fundamental techniques employed in location testing; (3) To present and develop alternative measures Of warehouse location; (4) TO construct theoretical location models utilized in classifying primary data; (5) TO develop a costing procedure and the rationale underlying its construction; and (6) TO emphasize the inter- relation Of each element in the research design. 59 GENERAL RESEARCH DESIGN The purpose Of this brief overview is to provide a general discussion Of the research design and its basic structural elements. In the intro- ductory chapter, the research problem was stated as threefold: (1) TO compare non-mathematical and mathematically derived location solutions; (2) To compare alternative measures available for use in mathematically determined solutions; and (3) TO introduct and evaluate a location measure which allows the force Of delivery time tO be influential in location selection. The research design has the Single purpose Of developing a structure capable Of providing insights concerning this problem. The fundamental cornerstone of the research design is the structure for primary data collection. For purposes Of experimentation, primary data utilized are based upon operating experiences Of two firms . In order to render a contribution broader than special case studies, location models are utilized tO classify primary data. Location models represent a simulation Of geographical retail market patterns commonly experienced in the supermarket industry. Thus, while the primary data limit the experimentation tO a case-study approach, the development Of location models provides a more universal basis for generalizing study conclusions. In order tO utilize the primary data in selecting distribution center locations, two types Of analytical techniques are employed. One type is referred to as non-mathematical and consists primarily Of a standard method for applying management judgment to location selection. The 60 second method, a mathematical technique, permits the use of various measures to solve the location problem. In utilizing the mathematical technique, a geographical differential normally results, depending upon the location measure employed. In the research process, four different location measures are used as inputs for the mathematical technique with the fundamental difference among the various measures being the data contained in their formulation. A standard transportation cost model is used in evaluating alter- native locations. The standard model simulates the cost structure Of a private carrier fleet. From each location selected, secondary data are Obtained. These secondary data represent the magnitude Of cost determinants estimated from each potential location. By applying these cost determinants to the transportation cost model, an estimate Of total distribution expense is found for each proposed distribution center location. A comparison Of these total cost projections provides the basis for evaluating alternative locations. The total research process is designed to generate six location solutions for each location model, or twelve solutions in total. Considering only one model, the first solution is assumed as an initial warehouse 1 . location. Total distribution costs estimated from this assumed location lAn assumed location, rather than the current location Of the distri- bution center operated by the chains studied, is selected as the initial location. An initial location is necessary in order to enter into the mathe- matical trial-and-error procedure explained in the section covering location measures. The use Of an assumed location avoids unnecessary criticism Of locations tO which cooperating firms are currently bound. The initial location is simply the geographic center Of the market area. 61 provide a comparative reference for other costs derived from experi- mentation. A second location solution is derived from the application Of the non-mathematical technique. The remaining four solutions are Obtained by utilizing the mathematical technique with four different location measures. This process employed to each Of the location models provides twelve location solutions. The secondary data Ob- tained from each Of the twelve solutions are used tO develop inputs for the transportation cost model in order to estimate total distribution cost from each location. These estimated costs provide the vehicle for comparing alternative locations and the foundation for testing hypotheses. The structure Of this research design has the desirable feature Of holding all basic research elements constant except the variable under examination. The procedure for determining locations varies from a non-mathematical to a mathematical technique. However, once the alternative location measures are applied, the mathematical technique is held constant. Finally, a unique feature Of the structure is the uniform use Of a standard transportation cost model in estimating the cost Of distribution from each location. The threefold problem under analysis is examined as follows; (1) Varying only the technique between standard mathematical and non-mathematical approaches provides the foundation for evaluation of the location solutions as determined by each; (2) Once the stage Of using the mathematical approach is reached, varying only the measure results in solutions necessary for evaluating 62 alternative measures; and (3) Including a location measure which contains the time influence provides the evidence for judging the effectiveness Of this suggested measure. A comparison Of the results Obtained from each location model provides the basis for observing the applicability of the research to different geographic market configurations. TERMINOLOGY Prior to a detailed discussion Of the basic research elements, the terms introduced above require definition. Analytical Technique--A mathematical or non-mathematical procedure for selecting a distribution center location. Cost Determinants-—Secondary data converted to inputs for the standard transportation cost model. FOOd Distribution Center--A warehouse receiving bulk shipments from processors and manufacturers, grouping such shipments into customized retail orders, and performing the function Of shipping such customized orders to retail outlets on a regular basis. Geographic Retail Market Area--A geographical area containing any number Of retail stores served from one distribution center. Least-Cost Location--That location from which the dollar cost Of replenishing the inventory Of all retail outlets from a distribution center is minimized during a designated time period. 63 Location Model--A simulation of a geographic retail market area commonly experienced in the supermarket industry. Market Area Location Solution——A point within a geographic retail market area at which a distribution center is positioned. Mathematical Technique-—A predetermined formulation of one or more quantitative factors designed to determine the value of a dependent variable. Measurement Device—-A quantification of a factor(s) to be utilized as an input(s) for a mathematical technique designed to isolate a location solution. Non-Mathematical Technique—-A predetermined procedure for selecting a distribution center location not using mathematical formulation. Primary Data-~Operating information Obtained from retail food chains studied in the research. Secondary Data--Operational information resulting from the selection Of a distribution center location. Utilized to estimate the value of cost determinants. Standard Transportation Cost Model—-A simulation of the cost structure of a private carrier fleet emphasizing cost categories and accounts and their dollar characteristics. 64 Supermarket Industry-~An industry consisting of chains operating eleven or more supermarkets, each with a minimum annual sales volume of 500, 000 dollars. Supermarket, Retail Store or Retail Outlet--A consumer purchase point served from the distribution center whose location is given and assumed constant throughout the research. Total Cost of Distribution-~The dollar expense estimated for satisfying all deliveries in a geographical retail market area from a proposed distribution c enter location. ANALYTICAL TECHNIQUES As noted above, two basic types of analytical techniques are employed in the research design--mathematical and non-mathematical. Each type Of technique presents a procedure for selecting distribution center locations. The purpose of this section is to describe, in detail, the nature Of the techniques employed. NON-MATHEMATICAL TECHNIQUES A non-mathematical technique represents a method for selecting a distribution center without the help Of precise mathematical formu- lations. While very little has been written on the use Of non-mathematical techniques, it is safe to generalize that, historically, most distribution centers were located in a non-mathematical manner. 65 The most unscientific method of selecting a location is here labeled V(the managerial preference technique. The process is to select a location which, on the basis of managerial experience, appears the logical solution. This solution may be based upon a rational evaluation of the situation or may be merely the product Of a favorable attitude developed by management concerning a Specific city. While information is not available concerning the number of locations selected in this manner, one indication is the large number of new distribution centers located in the same city as the warehouse they replaced. Probably the earliest non-mathematical, but scientific, technique employed, and apparently the only one published, is referred to as the V Keefer system. 2 Keefer, attempting to select a warehouse location, employed a piece Of cardboard to represent the geographical market area. He then placed BB shot at the location of each retail store, weighted in proportion tO annual sales. The location solution was then determined by moving a pencil under the cardboard until the fulcrum Of balance was determined. This point was assumed to be the least-cost location. The implicit assumption was that the center Of gravity represents the least-cost location. Although Keefer introduced his unique System in 1934, it was not commonly used to select distribution center locations. A more common \. method may be referred to as the cluster method. The cluster method 2K. B. Keefer, "Easy Way TO Determine the Center Of Distribution," Food Industry, October, 1934, pp. 450-51. 66 is very similar to the managerial preference method in that a location is selected based upon judgment. The basic difference in the cluster method is the procedure of plotting all stores on a map of the geographical market area. Once this plotting is completed, the distribution center is located in close proximity to the largest cluster Of retail stores. Implicit in the cluster method is the assumption that a distribution center positioned in close proximity to the major cluster Of stores will result in a satisfactory approximation of the least-cost location. \/‘A fourth non-mathematical method is the one employed in this research. This method is referred to as the polar technique. Similar tO the cluster method, all stores are plotted on a map. However, rather than selecting a location near the major cluster Of stores, the polar stores are connected. By drawing a straight line on the map from the store furthest north tO the store furthest south, the supermarkets located on each Of the cardinal direction peripheries are connected. A Similar procedure is followed for stores on the east and west extremities. The point at which the two lines cross is selected as the distribution center location. The polar technique is employed in this research since it provides a method Of location selection which does not involve managerial preference or judgment. 