USING SPATIAL RELATIONSHIPS TO ESTIMATE DEMAND IN BUSINESS SIMULATIONS Developments in Business Simulation & Experiential Exercises, Volume 11, 1984 244 USING SPATIAL RELATIONSHIPS TO ESTIMATE DEMAND IN BUSINESS SIMULATIONS Dr. Dick D. Teach, Georgia Tech ABSTRACT This paper presents an additional, approach to modeling and simulation that combines the economic factors with a set of physical, product characteristics factors to determine the allocation of demand to the competing firms. The product characteristics are modeled using a growth flow model,. A market segment is defined which desires an ideal, or best product based on the characteristics of the product. Although all products are purchased, the amount demanded is a function of the difference between each actual product and the ideal, product. This paper then expands the concept from a single market, multi- firm-single product model, to a multiple market segment mode’ in which each firm has the capability to produce several, different products. The Model. Most business simulations have been developed to represent competitive firms in an oligopoly where all firms start with equal, asset structures and sales Substantial, care has been taken to develop demand equations that represent kinked demand curves with appropriate industry and firm price and other marketing variable elasticities.1 Last year at the ABSGL meeting, Gold and Pray reported on a set of generalized econometric equations that would be suitable for the majority of business simul,ations.2 Most of these models represent pure oligopolies. That is, where a few firms are sellers of a homogeneous commodity to a large number of buyers. Almost, if not all,, consumer goods and the vast majority of industrial, products are differentiated from one another. This differentiation usually takes the form of differences in physical, characteristics, product attributes, packaging, brand names, etc. This fact of expected product differentiation has been recognized by authors.3 However, with the exception of Markstrat, these simulations all have compensatory demand functions.4 Excessive expenditures on one variable in the marketing mix will, compensate in the demand function for underspending on another variable in the marketing mix. There are numerous examples of products that failed in the market place, in spite of heavy expenditures on the marketing mix because they did not provide the product attributes demanded in the market place (the Edsel for example). Most of the multiproduct, and multiattribute product simulation approach this problem in a variety of ways. What is described in this paper is a generalized method to represent demand for products that includes competitive market response for the marketing mix variables as well, as a competitive market response for desired product attributes. A model, known as gravity flow works well to describe choice behavior in a situation where product attributes are both continuous and independent. As an example, consider a single market segment Si(L=1) a three firm simulation, with each firm producing one product Pj(j=1,2,3); and a two attribute space Ak(k=1,2) Pj'A1 A2 is then the two tupl,e attribute combination for product P. and SiA1 A2 is the ideal point or most desired product in the market. If one uses the standard gravity flow mode’ in which the attraction of product Pj is inversely proportional, its distance from S is then: Pd r M R i AkP jAkS iS j ∑       − − = 1 2 Where: dSiPj is the distance between the ideal, product for segment Si and the actual, product j, M is the number of attributes, and r is the distance function. If r=2, then Euclidean distance is used. If r1, then city block distance is used. While any value of r can be used, r=2 or 1 is recommended. From the example using r=2; The inverse of these distances are 1/d or 1/2.63 =. 38; 1/1 =1.00; l,/2.24 =.45; From the example, the shares are: P1=.38/1.83=.21 P2=1.00/1.83=.54; and P3=. 45/1. 83=. 25 To determine the size of the market segment S, use the market demand equation described by Gold and Pray (1983). To determine the actual demand for each firm, the results of the market share as derived by product attributes are averaged in a weighted fashion with the market shares as derived by the Developments in Business Simulation & Experiential Exercises, Volume 11, 1984 245 firm demand equation described by Gold and Pray (1983). All this requires is a weighting function W where 0≤W≤ 1; and w1+w2 = l; where w1 = W and w2 = 1-w1 W determines the proportion of weight placed on the product attributes. If AS. is the share based on product attributes and for product i and MMSi is the share based on the marketing mix variables for product i, then MSi=w1.ASi+ w2 MMSi is the final, market share for product i. Simply multiply this market share by the total’ market demand to determine the demand for each firm or product. If in the example all these firms had equal, expenditures in the marketing mix or balanced compensatory expenditure and if the weighting scheme were equal, or