MODELING A1TRLBUTES iN DEMAND FIJNCTIONS OF COMPUTERIZED BUSINESS SIMULATIONS: AN EXTENSION OF TEACH'S GRAVITY FLOW ALGORITHM Developments In Business Simulation & Experiential Learning, Volume 24, 1997 MODELING ATTRIBUTES IN DEMAND FUNCTIONS OF COMPUTERIZED BUSINESS SIMULATIONS: AN EXTENSION OF TEACH’S GRAVITY FLOW ALGORITHM Steven C. Gold. Rochester Institute of Technology Thomas F. Pray, Rochester Institute of Technology INTRODUCTION The modeling of demand in the marketplace is a critical aspect of any computerized business simulation. Business simulations in particular are supposed to give students insights into the functioning of the “real world.” As a result, it is important for the programs to be designed to capture the essential elements and characteristics of the business world. Teach (1984) found most business simulations made very simple assumptions about the marketplace and the way product attributes were modeled. Most simulations assumed homogeneous products and homogeneous consumer preferences. Marketing variables controlled the allocation of demand including: price, advertising, R & D, sales force, compensation, and channels of distribution. Teach found a few simulations incorporated product attributes directly but only one ideal product was assumed to exist in each market segment; and the market segments were independent of each other. Considering these problems Teach (1985) developed a demand model allowing for heterogeneous consumer preferences and products with multiple market segments. Within each market segment he created a set of “ideal” product attribute mixes. A firm gains demand within any market segment by developing a product with a mix of attributes that is closer to one of the consumer's “ideal” preferences, but may lose some demand by moving further away from the ideal attribute mix of other consumers. The demand is also affected by marketing variables such as: price, advertising, promotion, and R&D. Demand is linked to the Gold and Pray (1983) demand model. To succeed, the firm must understand the preference mapping of the consumers within each market segment, and their relative importance to standard marketing variables. The attribute model is a significant contribution to demand modeling. The purpose of this paper is to further evaluate and extend the attribute model developed by Teach and link it in a more direct way to the Gold and Pray demand function. The paper proceeds by (1) reviewing the Teach (1985) attribute model; (2) identifying important strengths and weaknesses; (3) developing a revised attribute model with direct links to the Gold-Pray function; and (4) illustrating the revised demand system with a set of examples, evaluating its sensitivity to changes in attributes and elasticities. The importance of our findings and areas of future research are identified. REVIEW OF TILE TEACH ATTRIBUTE MODEL The model assumes a simulation of an industry with three firms (1 = 1,2, or 3), each producing a product (Pi) but with different mixes of two attributes (A1 and A2) There are three different market segments (S1, S2, and S3) with different preferences but consumers are willing to purchase any product. Market segment 1 prefers only small amounts of attributes 1 and 2. Market segment 2 prefers a large amount of attribute 1 but only a small amount of attribute 2. Market segment 3 prefers a large amount of attribute 2 and a mid- level amount of attribute 1. Table 1 quantifies the “ideal” levels of product attributes in each segment (Si). Table 2 quantifies the actual levels of attributes 1 and 2 by firm (Pi). 132 Developments In Business Simulation & Experiential Learning, Volume 24, 1997 The distance each firm (1) is from the ideal mix in each segment (j) is calculated with the formula and the results given in Table 3: The inverse of the distance of the firm, relative to the total distance of all arms in the market, determines the market share. This model is similar to the gravity flow model font physical science. In Table 3 the highest market share (46%) in segment 1 goes to grin 2 (P2) with the smallest distance (1.60); and likewise for all other segments The market share for firm I in segment 1 (46%) is calculated as the inverse of it’s distance 1.60 divided by the sum of the inverses of all firms (0.50 + 0.63 + 0.24 1.37). Shadow Products Teach also discusses the concept of a shadow product and unmet needs or unfilled market niches. Showing a three- dimensional space configuration of market products and segments, he argues “each of the shadow product’s locations will have the same co-ordinates as the market segment, but N units away, on an orthogonal axis, from the market segment. Teach gives an example arbitrarily selecting an “N” of 2. Without showing the intermediate steps, he calculates the impact of adding the shadow product. The results show (1) total industry sales decline from 3500 to 2196, representing unfilled or unsatisfied demand of 1304 units (2) the closer the shadow products are positioned to the market segments (smaller “Ne), the total unmet need will increase. Adding Economic Variables To the Attribute Model Economic variables like price and advertising are added to the attribute model Teach modifies the Gold and Pray (1983) functional form for demand to calculate, a distance factor for each firm’s economic variables. Using the gravity flow concept, he calculates a total distance by taking the square root of the sum of distances squared for each economic variable. Market share based on economic variables alone is determined by each firm’s distance relative to the total distance. The final marks share considering both economic variables and attributes is determined in a similar 133 Developments In Business Simulation & Experiential Learning, Volume 24, 1997 fashion. The distance for the economic variables is the inverse of the market share based just on this criteria. The distance for the attributes is the inverse of the market share based just on this criteria. The total distance for both criteria is the square root