67 3 MATHEMATICAL TECHNIQUE The mathematical technique employed in the research evolves from an application Of analytic geometry to the location problem. The fundamental system of orientation is based upon Cartesian coordinates. The basic principles underlying this mathematical technique may be traced historically to René Descartes (1596-1650), who is credited with combining geometry and algebra into analytic geometry. 4 Utilizing only the positive or north-east quadrant, the geographic market area under examination is simulated by establishing uniform mileage scales along the X and Y perpendicular axes. Given this system Of orientation, it becomes possible to locate any point in the two-dimensional plane by identifying the relevant coordinates. In a system of Cartesian coordinates, the horizontal, or east—west, axis is traditionally labeled the X axis. The vertical, or north-south, axis is labeled the Y axis. Together, these two axes identify four quadrants, which are customarily numbered as illustrated in Chart VIII. Any given point in Quadrant I can be identified with reference to the X and Y coordinates. The Y coordinate Of a point is called its ordinate. 3The mathematical technique employed in this research is based upon the following article: ”Warehouse Location Based upon Trucking Cost, " op. cit., pp. E84-E86. In addition, the following basic sources were used: John W. Cell. Analytic Geometry. New York: John Wiley & Sons, Inc., 1951; Joseph B. Rosenboch, Edwin A. Whitman, and David Moskovitz. Plane and Spherical Trigonometry. New York: Ginn and CO. , 1951. 4Cell, ibid., p. 3. 68 CHART VIII CARTESIAN COORDINATES Y III IV CHART IX LOCATION OF A POINT IN THE POSITIVE PLANE OF CARTESIAN COORDINATES Y Abscissa Y A l Ordinate O X 69 The ordinate is found by measuring its distance from the X axis, parallel to the Y axis. The X coordinate Of a point is referred to as its abscissa. This is the distance from the vertical Y axis, measured parallel to the X axis. Taken together, the abscissa and ordinate form the coordinates Of a given point with the abscissa being given first. Chart IX illustrates the abscissa and ordinate Of point A in the positive quadrant. In Chart IX, the distance OX equals the abscissa Of point A, and the distance OY equals the ordinate. Assuming the values Of 30 miles for X1 and 40 miles for Y1, the coordinates Of point A would be read as A (30, 40). Utilizing this basic system Of orientation, it is possible to Simulate the geographic market area in which the distribution center is to be located. All retail stores are plotted in the Cartesian plane. Each store is identified by a subscript and placed into the simulated market with reference to its coordinates. In other words, retail stores are plotted with reference tO their abscissa and ordinate, measured in a uniform mileage scale. The algebraic method for solving the location problem identifies the coordinate position Of the proposed distribution center. The problem is essentially a weighted average Of a given number Of independent variables, with the dependent variable being the warehouse location. Thus, the algebraic process solves for the abscissa and ordinate Of the warehouse. Consequently, it is necessary to solve independently for the X and Y coordinate locations Of the warehouse. The formula expressing this calculation depends upon the independent variables under consideration 7.0 which are expressed in the location measure employed. Therefore, the exact formulations will be presented in the following section, which deals with location measures. The adoption of a Cartesian coordinate reference system does not imply that this is the only mathematical method available for attacking the location problem. At least two other currently published methods are worthy Of comment: (1) linear programming and (2) the grid-coordinate method. In recent years, Vthe terms linear programming, location and distribution have become almost synonymous. When one Speaks Of a location problem, it is Often assumed that linear programming Offers the most efficient method Of determining an optimum location solution. However, it is interesting to note, in current textbooks, 5 the general lack Of models to attack the market area location problem. Rather, given a series Of locations, one finds models for optimizing equipment utilization or minimizing other Objective functions. For example, the transportation model provides a comparatively Simple method for deter- mining which warehouse should supply which customer during the shipping period. Disregarding the multiple warehouse aspect, one prerequisite 5See: Robert Dorfman, Paul A. Samuelson, and Robert M. Solow. Linear Programming and Economic Analysis. New York: McGraw-Hill Book Co. ,1958; or Dakota Ulrich Greenwald. Linear Programming. New York: Ronald Press Co. , 1957; or Nyles V. Reinfeld and William R. Vogel, Mathematical Programming. Englewood Cliffs, N. J. : Prentice Hall, Inc. 1958. 6Reinfeld, ibid., Ch. 111. 71 for programming this problem is the predetermined location of each warehouse point--precisely the dependent variable in the current research. It is possible to determine the market area solution utilizing a modified version Of the transportation or distribution model. This requires an assumption Of an array Of warehouse locations, with the least-cost location among that array being isolated. However, a possibility of error is involved in the selection Of an array Of alternative locations. The true least-cost location could fall well outside the initial range Of location alternatives. 7 The analytic geometry method Of Cartesian coordinates does not involve the same difficulty since the procedure for determining the location solution initially includes all potential alternatives. \xThe grid-coordinate approach tO the market area location solution represents a modified Cartesian coordinate system. 8 Working in the positive quadrant, the plane is expressed in areas referred to as grids. Location data are quantified by grids, and the algebraic solution isolates the best grid, depending upon the variables under consideration. —The grid method is particularly adaptable when it is impossible tO isolate 7However, Greenwald Offers a technique using the Simplex Algorithun, which appears adaptable, although it is unduly complicated for the problem at hand. Greenwald, op. cit., pp. 9—12. 8Edward W. Smykay, "Formula To Check for a Plant Site, " Distribution Age, VOl. LVIII(January, 1959), pp. 32-34; for another modification using an analog computer, see; Edward L. Brink, "A Simplified Solution for the Location Of Marketing Outlets Using an Analog Computer, " Marketing's Role in Scientific Management. Chicago: American Marketing Association, 1957, pp. 468-75. 72 Specific delivery points and/or when common, rather than private, carriers are utilized. The procedure for quantifying data by areas simplifies the process. The basic limitation Of the grid method is the inclusion Of an averaging error for each grid. The inclusion Of this error is not necessary in the food distribution center location problem since the precise location Of each delivery point is known. While, undoubtedly, there are additional mathematical methods for selecting market area locations, these three appear to be most frequently found in the literature. It is not the Objective Of this research tO test alternative mathematical techniques. The Cartesian coordinate method is used in this research because Of its basic simplicity. MEASUREMENT DEVICE The measurement device represents a quantification Of primary data utilized as inputs for mathematically determining location solutions. The data contained in the measurement device represent independent variables. The resultant warehouse location is the dependent variable. The location problem is structured with identical service standards required from all distribution center locations. [Given this service standard, the location goal is to minimize distribution costs. Therefore, the Objective Of evaluating alternative measurement devices is accom- plished by Observing which measure isolates the lowest cost location. Generally, it is well accepted that private carrier trucking costs are a function of time, weight, and distance. However, historically, 73 when mathematical techniques were employed, not all of these cost factors were included as independent variables in the measurement device. In the current research, four measurement devices have been selected for analsis: (1) ton-center solution; (2) mile-center solution; (3) ton-mile center solution; and (4) time-ton-mile center solution. As the titles suggest, the first three contain combinations Of only those variables related to weight and distance. The fourth measurement device includes all three cost-influencing factors. The solution derived by utilizing this measure should render a superior location. Utilizing the Cartesian reference system and related algebraic formulations, the location problem is solved by employing all Of the measurement devices. The nature Of each measurement device and the appropriate algebraic formulation is discussed in this section. TON-CENTER SOLU TION The tOn-center solution mathematically achieves the same location Keefer Obtained with BB shot and cardboard. 9 The point located represents the center Of gravity or center Of movements in the market area. When Obtaining a ton-center solution, the assumption is that the center of movements represents the least-cost location. However, accepting cost as a function Of time, weight, and distance points out the basic limitation of this measurement device--on1y weight is given C)Keefer, op. cit. 74 consideration. Since the center-of—movements solution has been used, a computation of the ton-center location is completed for each model. All stores are plotted in the Cartesian plane and identified by subscripts. TO express tonnage requirements to each supermarket, annual tonnage is reduced to standard trailer units. The standard trailer employed is a 36-foot semi-van capable of handling 35, 000 pounds of dry grocery merchandise. Once each supermarket location is determined and the total trailers tO each are known, the warehouse location may be determined. The location solution is found by adding the products of store location and trailer frequency for each supermarket from the X coordinate and dividing by the total number Of trailers. The same process is repeated from the Y coordinate. The result is a location in terms Of X and Y for the distribution center. In total, the location solution indicates that point which provides the balance Of weight between stores for the given time period. This basic algebraic procedure is followed for all mathematically derived location solutions with appropriate modifications necessary to handle the inclusion of different variables. The algebraic formula for the ton-center computation is as follows: 75 Where: X. Y 2 unknown coordinate values Of the distribution center, xn, yn = supermarket locations designated by appropriate subscript, Fn 2 annual tonnage to each supermarket expressed as standard trailers identified by appropriate subscript. MILE - CENTER