W=.50 then the resulting market shares would be: Market Market Market Share Share Share of of of P1 = (.5*.21) + (.5*.33) = .27; P2 = (.5*.54) + (.5*.33) = .44; P3 = (.5*.25) + (.5*.33) = .29. A problem. The development of this mode’ and the corresponding example appear to work, however, if the ideal, point for a segment and the product attributes of any particular product are exactly the same, the distance between becomes zero and the inverse is undefined. Luckily, there is a simple solution and one that adds versatility to the model,. There is nothing limiting the dimensionality of this mode’ to two dimensions. The number of dimensions can be defined as one greater than the number of attributes. The extra attribute dimension has a value of zero (0) for each product. The value of the market segment on this dimension can take on any value. The greater the value, the less important product differentiation becomes. This feature becomes more important when additional, market segments exist in the market place. The example can be continued to show the result of defining a third dimension. Each product has the value of zero (0) assigned to this attribute and the market segment has the value of one (1). The distances become: The corresponding shares are P1 = .33/1.44 - .23; P2 =.70/1.44 = .49; P3 = .41/1.44 - .28 The reader can verify that as the market segment value along the extra axis becomes larger, the corresponding market shares asymptotically approach equal shares. Relationships Between the Spatial, and Economic Models The size of the market segment is a direct function of the marketing mix variables. Gross margins which frequently affect the marketing expenditures end the prices can be affected by the product attributes. Let the previous example be defined as a soft drink market which attribute one being sweetness and attribute two being carbonation level,. Assume linear costs of both attributes. Five cents per unit of sweetness and four cents per unit of carbonation should have the effect of altering the optimal prices of the brands. As a result, interaction effects between the spatial and the economic model, can be developed. Extensions. The spatial model, has been developed using a single market segment and a set of firms, each producing a single product. Neither of these constraints are necessary. In fact, the spatial, mode’ enhances the simulation as firms develop additional, products to meet the demand for multiple market segments. When several, market segments exist in the market place, interesting and realistic strategy problems can be developed and explored. In order to show the value of these extensions, consider the following possibility. Assume a three market segment situation -- say in the soft drink industry and the product differentiation is based on sweetness and carbonation level. Let S1 represent the teenage market which is not price sensitive but highly sensitive to advertising. This market strongly prefers high sugar drinks with low carbonation. S2 represent the adult away from home market which is much smaller than the teenage market, slightly more price sensitive, less sensitive to advertising and have a lot of carry over effects. This market prefers a much less sweet drink and wants more carbonation. S3 represent the at home consumption which is highly price conscience with low advertising sensitivity and very long carry over effects but no strong product characteristic requirements. Also assume each firm can produce multiple products. Each segment has a Gold-Pray type demand equation with different parameters. The varying in carry over effects can be modeled using different exponential, smoothing values. Segments S1 and S2 are far apart on the two dimensional plane but close to the surface -- (The third dimension equals about one). Segment S3 would appear in the middle but away from the surface. (The third dimension in this case could equal, four or five.) A firm could produce products for each market or produce multiple products for a single market. Is the same way they could allocate their promotion to any segment but each segment would see the same price structure. Developments in Business Simulation & Experiential Exercises, Volume 11, 1984 246 In conclusion, this hybrid model is simple to implement in modeling and simulations but adds greatly to the realism of the games. Marketing strategies can be developed which are firm specific and different strategies can be successful,. Thus, the firms in the simulation do not have to converge to a one best strategy situation. FOOTNOTES 1For an analysis of eight simulation’s demand equations, see Thomas F. Pray and Steven Gold, “Inside the Black Box:” in Development in Business Simulations and Experiential Exercises Vol.., 9 Editors David Fritzsche & Lee A. Grof, 1982. pp. 110-115. 2Gol,d and Pray “Simulating Market and Frim Lever Demand - A Robust Demand System” in Development in Business Simulations and Experiential Exercises, Vol. 10 Editors Lee A. Grof and David M. Currie. 1983. pp. 101-106. 