SOLUTION The mile-center solution isolates that geographical point which results in the least distance tO all delivery points. The assumption under- lying the solution is that delivery costs are a function Of mileage. Therefore, if mileage is minimized, a least-cost location is determined. The basic deficiency in the mile-center solution is the omission of tonnage and time considerations. Unlike the ton-center solution, the mile-center solution cannot be determined simply by solving for the weighted average along each coordinate. In order tO find the mile-center, it is necessary to differen- tiate each store location from an original warehouse location, thereby Obtaining a mileage value. This mileage value is determined by utilizing the general distance formula for finding the length Of a straight line connecting two points. The exact procedure for this measurement is developed below in the discussion Of formulation. Since the solution requires an initial X and Y value for the distribution center, the final solution is found by a trial-and-error pro- cedure. Starting with initial values for X and Y, each time a computatiaon 76 is completed, new values are generated for the distribution center in terms Of X and Y. The location problem is solved when the new values are equated to zero or within an acceptable tolerance Of the last previous values. For example, if the initial values Of X and Y are 30 and 40, respectively, the location solution is Obtained by utilizing these values to determine the new distribution center coordinates. Assuming that the new values Obtained are X = 36 and Y = 43, then the procedure has failed tO set the new values equal to the original values. Thus, additional computation is required. For the second computation, the most recent values, X = 36 and Y = 43, are employed. If the second computation results in the values Of X = 36 and Y = 43, then the location solution equates to zero, and the problem is completed. In all trial-and-error solutions calculated in this research, an acceptable tolerance Of I: one mile is established for the X and Y distribution center coordinates. This means that all solutions are correct within a four-mile square area. If through the trial-and-error procedure a value for X and Y within this tolerance is reached, the location is accepted as the center Of the four-mile square area. This results in a maximum location error Of one mile. The algebraic formula for determining the mile-center solution is as follow 5: Ms elm [V]: (LIFT H II H M5 Qa|,_, 71M: '5 HQ'H He 11 H 77 Where: X, Y 2 unknown coordinate values Of the distribution center, xn, yn = supermarket locations designated by appropriate subscript, dn : supermarket location differentiated in miles from the initial distribution center location and sequentially from each new location until the trial-and-error procedure is completed. The value for d expressing the distance from a distribution center location can be determined from direct measurement on the coordinate plane or by utilization Of the following distance formula: d =\/(x -X>Z+2 n n n Where: dn : mileage distance between store and distribution center designated by appropriate subscript, X, Y : given coordinates Of distribution center, Xn’ yn : supermarket location designated by appropriate subscript. Since the value Of d for all supermarkets changes each time a new set of distribution center coordinates is determined, the distance formula is utilized in each step of the trial-and-error procedure. TON-MILE CENTER SOLUTION The ton-mile center solution combines the variables Of weight and distance in selecting the distribution center location. The assumption 10Cell, op. cit., p. 6. 78 is that costs are a function Of ton-miles. The ton-mile solution is superior tO the mile-center solution since it takes frequency of delivery to each store into consideration in selecting the location. It is superior to the simple ton-center since the impact Of distance is taken into consideration. The solution once more calls for a trial—and error procedure since (1 is included in the formulation. The ton-mile center formulation is as follows: MD Hx CL HIT] 'Mb .5 {L H71 :1 1 :1 1 x = 1 Y = 1 n 5 n E Z a. Z a. 1:1 1 1:1 1 Where: X1, Y1 2 unknown coordinate values Of the distribution center, x , y : supermarket locations designated by appropriate subscript, n n F : annual tonnage to each supermarket expressed as standard n trailers identified by appropriate subscript, d : supermarket location differentiated in miles from the n initial distribution center location and sequentially from each new location until the trial-and-error procedure is completed. TIME TON-MILE CENTER SOLUTION The fourth location measurement device includes all cost- influencing variables. Since costs are a function Of time, weight, and distance, the distribution center location derived as a product Of this 79 device should represent a superior least-cost location. The procedure for selecting the time-ton-mile solution is trial-and-error Since both the time and distance factors are differentiated from a given distribution center location. The formulation is as follows: n n F F X Xi i Z yi 1 M- M ':1 1 .21. 1 x = .1—___ Y e 1 n F. n F X 1 Z 1 i=1 Mi i=1 M1 Where: X, Y = unknown coordinate values Of the distribution center, xn, yn = supermarket locations designated by appropriate subscript, Fn 2 annual tonnage to each supermarket expressed as standard trailers identified by appropriate subscript, M : supermarket location differentiated in terms Of miles per n minute from the initial distribution center location and sequentially from each new location until the trial-and- error procedure is completed. In order tO arrive at a value for M , it is necessary tO ascertain n both the distance and time to all supermarkets from the given distribution center location. The distance value is determined by use Of the basic distance formula. The time in minutes to each supermarket is found by calculating a time value from the coordinate plane. An estimate Of 80 delivery time must include number Of miles, type Of highway, and traffic. A general rule is that time per mile decreases as the number Of miles per Stop increases. 11 In order to account for these basic factors influencing driving time, zones representing different attainable movement rates are constructed in the simulated market area. These zones consist Of two basic types-—rural and urban. Movement rates accounting for the influence Of the above factors are adopted for each zone from a Department Of Agriculture publication. 12 This publication represents a study of eight wholesale grocery firms' trucking operations. The purpose Of the study was to develop methods for establishing time standards for dry grocery delivery in urban and rural areas. Two master estimation tables were developed which can be utilized for estimating delivery times between two points. For use in a distribution center location problem, the development of such estimating tables represents substantial savings in research cost. Utilizing these tables, total time necessary to transverse the distance between a given distribution center location and a supermarket can be rapidly estimated. This replaces the necessity of conducting expensive engineering time studies for each alternative distribution center location. The time zones and respective movement rates are presented in Table 1. 11 . 12 , Crossed, op. cit., p. 4. Ibid. 3Table l is adapted from Tables 2 and 4 Of the above-mentioned research of the Agriculture Department. Ibid., pp. 8 and 14. 81 Table 1 TIME ESTIMATION TABLE URBAN AREA RURAL AREA Distancein Minutes Distance in Minutes miles per mile miles per mile Under 1 8. 8 All rural 2. 2 1. 0 - l. 5 7. 0 1. 6 — 2. 0 4. 8 2 1 - 3. 0 4 0 3 1 - 4. 0 3 5 Over 4. 0 3. 4 Example: If a delivery trip consists Of 16 urban miles and 38 rural miles total time would be 138 minutes (16 x 3. 4) + (38 x 2. 2). In this location study, urban zones are identified as the geographic area of all cities with a population greater than 25, 000. All other areas are considered rural. Given the values of distance and time through rural and urban zones, M is calculated in the following manner: n (1 Where: Z attainable miles per minute to the appropriate supermarket from a given distribution center location, 2 _ 2 \flx -X) + n n I1 total time to store in minutes. CL ll fl II 82 LOCATION MODELS Location models utilized in the research provide a method for classifying primary data. The location models represent geographic retail market areas commonly found in the supermarket industry. In this particular industry, three geographic market patterns may be simulated. These patterns are representative Of normal spatial relationships between retail outlets served from a single distribution point: (1) spatially concentrated; (2) spatially dispersed--proportionally distributed; and (3) spatially dispersed--non-proportionally distributed. CHART X GEOGRAPHIC RETAIL MARKET AREA MODELS=z= MODEL A MODEL B Spatially Concentrated Spatially Dispersed-- Proportionally Distributed MODEL C Spatially Disper sed— -Non-proportionally Distributed i. ”Supermarket locations are illustrated by points within the enclosed areas which represent geographic retail market areas. 83 A system of stores spatially concentrated is represented in Model A, Chart X. The essential characteristics of this model are the close geographical relationships Of all supermarkets and the relatively small total mileage included in the total market area. A system Of spatially dispersed supermarkets proportionally distributed within the geographic retail market area is simulated in Model B, Chart X. The fundamental difference between Models A and B is the larger geographic market area in Model B. The supermarkets are located in a uniform frequency within the market area of each model. Model C is differentiated from Model A by an increased geographic area and from Model B in terms Of store distribution. Rather than supermarkets occurring in a proportional distribution, they appear in uneven frequencies giving rise tO an irregular market area. The market area simulated in Model C represents only one Of an infinite number Of potential combinations. Simulation Of these three models provides a framework for location testing. Model A is not tested because Of the unique nature Of its market area. Retail fOOd chains having supermarkets Spatially concentrated are commonly found in large metropolitan areas. In such concentrated areas, the distribution center location is dictated by a unique set Of require- ments dissimilar tO those experienced in the other models. The small geographic area under consideration will, at any given time, have only - . 14 a limited number Of location sites available for construction. 14For example, Jewel Tea Company had less than five Sites which could be economically purchased for their Melrose Park distribution center to service the greater Chicago market. 84 Therefore, under these circumstances, the most efficient procedure is to identify sites having the necessary characteristics and then to select the one which provides the least—cost location. The reason for con- structing Model A in the current research is that theoretical insights are Obtained in contrast to Models B and C. The fundamental purpose Of simulating retail market patterns is to achieve a method for generalizing the research findings beyond the limitations of a case—study approach. In the experiment, operating information from two retail food chains is used. These operating statistics are referred to as primary data. They represent supermarket locations and annual tonnages shipped to each. One chain under study has the physical characteristics simulated in Model B and the other represents a case of non-proportional distribution simulated in Model C. By contrasting the various mathematical and non-mathematical location solutions for each model, insights concerning the impact Of geographic market area upon distribution center location, are gained. Alternative locations are evaluated by comparing distribution costs Obtained via the transportation co st model. TRANSPORTATION COST MODEL The transportation cost model represents a vital element in the research design. Given various distribution center locations, a standard cost model is utilized to determine total cost Of distributing tonnages to supermarkets from each location. Alternative distribution center 85 locations are evaluated by comparing total distribution costs. Therefore, the transportation cost model provides the basic framework in analyzing research results. The fundamental problem is to develop a structure which will reflect the impact of various cost determinants in an unbiased manner. This requires: (1) An elaboration Of underlying assumptions which establish the cost model; (2) the identification and classification Of cost accounts into functional categories; (3) the assignment of dollar values to each account; and (4) the development Of a standard procedure for estimating distribution costs from alternative locations. These several functions are explored in this section. MODEL ASSUMPTIONS To develop a standard model, certain underlying assumptions are established. These assumptions structure the framework within which each location is assigned a total distribution cost. Depending upon the operating policies of a specific firm, these assumptions may require modification tO fit local Specifications. However, in all cases an attempt has been made to simulate operating conditions commonly confronted by retail food chains. The following assumptions are employed: 1. A movement unit consists Of a standard tractor and trailer. 2. The maximum utilization time Of a movement unit is estab- lished at twelve hours per working day. The remainingtwelve hours Of the day are reserved for the delivery Of other than dry groceries, preventative maintenance, overhaul, and warehouse loading. 86 3. Maximum movement days in a calendar year are established as 240. Remaining days are lost tO weekends and holidays. 4. Normal driver work time is established as eight hours per day, 220 days Of the year. In addition, each driver is limited to two hours Of overtime on any normal work day. 5. Driver's paid-days are established as 240 days per year. The difference between work days and paid-days is allocated to holidays, vacation, and sick leave. 6. All movement units are scheduled direct to a given supermarket and returned to the given distribution center location under outbound truck-load specifications. 7. Two hours are allocated for unloading time at each supermarket. COST CATEGORIES AND ACCOUNTS The second step in developing a cost model is to identify and classify cost accounts into categories. The total cost Of distribution from a potential location is defined as the sum Of fixed and variable costs. Fixed Costs Fixed costs are defined as costs incurred in operating a trucking fleet independent Of the number Of over-the-road miles and the time Of equipment utilization. Fixed costs are divided into the categories Of basic and Overhead cost. Basic costs are defined as costs associated with the ownership of a movement unit. Given the number Of movement units, basic costs are 87 fixed; however, the magnitude of such costs varies in equal increments as the number Of units increases or decreases. The following cost accounts are classified in the category of basic costs: (1) operating fees; (2) insurance; (3) depreciation; and (4) interest cost Of capital. Overhead costs are defined as those costs associated with the supporting facilities Of a private fleet. Similar to basic costs, given the number of movement units, overhead costs are fixed, varying in magnitude as the number of movement units increases or decreases. Unlike basic costs, the amount Of overhead costs do not vary in direct proportion to the number Of movement units. This is due to the occurrence Of scale economies as the number Of movement units increases. The following cost accounts are classified in the category of overhead costs; (1) garage expense, and (2) supervision and administrative expense. Variable Costs Variable costs are defined as charges against the movement unit On a line haul basis. Included are all cost accounts which experience variable magnitude as a function Of miles and time which movement units are operated. Variable costs are distinguished from fixed costs by the fact that they increase in direct proportions with the utilization Of movement units. NO appreciable scale economies are represented in the rate Of normal variable cost assessment since the scale Of such costs is predicated on the attainment of the maximum potential Of sixteen 88 utilization hours per working day. 15 Variable costs are divided into the categories of distance, time, and overtime cost. Distance costs are those costs which are associated with the per— mile operation of a movement unit. Given the aggregate miles generated during the time period, such costs are assigned on the basis of a ,‘ standard cost per mile. The following cost accounts are classified under the category of distance costs: (1) fuel and oil; (2) tires and tubes; and (3) maintenance repairs. Time costs are defined as costs based upon the number Of hours a movement unit is Operated during the designated time period. Given the aggregate hours of Operation, time costs are assigned on the basis of a standard cost per hour. Time costs consist of one account--drivers' wages, which include base rates and fringe benefits. Overtime cost represents a special type of variable cost which occurs from the Operation Of movement units in excess of the normal eight-hour driver work day. When overtime hours are experienced, a premium cost per hour is assigned to cover the expense of such Operation. ASSIGNMENT OF COST ACCOUNT VALUES The third step in constructing a transportation cost model is to assign dollar values to each cost account. Account values, once assigned, are held in constant relationship. Consequently, the influence of various 15 . . . This represents a standard procedure among distribution researchers due to the small magnitude of dollar change resulting from the laborious process Of setting up diminishing unit cost schedules. 89 cost determinants at each location are directly reflected in dollar amounts. While an attempt has been made to approximate actual costs experienced in operating a private transportation fleet, absolute values assigned to accounts are not Of fundamental importance provided the following three conditions are satisfied: (1) the cost model allows each account to fully reflect the dependent relationship of that account to inputs; (2) the accounts are held in constant relationship without variation in basic values as the model is employed to estimate total distribution costs for various locations; and (3) the values assigned to accounts represent the relative relationship of values which are . . . 16 experienced in actual fleet Operation. Basic Fixed Costs The assignment of basic fixed cost values represents the most discreet of the cost accounts. Since basic fixed costs are a function of the number Of movement units, the process is simply one Of determining the costs associated with one movement unit for each account. The values most easily assigned are those related to the accounts Of Operating fees and insurance. Operating fees contain the following expenses: 16 The account valuations used in the cost model are adopted from the following: ”Improving the Truck Delivery Operations Of a Wholesale Grocer, " Marketing Research Report NO. 127, Department of Agriculture, Washington, June, 1956; Crossed, Op. cit. ; Explanation of the Develop- ment Of Motor Carrier Costs with Statement as to Their Meaning and Significance, op. cit. ; California Case NO. 5432, op. cit. ; plus inter- views with consultants from A. T. Kearney 8: Company and Booz, Allen, and Hamilton. 90 (1) registration fee; (2) weight fee; (3) license fee; and (4) highway use tax, all of which are based upon state laws. For the standard movement unit employed in the research, these are established at 700 dollars per unit. The unit insurance rate is established as 1, 000 dollars per move- ment unit. Each cost account is expressed as a yearly rate. / Depreciation represents a somewhat more difficult value to assign since a number Of different methods Of depreciation are currently used ‘ depending upon accounting procedure and managerial preference. The present procedure is to use a method of straight line depreciation . based upon purchase price and a fixed equipment life span. Movement units are depreciated to a resale value established as 25 per cent of purchase price. TO determine the annual depreciation, the purchase price less resale value is divided by the expected life span. The standard movement unit utilized in this research has a combined purchase price of 16, 000 dollars for both the tractor and trailer. The life span is estimated at six years. Therefore, the annual depreciation is established as 2,000 dollars per movement unit. The fourth account included in the category of basic fixed cost is interest on capital invested in movement equipment. While investment 17 . . . . . Two baSIC methods Of depreCIation are used in private truck Operations. The first method is based upon distance and is used in high mileage Operations. The other method, with many variations, is based upon time utilization of equipment. For a complete discussion, see: "Truck Delivery Operations of a Wholesale Grocer, " op. cit. , pp. 30- 32; or Cost Record Book, White Motor Company, Form AD-425, B—8- 58-5M, p. l. 91 is not always included as an expense item, the basic fact remains that monies are invested which could be employed in alternative uses. This type Of expense becomes increasingly important depending upon the amount of external financing required by the firm. Given the fact that interest on capital invested is a legitimate expense, the problem of establishing an appropriate rate still remains. Similar to methods of depreciation, several different rates have been suggested. 18 For purposes of simplicity, a rate of six per cent per annum is employed in the standard cost model. Capital invested is assumed to be the full cost of each movement unit. Accordingly, the annual investment expense is estab— lished at six per cent of 16,000 dollars or 960 dollars per movement unit. Overhead Fixed Costs Overhead fixed costs, unlike basic fixed costs, cannot be assigned in equal increments to each movement unit in the fleet. While the magnitude of overhead fixed cost increases as the size of fleet increases, due to scale economies, the incremental addition to total costs has a decreasing dollar value. Garage expense includes all labor and supplies for lubrication, Wa shing, etc. Supervision and administrative expense includes the cost 8For example, at a recent conference on Physical Distribution held at Michigan State University, executives stated that their firms used a cost—Of—capital percentage which ranged from a low of four per Cent to a high of 33 per cent. Also, see: "Improving the Truck Delivery OPe rations of a Wholesale Grocer, " Op. cit., pp. 35-36. 