3Ness and Day, 1978, in Marketing in Action; Faria, Nelson, and Wozine, 1974, in Compete, Brolest and Bush, 1979, in Marketing Simulations; Larreche and Categmon, 1977, in Markstrat and others. 4Davis R. Lambret, “On Compensatory Demand Functions in Marketing Simulations, Experiential Learning in the 80’s. Editors Daniel C. Brenenstuhl and Williams Biggs, 1980, pp.80-82. Table of Contents Volume 11, 1984 Simulation Gaming as a Means of Researching Substantive Issues: Another Look A Further Test of the Group Formation and its Impacts in a Simulated Business Environment Impact of Economic Patterns on Student Performance in Computer Business Simulation Games Majority Fallacy Game with Independent Student Simulation and a Case Introducing the Marketing Channel Laboratory A Comparative Evaluation of a Marketing Game A Study of Comparative Effectiveness of Problem-Solving Technologies The Impact of Hierarchical and Egalitarian Organization Structure on Group Decision Making and Attitudes Risk-Free Decision Making The EX-STRA Export Strategy Game Computer Education for Management Students Developing a Computer Game/Job Simulation to Teach Functional Literacy Skills Experiencing Socialization First Hand: An Experiential Exercise in Organizational Socialization Networking Distributive Versus Integrative Approaches to Negotiation: Experiential learning Through a Negotiation Simulation Managerial Education and the Real World: Foudations for Designing Educational Tools Diagnosing Group Climate to Improve Supervisory Effectiveness Student background as a Factor in Simulation Outcomes: The Collective bargaining Example The Use of Pre-Plays in Management Education Experiencing the Process Debrief: A Workshop ABSEL Megatrend Roots MEGATRENDS for Business Simulation and Experiential Learning The Effects and Consequences of the Megatrends on Simulation Gaming: One View Opportunities for the Future: ABSEL's Role Experiential Learning-Based Discussion vs. Lecture Based Discussion: A Comparative Analysis in a Classroom Setting An Evaluation of the Minitab Package in Teaching Business Statistics Concepts A Path Analytic Study of the Effects of Alternative Pedagogies Developing and Using Weighted Application Blanks: An Experiential Exercise Building Airplanes Individual vs. Group Grade: An Exercise in Decision making A Marketing Plan Exercise: Development of Interteam Cooperation Using a Coordinated Experiential Approach Using Student Experience as the Basis for a Consumer Behavior Learning Exercise Student Evaluations of Instructors: What do Students Believe? A Description of the SOFTCAT Computer Assisted Teaching System Comparisons of Practitioners' and Professors' Perceptions of Business Policy Content and Learning Methods The Perceived Relationship Between Pedagogies and Attaining Course Objectives in the Business Policy Course The Use of Simulation in the Teaching of Business Policy A Research Study on Strategic Decisions in a Business Simulation Strategic Management Decision Making Researched Via Simulation Gaming Using Simulation to Investigate Factors in Competitive Bidding Combining Experiential Learning and management Assistance A Model for Teaching Management Skills Putting Experience Back into Experiential Learning: A Demonstration The Teaching and Behavioral Measurement of Managerial/Organizational Competencies: Developing Experiential Exercises and Simulations A Simulation Game Model for Conglomerates QCLAB - A Microcomputer Laboratory in Quality Control CTSS: A Commodity Trading Simulation System Problem Solving: An Exercise on Learning, Coaching, and Operant Conditioning A Demonstration of the Effects of Feedback as a Category of Reinforcement The Assessment of Feedback and Disclosure in Interpersonal Relations: An Experiential Exercise A Study to Determine Whether the Teaching of Basic Grammar Skills in Business Communication Classes Improves Students' Business Letter Writing Corporate Maladies Through the Eyes of the Memo Writer: A Seldom Used Experiential Tool Executive Bailout at Shake & Spear, Inc. The H.E./L&P Merger Intercultural Nonverbal Communications: An Experiential Exercise The Evolving Business Policies Course - Is Management Gaming the Logical Pedagogy? The Use of Decision Simulations in Management Training Programs: Current Perspectives Humanizing the Business of Medicine: The Use of Simulated Patients to Train medical Students Systematic Integration of Simulation Methods in a Graduate Management Curriculum Modeling Non-Price Factors in the Demand Functions of Computerized Business Using Spacial Relationships to Estimate Demand in Business Simulations Two Algorithms For Redistribution Of Stockouts In Computerized Business Simulations Leadership And Strategic Behavior A Comparison Of Two Business Strategy Simulations For Microcomputers Incorporating Decision Support Systems Into Management Simulation Games: A Model And Methodology Using Micro-Computers To Support The Analysis Of Complex Cases: It's As Easy As 1-2-3 Strategic Formulation Consistent With Pims: A Micro-Computer Application