92 of dispatching, record keeping, etc. To illustrate the occurrence of scale economies, consider the following example of garage labor. If one man can service a movement unit each Of the five days of the week, it follows that he is capable of servicing five movement units a week. A total cost curve illustrating service labor expense would contain a step function occurring each time the movement fleet is increased by five units. However, between unit one and unit five, the labor costs pro—rated across the movement units in the fleet would indicate a decreasing per-unit cost curve. Cost schedules are simulated for each account in order to reflect the occurrence of scale economies. Schedule A, Table 2, represents garage cost. The value to be assigned a given fleet is based upon the number of movement units and is read directly from the schedule. The same procedure is employed in obtaining the appropriate value for super— visory and administrative cost which is represented by Schedule B, Table 2. 93 Table 2 ANNUAL TOTAL OVERHEAD FIXED COST SCHEDULES SCHEDULE A SCHEDULE B Annual garage Number of Annual supervisory expense movement units and administrative expense $ 5, 000 l - 5 $ 2, 500 9. 500 6 - 10 4, 800 13,500 11 - 15 6,900 17, 000 16 — 20 8, 800 20, 000 21 - 25 10, 500 22, 500 26 - 30 12,000 24,500 31 - 35 13, 300 26, 000 36 - 40 14, 400 27, 000 41 — 45 15, 300 27. 500 46 - 50 16,000 Distance Variable Costs Distance variable costs represent the per—mile expense incurred by the operation Of movement equipment. In assigning values, the impact of a decreasing per-mile cost function is not considered, assuming rather a constant per—mile assessment. Distant variable costs must be assigned for both the tractor and trailer components of the movement unit. Table 3 illustrates the values assigned to each account for both components. 94 Table 3 BREAKDOWN OF VARIABLE DISTANCE COST VALUES “2:135:23? T222131:- Fuel Cost per gallon $0. 248 ---------- Miles per gallon 3. 8 ---------- Cost per mile $0.065 ----- $0. 065 Oil 0. 003 ----- 0. 003 Tires and tubes 0.010 0.009 0. 019 Maintenance & repairs 0. 050 0. 010 0. 060 Total $0. 128 $0. 019 $0. 147 Time Variable Costs Time variable costs contain only one account—-drivers' wages and fringe benefits. In a common carrier operation, the assignment of time variable cost represents a complicated problem Since driver wages can vary depending upon time, mileage, and tonnage. In a private fleet Operation, the problem is simplified Since drivers are normally employed by the firm on an hourly basis. Therefore, for purposes of arriving at an hourly cost, it is necessary tO determine only a base rate and tO assign an increase to cover the cost Of fringe benefits. Fringe benefits are defined as the expenses occurred from: (1) compensation insurance, 95 (2) payroll charges, and (3) health, welfare, and pension costs. To determine the per-hour value to be assigned, a base rate of 3. 50 dollars is utilized, and fringe expenses are assumed tO represent 33 1/3 per cent of base rate. Accordingly, total expense assigned to drivers' wages and fringe benefits is 4. 67 dollars per hour during the normal work day. Overtime Variable Costs The assignment of values to overtime cost requires an adjustment in normal per—hour variable expense to cover the expense of working drivers' overtime. This adjustment is relatively simple since the usual charge for overtime labor is time and one—half or a 50 per cent increase in base pay. Therefore, the premium cost for overtime driver expense is established at 1. 75 dollars per hour or 50 per cent of driver's base rate. Account Valuations Summarized The completed cost model, including cost categories and valuations, is presented in Table 4. It is by application of this model that cost estimates are made for each potential distribution center location. Table 4 96 CLASSIFICATION AND VALUE OF COST ACCOUNTS Account Expense Fixed Costs Basic fixed costs Operating fees Insurance Depreciation Interest cost of capital Overhead fixed costs Garage Supervisory and administrative Variable Costs Distance costs Fuel Oil Tires and tubes Maintenance and repairs Time costs Driver wages and fringe benefits Overtime costs Driver wages $700. 00/ unit/ year $1, 000. 00/unit/ year $2, 000. 00/ unit/ year $960. 00/ unit/ year Table ,3, Schedule A Table 33/, Schedule B $0. 065/ mile $0. 003/ mile $0.019/mi1e $0. 060/ mile $4. 67/ hour $6. 42/ hour 97 COSTING PROCEDURE The final step in developing a cost is to establish a procedure for determining total costs of distribution from a proposed location. This procedure consists of three steps: (1) development of a location data table; (2) qualification Of secondary data; and (3) quantification of cost. LOCATION DATA TABLE In order to quantify the magnitude of cost determinants, the procedure is to first develop a data table for the distribution center location under consideration. Table 5 illustrates a location data table partially loaded with assumed data. All supermarkets (column one) and the number of deliveries in standard trailers (column two) are listed in the table. Next, the mileage (column three) and delivery time in minutes (column four) from the distribution center to each store and return is placed into the table. The mileage and delivery time values are read from the coordinate plane by use Of a time and distance scale. Prior to entry, the delivery time and distance values are multipled by , 1 two in order tO arrive at roundtrip values. 19One implicit limitation Of the locations selected by experimentation is the fact that they are based upon air miles rather than road miles. Some consulting firms utilize road—air mileage adjustment ratios in order to arrive at more accurate cost estimates. This procedure could have been employed in this research, and the cost estimates would have been uniformly adjusted upward. However, this would have no influence upon locations selected and would only increase all cost estimates by a constant multiplier; consequently, the procedure is rejected as ancillary. 8 9 mwm .m X X X oow d». X X N 33309 «mo ooo Om 000 AN 000 .mm 0mm .mH com on mnfi mo oar 036m 03.3 26.3 oS.w Sm om am we New 3:. .5 cum .: own .3 omo .N os om 8; mo New com .3 3% «N com om owo .w 02 S. mom No Nam omoém omm.: oowdfi oom .m owH do 0: Ho Apopcdoi moudcag moadcficu mondsficc owmoig woodcut ommofig moio>flop Deviance mhdos . wcfipdofia annex/Sop . 63.3 QTS. Hoses/w HMSCQ< fiddccafl t .H 09.6 Massages Hedccafl Hoses/w I pedom . padom Himmjwh. long—rangejflanning,the bashztechniquesrnay'be used as an aid in daily decision making. For example, it may not be possible to purchase a distribution warehouse Site at the exact point indicated by the time-ton-mile solution. Each alternative site may be evaluated by simply estimating distribution cost through the transpor- tation model. These distribution cost estimates can then be compared vdth purchase pricein order Miselectthe best n mothe desired location as indicated by the time-ton-mile solution. This additional application may be conjoined with a static analysis or with the long-run comparative static analysis, the basic difference being simply the time point. 145 Thus, with imagination, the basic location tools presented in this research may be adapted to either long-range planning or day-to-day decision making. The research contributes both theoretical and analytical guides to these basic management problems. SUGGESTION AREAS FOR ADDITIONAL INVESTIGATION Scientifically, it is only proper that any research project should culminate in a series Of suggestions to guide continued investigation in the problem area. Many of the suggestions which follow stem from the limitations outlined at the inception Of this research. Others evolve from the research findings and problems encountered during experimentation. Several operational practices Of supermarket chains were omitted from the static experimentation in order to concentrate upon the problems under analysis. For example, chains commonly load trailers with orders from a number of small supermarkets and deliver to all in one trip. It is also a common practice to drop trailers at supermarkets located near the distribution warehouse. Many firms emphasize the cost—reducing practice of picking up merchandise from suppliers, thereby gaining transport economies of back haul. All these practices were eliminated from consideration by the basic assumptions of the research. The basic form Of analysis should be extended to include such variables. Several different methods Of accounting for the cost influence of such practices should be developed and tested. 146 The inability of the time-ton-mile formulation to select a location with substantial cost savings over other locations suggests continued evaluation. This research included all cost determinants formulated with time-ton-miles in the exact proportion represented in the primary data. The result was a slightly superior solution. It is suggested that experimentation be undertaken with alternative methods for weighting these cost determinants in proportion to their impact upon distribution cost. Determining appropriate weights would require continued analysis of the distribution cost structure. The Cartesian coordinate approach is based upon determining weighted averages along the locational axes and, therefore, theoretically justifies continued exper- imentation along these lines. The long-range planning applications suggested in the previous section provide other apparently fruitful areas of continued research. If one has a basic belief in the Spatial approach to studying business systems, the rewards Of combining substitution and simulation as a form of comparative static analysis appear unlimited. The current research was limited to the supermarket industry in which inbound movements were eliminated due to their limited importance to the food distribution center location problem. This analysis may be expanded to include other industries and to account for their special problems, which might include inbound movements. 147 In the completed research, the basic techniques were limited to one mathematical and one non-mathematical. The problem was not to test the competence of different techniques but, rather, to test different formulations of location measures. Developing and testing other mathematical techniques and location measures may well be an area of profitable research. Continued analysis of techniques and measures is fundamental to all research. A basic challenge to all business research today is to develop procedures for implementing theoretical insights. The abstract provides basic requirements for generally understanding the business environment. However, advancements in economic and social efficiency can evolve only from the development of rules and procedures for implementing these normative bench marks. 148 APPENDIX A COMPUTER FLOW CHARTS INTRODUCTION Consideration was given to the use Of a high speed digital computer for determining the mathematically derived location solutions. Using an IBM 650 Magnetic Drum Computer, the total problem would have required two custom programs with a considerable number of branch operations. One Of the two custom programs required a design for a trial-and-error procedure. This trial-and-error program necessitated four branch operations. The first was necessary to figure square roots required for calculating the distance between two points in the problem. The other three sub-routines modified the program for handling the various formulations. The first step in considering the use Of the digital computer was to complete flow charts for each of the basic programs. Based upon these charts, the following decisions were made: (1) to eliminate the computer for the basically simple non-trial-and-error program; (2) to initiate and test detailed programming of the trial-and-error pro- cedure; and (3) to investigate the applicability of a desk analog computer to solving the trial-and-error solutions. Detailed programming was completed for the trial-and-error procedure; however, considerable difficulty was encountered during 149 the test runs. These testing sessions on the IBM 650 computer showed that a considerable amount of rework would be required to render the program operational. On the other hand, the results of the investigation with the analog computer indicated that the problem was very manageable with manual calculation. Distance would be read directly off the coordinate plane, thereby eliminating the need to calculate square root. Additionally, several multiplications common to the various formulations considerably reduced the required calculations. Thus, comparing the quantity of additional programming required to the magnitude Of the problem, the decision was made to use the analog rather than the digital computer. In cases where the supermarkets tO be served by the distribution center are considerably larger and where excess computer capacity is available, the use Of a digital computer could result in a savings of total time. In anticipation Of this, the following flow diagrams con- taining the logic of the program are presented. FLOW DIAGRAMS PROCEDURE 1. X and Y values for all stores are read into the computer from cards and stored in successive locations. 2. Entering the starting values of X and Y prior to starting calcu- lation for d, the factor "d" is computed for each supermarket; 150 and that value is retained along with the stores' X and Y values. Each solution must be given a value, i. e. , 1, 2, 3. This enables the computer to decide which branch Of the programmed solutions to use. The program is designed to punch the X and Y values of a dis- tribution center location which is within 1. 0 of the previous location. Slight modifications will allow the programmer to punch (print) each X and Y value as it is calculated. In the solutions programmed, the following values are used: A. X : Position with respect to the horizontal axis. B. Y : Position with respect to the vertical axis. C. d : Distance in miles. D. F : Number of trailers. E. M : Miles per minute. F. Xn— Yn : Newest value, or initial value, developed for X - Y in the trial-and-error solution. G. X - Y : Previous value developed for X - Y in the trial— P P and-error solution. CHART XVI 151 CENTER OF TONS DIAGRAM thief: mmhg m/uef £160)” X and y 7600/ 77L x y value; for 72/1 ftoref \ anfL = ——+ M = r Save 1 '- £5ng 5 fave 4 ”Peat F - ' {fave 2 all 7n n - = {3ng; Java 2 27:735— av: (' j (I I5; = mi Jar/e } [p , I“!!! 4, fave 5 STORES A @“QOMPLETE? j x YE: CHART XVII 152 TRIAL AND ERROR DIAGRAM truer; J‘Zar/ mg 124/arr or x reaci/ I?» x 412% 7 value; {or all rtori/r I Cam t6 (36,, (0:) = <7 A @fy/Z: B (j, I:+.B : C {Pr/peat fir J! All JWar C ,_. 47’; It ,. -—@ YES 153 I kit/(0r 501mm A/a Q! U / C @ . than? ) - m —@——m —-®-—N +— x) t 1.3 g @ .- 2745; - k .t'me brie/”IQ ¥ ij ’ Jalutt'on/ ) r © C1 4—@.._j 9 IVIILE CENTER SOLUTION ROUTINE 154 " I ——>CP.Z;‘75; @U—e? IA > .292 +4]? = Ran/a9 .XF 51072.2(}, £77 fflVe 11 wit/1 Jr fat/,9 4 7%me fir 1",, .—' dry = Hat 1,, FEM/me out ”77 fly/2f fay/a 2 @ firm, #6— m/a/fm, for flunr/ P x /I II 1 -:- at, = l /( L. Jam 5 a 775,0 [[6 7 , " J T?” g 7 I ... (f) 650' >{mi/z 94, _@ @m (amp/£225 l j fforr 7,, zrz @ MW 5 g V 1’ [Java] _ 3122:7070: “$3, g (anti/mu; f0 <:>—‘* z raw} ‘ 7 7 next 11‘er I ’97 Quit/OI? [84. l ' Hm .29, I J, —>—< 53m >>.-—) .2?me 2 : flex/w! ‘2 @ X Jab)? 5 ,_>..' @ 7n PUNC H ‘ 563V? 4 , Jaw 5 \/ TONHWLE SOLUTION ROUTINE 155 Rqardfflr d// .rfarri‘ 9K. V 3 @fi’f (amp/m3 I O ‘ I CE) TIA/IE TON-MILE SOLUTION ROUTINE I > ONJ 015 z’merf t fir 9‘71 n all raj/tr from/M 172 Jaw 6 Rrpmf 0r 4 / ifmv 156 157 APPENDIX B LOCATION LITERATURE REVIEW Current business and economic literature contains a limited number of contributions concerned with theory and practice of location strategy. The contributions available fall into three categories: industrial, retail, and wholesale location. The majority of these writings are concerned with industrial plant and retail store location with little available concerning wholesale location. The current point of interest is the maturity of writings concerned with each dimension Of location. Specifically, have theories concerning these several location dimensions evolved? If so, to what degree are they refined? From the perspective Of this research, the more holistic question--how do such theories explain the logic of distribution center location ?--is directly attacked in the main body Of Chapter 11, ”Distribution Center Location Theory and Strategy. " This appendix provides a broader foundation for that discussion. To accomplish this, a selected number Of contri- butions are reviewed. INDUSTRIAL PLANT LOCATION LITERATURE The origin Of modern plant location literature is traced to the early contributions Of the German classical school of economics. To 1 2 this writer's knowledge, the works of Newman, Isard, and 1Philip C. Newman. The Development Of Economic Thought. New York: Prentice Hall, 1952. 158 Greenhut3 include the best current reviews of the over-all development Of plant location literature. Newman points out the neglect of English- speaking countries to include a theory of space as a vital part of economic analysis. He concludes that this vacuum results, in part, from the adoption of Ricardo's differential rent theory as opposed to von Thunen's location theory. Von Thunen's theory Of agricultural location, published in 1826, can safely be denoted as the first abstract theory Of location. Von Thunen's contribution influenced the work of another more famous German, Alfred Weber. 5 Weber's work, which appeared in German in 1909, is generally credited as the first attempt to construct a general theory Of industrial location. Working from a model of pure competition, Weber pointed out many forces influential in plant location. He saw the location problem as basically one Of selecting the least-cost location. The primary deficiency of his work, however, is the general neglect Of demand and competition. Still, Weber’s work is the forerunner Of modern location theories. His classification Of locations and discussion Of agglomerative forces still permeate location literature. 2 Walter Isard. Location and Space Economy. New York: John Wiley 8: Sons, 1956. 3Melvin L. Greenhut. Plant Location. Chapel Hill: University Of North Carolina Press, 1956. 4Johann Heinrich von Thiinen. Der isolierte Staat in Beziehung auf Landwirtschaft und NationalOkonomic. Hamburg, 1826. 5Carl J. Friedrich. Alfred Weber's Theory Of the Locations Of Industry. Chicago: University Of Chicago Press, 1929. 159 Some additional attempts to fit location into general economic . . ,. . 6 analySIS were made by German writers, Predohl in 1928 and Palander , 7 in 1935. However, the most successful attempt was completed by .. . 8 .. . Losch in 1940. Losch developed an abstract theory of location which applied to conditions of imperfect competition. In his famed work, he developed demand cones and hexagonal market patterns. This work is reviewed in more detail in the body of Chapter II. It is safe to generalize that, while the last of the main stream of German writers, LOsch was the most influential in molding contemporary location theory. His discussions of industry concentration and the over-all inclusion Of demand intensity rendered his work outstanding. The earliest significant American contribution was completed by Holmes in 1930. 9 Holmes presented one of the first attempts at describing the process for selecting individual plant locations. His work remains representative Of modern works concerned with location procedure. 6Andreas PredOhl, "The Theory Of Location in Its Relation to General Economics, " Journal Of Political Economy, Vol. XXXVI (June, 1928), pp. 371-89. 7Tord Palander. Bertrage Zur Slandortstheorie. Uppsala, 1935. 8August LOSch. The Economics Of Location. New Haven: Yale University Press, 1954. C)Gerald E. Holmes. Plant Location. New York: McGraw-Hill Book CO., 1930. 160 During the late twenties, and sporadically until the early forties, a number of theoretical arguments appeared in the literature. Building upon the models of Cournat and Edgeworth, the optimum location of firms engaged in duopolistic competition was subjected to considerable . . . . . 1 debate. The primary contributors to these discus Sions were Hotelling, , 11 . . 12 _ . Lerner-Singer, and Smithies. These articles presented the first attempts among American economists to study location strategy. . . . . . 13 These contributions, coupled With Chamberlin's classmal work, clearly emphasized the importance Of location strategy under conditions Of imperfect competition. Relevant insights into the concept of spatial monopoly evolve from these works. Hoover's earliest contribution to location analysis, 1937, was among the first Of many empirical studies found in American literature. In these studies, forces leading to the concentration of industries in specific geographic areas were examined. Hoover, in his more famous OHarold Hotelling, "Stability in Competition, " Economic Journal Vol. XXXIX (1929), pp. 41-57.» 11A. P. Lerner and H. W. Singer, "Some Notes on Duopoly and Spatial Competition, " Journal Of Political Economy, Vol. XLV (1937), p. 145. 2 . . . . . . Arthur Smithies, "Optimum Location in Spatial Competition, " Journal of Political Economy, Vol. XLIX (1941), pp. 423-39. 3Edward H. Chamberlin. The Theory of Monopolistic Competition. Cambridge: Harvard University Press, 1956 (Original, 1933). l4Edgar M. Hoover. Location Theory and the Shoe and Leather Industry. Cambridge: Harvard University Press, 1937; and Edward H. Cotterhill. Industrial Plant Location, Its Application to Zinc Smelting. St. Louis: American Zinc, Lead and Smelting Co. , 19 50; and Joe Summers Floyd. Effects of Taxation on Industrial Location. Chapel Hill: University of North Carolina Press, 1952. 161 15 . . . work of 1948, was the first American attempting to develop a general theory of economic location. His ambitious task was to formulate principles governing the interrelation of plant locations, the signifi— cance of location change, and the legitimate scope of public planning and control. Hoover did much to overcome the Anglo—Saxon bias by including a theory of location as part of general economic analysis; however, his major contribution was to modernize the works of Weber, et a1. , but with little modification to the locational force of market demand. The outstanding American contributions to location theory . 16 17 appeared in 1956. Isard and Greenhut greatly expanded and refined plant location theory. Greenhut presented a location theory based upon deductive investigation of plant location literature and empirical study of eight industrial firms. In his theory, he included demand influence and personal preferences in the process of site selection. In addition to this major contribution, Greenhut authored, among others, an interesting . . . l8 rev1ew of plant location theories. 15Edgar M. Hoover. Location of Economic Activity. New York: McGraw—Hill, 1948. l élsard, op. cit. l 7.Greenhut, op. cit. 8Melvin L. Greenhut, "Integrating the Leading Theories of Plant Location, ” Southern Economic Journal, Vol. XVIII (April, 1952), pp. 526— 38. 162 In Isard's 1956 contribution, he reviewed and snythesized early location literature in an effort to develop a general space economy, which he described as a hierarchy of location points and transportation and communication routes. He drew heavily upon the substitution approach to location analysis suggested by Predohl and attempted to lay the foundations for a general model of the economy. In other works. Isard expanded the use of input-output analysis as a method of building a space economy model. Some of Isard's additional contributions appeared in 1949,19 1955, 20 and 1960. 21 With the appearance of Isard's and Greenhut's works in 1956, location literature was divided into those concerned with general macro—economic analysis and those concerned with micro-economic analysis. The former focused upon the explanation of general location forces influencing the concentration and dispersion of industries, while the latter placed more emphasis upon the firm's use of location strategy under conditions of imperfect competition. l c)Walter Isard, "The General Theory of Location and Space Economy, ” Quarterly Journal of Economics, Vol. XLIII.(November, 1949), pp. 476—506. ZOWalter Isard, “Interregional and Regional Input-Output Analysis: A Model of a Space Economy, " Review of Economics and Statistics, Vol. XXXIII, pp. 318—20. ZIWalter Isard, et al. , Methods of Regional Analysis. New York: John Wiley and Sons, 1960. 163 A third location work by Yaseen truly labeled 1956 as the golden year of American location contributions. 22 Yaseen's work, based upon his consulting experience, was devoted to location procedure. Yaseen approached the problem of site selection in a manner similar to Holmes. Prior to Yaseen's major work, Atkins had kept procedural . . . . . 23 interest alive With an excellent article in the Harvard Business Review. Concerning a theory of plant location, it is concluded that these major works, together with several less prominent contributions, present a refined body of knowledge. To summarize, the contributions have taken three main lines of concern since early German contributions: (1) the development of a conceptual framework explaining general economic growth; (2) location strategy as a competitive weapon of a firm under conditions of imperfect competition; and (3) procedure for selecting a specific plant site. Continued development of theory, aimed at expanding knowledge of forces contributing to plant location, will provide executives with a conceptual framework of critical factors to be considered in selecting a new location. The primary inadequacy of this approach stems from a lack of practical relevancy. For example, the influence of consumer Leonard C. Yaseen. Plant Location. New York: American Research Council, 1956. 23Robert M. Atkins, "A Program for Locating the New Plants," Harvard Business Review, Vol. XXX (November-December, 1954), pp. 113-21. 164 demand is usually presented with assumptions of homogeneous products, uniform geographic disbursement of consumers, identical process costs, linear transport rates, general consumer product indifference, etc. The challenging frontier today is to extend this rigorous economic analysis to include a method of microscopic implementation. Greenhut, Isard, and Yaseen substantially bridged this gap. One of my earlier . . . . 24 works was aimed at partially achievmg that goal. New works currently being completed by Reifler and, also, Greenhut, Smykay, . . . . 25 _ and Bowersox jOintly promise to offer refinement. From the View— point of understanding distribution center location, plant location literature provides a fundamental insight into the industrial origins of logistic systems. RETAIL LOCATION LITERATURE Selection of retail locations has received interdisciplinary attention since the early twenties. Unless one wishes to interpret 24Donald J. Bowersox. "A Study of Theoretical and Practiced Procedures in Plant Location and Analysis of Highway Locational Influences, " unpublished Masterls thesis, Michigan State University, 1958; and Edward W. Smykay, Donald J. Bowersox and Frank H. Mossman. Physical Distribution Management. New York: Macmillan Co.. scheduled for publication, 1961. 25 . . . . Ronald Reifler, doctoral dissertation now in process at University of Chicago; and Melvin L. Greenhut, Edward W. Smykay, and Donald J. Bowersox, an empirical study of industry location now in process. 165 early German contributions as the foundation of retail location theory, treatment of this dimension is primarily an American phenomenon. A noteworthy exception is Losch's work in which he discussed interesting implications concerning the retail market area. Concern with retail location appears to have evolved at the time chain store operations became prominent in American business. For the most part, factors to be considered when selecting a retail site were emphasized. Some of the more detailed contributions tackled the problem of establishing procedures to guide site selection. The following is a representative sample of early retail location literature: 27 9 2 2 2 Nystrom, 1915; 6 Hayward, 1924; Pyle, 1926; 8 Reilly, 1929; 3 31 32 Dentsch, 1931; O Ratcliff, 1939; and Converse, 1943. Of ZéPaul H. Nystrom. Retail Store Operations. New York: Ronald Press, 1915. 27Walter Hayward. The Retail Handbook. New York: McGraw-Hill, 1924. 28J. F. Pyle, "Determination of Location Standards for Retail Concerns, " Harvard Business Review, Vol. IV (April, 1926), pp. 303-12. 29William J. Reilly. The Law of Retail Gravitation. New York: Pillsbury Publishers, Inc. , 1953 (Original, 1929). 30H. Dentsch, "Good—by to the Chain Store Advertising Location, " Advertising and Selling, Vol. XVI (March 18, 1931), pp. 17-19. 31Richard V. Ratcliff. The Problem of Retail Site Selection. Ann Arbor: University of Michigan Press, 1939; and Richard V. Ratcliff. "100 Percent Concept in Retail Location Analysis, ” Journal of Land and Public Utility Economics, Vol. XV (August, 1939), pp. 350- 53. 32P. D. Converse. ”Is There a Law of Retail Gravitation ?" Printer's Ink, Vol. CCIV (September 10, 1943), p. 36. 166 particular interest are the contributions of Reilly and Converse. They dealt with the problem of determining the geographic confines of a retail trading area. Reilly developed the now famous law of retail gravitation. Converse presented some comments concerning the validity of Reilly's contribution--a topic still receiving considerable attention. A review of early literature also reveals the roots of the shopping center movement. The following elaborated upon this trend: Printer's 34 35 3 Ink, 1927; Lonberg-Holm, 1931; Stein and Bauer, 1934; 6 37 3 3 Gruzen, 1934; Architectural Record, 1935; 8 DeBoer, 1937; 9 40 and Doherty, 1941. Many of these early contributions were case studies of successful shopping centers. 33See Allen F. Jung, ”Is Reilly's Law of Retail Gravitation Always True ?" Journal of Marketing, Vol. XXIV.(October, 1959), pp. 62-63. 34”As the Store Rent Goes Up, Net Sales Cost May Come Down, " Printer's Ink, Vol. CXLI (December 8, 1927), pp. 144—45. 35K. Lonberg-Holm, "Planning the Retail Store, ” Architectural Record, Vol. LXIX (June, 1931), p. 499. 36C. S. Stein and C. Bauer, “Store Buildings and Neighborhood Shopping Centers, " Architectural Record, Vol. LXXV (February, 1934), pp. 174-87. 37Summer B. Gruzen, “Automobile Shopping Centers, ” Archi- tectural Record, Vol. LXXVII (July, 1934), pp. 47-48. 38"Retail Store Planning, " Architectural Record, Vol. LXXVIII (July, 1935), p. 49. 398. R. DeBoer. Shopping Districts. Denver: Bradford Robinson Printing Co. , 1937. 167 Literature appearing during and after World War II reached a high level of refinement concerning factors influencing retail location and the development of planned shopping centers. Outstanding contri- butions to locating shopping centers were made by Baker and Funaro in 1951, 41 Smith in 1956, 42 and Kelley in 1956. 43 Some refinements 4 on independent retail location analysis were made by Reiss in 1947, 4 45 46 4 Muller in 1953, Harb in 1953, and Cohen and Applebaum in 1960. 7 Both Harb and Muller presented interesting observations of fringe locations for small independent food retailers. They pointed out the 4 0Richard P. Doherty, ”The Movement and Concentration of Retail Trade in Metropolitan Areas, " Journal of Marketing, Vol. VI (April, 1941), pp. 395-401. 41Geoffrey Baker and Bruno Funaro. Shopping Centers. New York: Reinhold Publishing Company, 1951. 2 4 Paul E. Smith. Shopping Centers: Planning and Management. New York: National Retail Dry Goods Association, 1956. 43Eugene J. Kelley. Locating Controlled Regional Shopping Centers. Saugatuck: Eno Foundation for Highway Traffic Control, 1956. 44Joseph Reiss, ”Shopping Centers: A New and Growing Develop- ment in Distribution, " Printer's Ink, Vol. CCXXI (December 12, 1947). 45Robert W. Muller, “What's the Best Location for Today's New Store?” Progressive Grocer, Vol. XXXII (February, 1953), p. 50. 46Ray O. Harb, "Why Three Out of Four Stores Should Consider a New Location, " Progressive Grocer, Vol. XXXII (August, 1953), pp. 48-52. 47Saul B. Cohen and William Applebaum. "Evaluating Store Sites and Determining Store Rents, “ Economic Geography, Vol. XXXVI (January, 1960), pp. 1-35. 168 economic potential of offering maximum convenience from an otherwise inferior location. To date, the outstanding retail location publication appears to be 48 . . . Nelson's 1958 work. Similar to Yaseen's book on plant location, Nelson wrote for the retail executive interested in selecting a new location. Nelson identified and discussed eight location principles. The interesting feature of his book is the complete coverage given to all aspects of retail location, including shopping center site selection. Writers on retail location have not been as prolific, in a purely theoretical vein. The fruitfulness of Losch's work was previously . . . 49 noted. Chamberlin's famous contribution of 1933 appears to be the earliest attempt to construct a theory of retail location. Treated almost as a secondary thought, Chamberlin viewed a good location as a tem- porary spatial monopoly-~one aspect of the businessman's attempt to . . . . . . . 50 . gain competitive superiority. Isard and Whitney, in 1949, conSidered 51 site selection in a more theoretical perspective. Alderson, 1957, 48Richard L. Nelson. The Selection of Retail Locations. New York: F. W. Dodge Corp., 1958. 49 Chamberlin, op. cit. 50Walter Isard and Vincent Whitney, l'Metropolitan Site Selection," Social Forces, Vol. XXVII (March, 1949), pp. 51Wroe Alderson. Marketing Behavior and Executive Action. Homewood, Illinois: Richard D. Irwin, 1957. 169 further developed the theory of spatial advantage in his comparison of individual locations and trading center locations. In summary, American writers have been extremely active, primarily from a pragmatic viewpoint, in the area of retail location. Unlike plant location theory, the literature dealing with retail location procedure appeared prior to attempts at constructing a general theory. The word "attempt" is used loosely since most theoretical considerations of retail location appear as fragmentary works. Based upon available literature, one might justifiably conclude that a theory of retail location has not evolved; at best we currently only have bits of such a theory. Yet, in analysis, the factual similarity among authors is striking. Almost without exception, marketing texts agree on the fundamentals of site selection, and Nelson has reduced these fundamentals to eight general principles. Viewing retail location from this perspective, one is reluctant to conclude that a theory has not evolved. The challenge appears to be rigorous evaluation, a more exacting model of the total retailing structure, and a detailed analysis of the interrelation between locations. A forthcoming work by La Londe offers potential in this area. From the viewpoint of understanding distribution center location, retailing literature provides insight regarding the demands of retail 52Bernard J. La Londe, doctoral dissertation now in process, Michigan State Univer sity. 170 structure upon wholesale location. A distribution center strategically located to provide a cost-and-service benefit to retail stores is most economically located near the stores it serves. This allows maximum advantages of consolidated shipment with relatively short local delivery. Therefore, retail store location helps determine the alternatives available in selecting a distribution center location. DISTRIBUTION CENTER LOCATION LITERATURE Distribution center, or warehouse, location literature differs basically from plant and retail location literature in two ways: First, the majority of contributions are of contemporary vintage, appearing in post-World War II literature. Second, almost all writings agree upon the fundamental importance of minimizing transportation cost when selecting a distribution center location. Articles expressing concern with warehouse location sprinkled prewar journals. In the earliest article located, Edwards, 1922, 53 discussed the influence of highways upon the location of storage ware— 54 55 houses. Collier in 1932 and Keefer in 1934 expressed an early interest in warehouse location. Keefer is the only one who attempted 53R. N. Edwards, ”Warehouse and Its Relation to Highway Trans- portation. " Municipal and County Engineering, Vol. LXIII (November, 1922), pp. 163-65. 54 J. D. Collier, "Storage and Warehousing as Factors in Economical Distribution, " Chemical and Metallurgical Engineer, Vol. XXXIX (January, 1932), p. 32. 55K. B. Keefer, "Easy Way To Determine the Center of Distri- bution," Food Industry, Vol. VI (October, 1934), pp. 450—51. 171 to present a technique for selecting locations. Using a piece of cardboard to represent the market area, Keefer placed BB shot at the location of each retail store, weighted in proportion to annual sales. The distri- bution center location was then determined by moving a pencil under the cardboard until the fulcrum of balance was reached. Interest in warehouse location increased substantially after World War 11. Its origin may be traced to logistics experienced from military operations and to the cost squeeze resulting from increased freight rates in postwar America. The predominant characteristic of this later literature is the universal concern with selecting a location which minimizes transport cost. At least two general methods, each funda- mentally mathematical, for selecting optimum distribution center locations evolved. The first method involves various mathematical configurations for averaging transportation costs within a predetermined market area. The objective is to ascertain that geographic point from which inbound and outbound operations will result in the least—cost transportation expense. The general systems for solving this problem build upon a framework of Cartesian coordinates. The variables under consideration determine the mathematical formulations. In the following, various forms of this basic technique are discussed: Materials Handling 56 57 58 Manual, 1955; Eneborg, 1958; and Smykay, 1959. In this 56“Warehouse Location Based on Trucking Costs, ” Materials Handling Manual No. 1, Boston Publishing Company, Inc. , 1955, pp. E84—E86. 172 research, a modification and refinement of this technique is applied to the specific problem of food distribution location. The second method, currently popular in distribution literature, consists of applying various forms of mathematical programming for establishing optimum distribution movements. This technique relates directly to location since a basic problem is determining the optimum number of distribution points as well as establishing a program of transportation movements. The general technique is to establish an array of locations and then, via a controlled system of substitution, to select that system which allows a minimum function to be optimized-- normally, distribution cost. In more general models, the influence of inventory levels at alternative points is also considered in an attempt to minimize total distribution cost. Specific articles expressing this general technique were written 60 59 by Baumol and Wolf in 1958, Wester and Kantor in 1958, and 61 Brink in 1957. Introductory books, which can provide one with an 57C. G. Eneborg, "How To Plot the Ideal Location for a Ware- house,” Management Methods, Vol. XIII (January, 1958), pp. 52-55. 58Edward W. Smykay, ”Formula To Check for a Plant Site, " Distribution Age, Vol. LVIII (January, 1959), p. 32. 59W. J. Baumol and P. Wolf, "Warehouse Location Problem, " Operations Research, Vol. VI (March, 1958), pp. 252-63. 60Leon Wester and Harold H. Kantor. Optimal Location Allocation, Sixth Annual Meeting of the Operations Research Society of America, May 16, 1958. 61Edward L. Brink, "A Simplified Solution for the Location of Marketing Outlets Using an Analog Computer, " Marketing‘s Role in Scientific Management. Chicago: American Marketing Association, 1957, pp. 468-75. 173 understanding of the fundamental concepts of mathematical programming, . . 62 63 were written by Reinfeld and Vogel, 1958, and Greenwald, 1957. Providing one has a grasp of the fundamentals, the future of this analytical method appears unlimited. In addition, a few descriptive reviews of successful warehouse location and some discussions of the need for total distribution planning appear in the literature. Among the former are: Architectural Forum, 64 65 66 1951; Chemical Week, 1953; and Iron Age, 1956. Two out— 67 standing works in the latter group are by Magee, 1960, and by Lazer, 1960. 68 62 Nyles V. Reinfeld and William R. Vogel. Mathematical Programming. Englewood Cliffs: Prentice Hall, 1958. 3Dakota U. Greenwald. Linear Programming. New York: Ronald Press, 1957. 64"Room for Warehousing Is Big Bonus of Well Planned Suburban Location, " Architectural Forum, Vol. VC (July, 1951), pp. 148—49. 65"Warehousing Off the Sheets, " Chemical Week, Vol. LXXIII. (August 8, 1953), pp. 71-72. 66 . "WarehouSing To Move or Not To Move, " Iron Age, Vol. CLXXVII.(January 26, 1956), p. 29. 67John F. Magee, "The Logistics of Distribution, " Harvard Business Review, Vol. XXXVIII (July-August, 1960), pp. 89-101. William Lazer, "A Systems Approach to Transportation, " Distribution Age, Vol. LIX (September, 1960), pp. 33—35. 174 In summary, it appears that transportation cost is generally accepted as critical in warehouse or distribution center location. As in retail location, the pragmatic influence of contemporary America is clearly expressed. Techniques for minimizing transportation costs are available for both specific market solutions and more general dis- tribution; network solutions. A theory, in the classical sense, is totally lacking. In reading the literature concerned with distribution center location, it appears a theoretical frame of reference for classi— fying basic locations could be developed. Such a structure is contained in Chapter II under "Distribution Center Location Logic” and is based upon the fundamental fact that distribution center locations are derived from the production or retail locations served. Utilizing fundamental concepts in both retail and plant location, it is possible to develop insights into the economic role of distribution warehouses and, also, into their derived locale. This more general subject is the topic of Chapter II. 175 APPENDIX C PRIMARY DATA In Appendix C, the primary data collected from the two grocery chains selected to represent the location models are presented. These data consist of supermarket coordinate locations and the annual number of standard trailers of dry groceries delivered to each. The data for each chain are reported in a separate table for clarity. 176 Table 14 Primary Data— - Model B Store Coordinates Trailers Phunber X‘ Y 1 87 6O 54 Z 85 62 32 3 85 58 152 4 9O 60 132 5 91 22 24 6 68 26 33 7 7O 53 4O 8 93 72 41 9 86 73 49 10 8O 18 126 ll 44 84 85 12 46 86 56 13 46 88 69 14 36 63 104 15 102 89 27 16 102 91 116 17 168 82 81 18 170 84 6O l9 16 42 116 20 15 39 94 21 18 38 119 22 36 42 54 23 38 42 42 24 36 44 185 25 38 44 110 26 38 4O 23 27 33 28 54 28 44 11 61 29 172 86 102 30 18 4O 96 31 14 36 108 32 17 100 37 33 19 102 62 34 15 98 57 35 16 91 84 36 34 40 71 37 100 26 28 38 46 84 74 39 89 60 134 40 104 91 89 41 15 62 113 177 Table 15 Primary Data- - Model C Store Coordinates . Number X Y Trailers 1 150 64 56 2 162 70 78 3 145 74 77 4 143 73 85 5 157 29 78 6 151 73 135 7 86 95 48 8 87 100 77 9 158 71 45 10 115 54 52 11 152 60 82 12 158 66 68 13 153 69 83 14 86 91 132 15 157 68 89 16 185 170 190 17 156 72 54 18 89 92 62 19 83 95 42 20 130 72 88 21 95 101 85 22 168 64 59 23 159 65 93 24 162 27 91 25 88 97 73 26 85 98 42 27 148 61 79 28 143 77 93 29 139 77 60 30 151 71 61 31 151 76 90 32 134 58 64 33 155 69 66 34 146 77 84 35 134 78 38 36 154 58 71 37 159 68 34 38 153 71 4O 39 157 64 48 40 149 62 45 Table 15 (Continued) 178 Store Coordinates Phunber x Y Traflers 41 162 186 75 42 90 88 48 43 87 98 89 44 138 102 44 45 128 94 89 46 152 72 37 47 28 145 230 48 151 69 44 49 136 60 100 50 82 99 88 51 137 78 53 52 148 71 50 53 165 95 69 54 88 94 103 55 8 86 135 56 156 65 80 57 6 148 114 58 149 70 32 59 168 67 73 60 136 75 108 61 148 75 57 62 85 94 82 63 146 63 75 64 154 67 47 65 96 112 43 66 84 100 41 67 82 91 31 68 139 73 41 69 145 65 33 70 148 66 26 71 195 140 37 72 174 112 44 73 140 92 29 74 164 63 17 75 86 86 26 76 151 67 19 77 113 23 33 78 106 78 21 79 138 82 18 80 142 16 26 81 184 130 30 179 APPENDIX D ESTIMATED DISTRIBU TION COSTS Appendix D contains the detailed breakdown of estimated distri— bution costs from all determined locations in each model. The distribution center locations are coded in the following manner: (A) initial location; (B) non-mathematical solution; (C) ton-center solution; (D) mile-center solution; (E) ton—mile center solution; and (F) time-ton-mile center solution. The distribution cost for each location tends toward the conser- vative side since all estimates are based upon truck load deliveries. For many small stores, such a practice would not be satisfactory due to inventory perishability. Under these conditions, it would be necessary, in practice, to combine deliveries into a multi—store trailer. This practice would increase the distribution cost estimates. However, this specialized problem is locationally variable. 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