of the sum of the distances for each criteria squared. Teach also discusses the possibility of weighing the importance of the economic variables relative to the attributes. In this case Teach multiplies the distance from the economic variables by W. and the distance from the attributes by WB such that We is between 0 and 1; and Wf= 1-Wa. CONCERNS WITH TEACH’S MODEL In the examples, Teach assumes industry level demand is fixed at 3500 units and the distribution of demand is fixed at 15% in segment 1, 300/, in segment 2, and 55% in segment 3. This constraint reduces the flexibility and realism of the model. Market segments may not be independent. His reference to shadow products is not clearly defined. It is not certain whether the shadow product is a new product or just a new attribute. We infer a shadow product contains other attributes, say A3, that are desired by the consumers. In Teach’s example it is assumed no firm currently has A). It is not clear if it is possible in his model for a firm to acquire this product and the way in which this would impact his model. Teach only discusses the impact of all firms getting closer or further away from the shadow product and its impact on unsatisfied demand. If attribute 3 is included in the products of some firm but not others, it seems likely total market demand will increase but relative market shares of each of the firms in the three market segments will change. Teach mentions making the market place dynamic by changing the market segments, preferred product, or attribute mix. It is stated one could identify the beginning and ending ideal points and move the desired point each period of the simulation in a linear or nonlinear path. These are intriguing possibilities but there is no discussion of how this would be done and the sensitivity of the model to such changes. The way in which the economic variables are linked to the gravity flow model seems complex. The elasticity of any one economic variable or attribute is not defined owing to the way the model is pieced together. The sensitivity of the model to changes in attributes and economic variables is not tested and the stability of the system is not certain given its structure. More testing is needed to demonstrate the behavior of Teach’s gravity flow model. These concerns have prompted the authors to extend the gravity flow model and link it more directly to the Gold and Pray demand function. REVISED ATTRIBUTE DEMAND MODEL The system that we are recommending for modeling demand and allowing for market segmentation based on customer attributes is composed of three parts: (1) Gravity Flow Attributes, (ü)a Market Demand System; and (iii) Firm- Level Demand System Gravity Flow Including Shadow Attributes The gravity flow model is used to describe choice behavior in a situation where product attributes are both continuous and independent. Adding a shadow attribute (A3) directly to Teach’s distance formula yields: 134 Developments In Business Simulation & Experiential Learning, Volume 24, 1997 where: Dij= Distance between Product i and segment j P1A1 Product i level of attribute I SjA1 = Segment J ideal level of attribute I The distances Dij and the average distance for the segment (Dj) will serve as variable inputs in the Market Demand System. The Market Demand System The full market demand system developed by Gold and Pray involves 10 equations and is described in detail with examples in Gentry [19901. For purposes of this paper only the modifications to the market demand equation and the relevant elasticity calculations will be discussed: To determine the parameters the administrator must specify the desired elasticities of each independent demand variable at two levels. The elasticity formulas are as follows: Selecting two levels for the industry over a reasonable range gives two equations with two unknowns and allows the determination of the system parameters (for k=2,7). The selection of g1 will determine the initial market size for that segment. Unlike the constant segment proportion assumed by Teach, relative market segment size will be influenced by the economic variables, average distance, and the elasticities established apriori. The Firm-Level Demand System Instead of using the Teach approach, which utilizes the inverse of the distance and then normalizes them to determine firm-level demand, we have opted for the firm- level model described in Gold and Pray (1984). It is composed of a weighing function that uses both economic and attribute distance variables. The values assigned to the parameters k1,k2,k3..k6 depend on the designer's specification concerning the firm level elasticities. Equation’s (8-10) below are used to determine the values and are solved in the same manner as equations (4-6). 135 Developments In Business Simulation & Experiential Learning, Volume 24, 1997 where: Epj = firm price elasticity in segment j Emj=firm advertising elasticity in segment j Edj, firm attribute distance elasticity in segment j The share equation and firm-level demand calculations are given in equations (11 and 12). Total industry demand (Q) is the sum of all segments The firms total market share, considering all three segments is ILLUSTRATION OF REVISED ATTRIBUTE DEMAND MODEL The system will be described and illustrated via a simple example For comparison purposes we will start with Teach’s example described previously in Tables 1, 2, and 3. We have 3 firms producing 3 different products competing in the same market place with three different market segments. The product of each firm is characterized by two major attributes that impact the segments. Graphically it would look as follows: 136 Developments In Business Simulation & Experiential Learning, Volume 24, 1997 To determine the market and firm-level demand for each segment, equations 3 - 10 are used for each segment. Price is set up to vary between $25 and $35; advertising/marketing expenditures, between $500 and S 1200. Gravity flow distances based on the scales have their elasticities controlled over the range from 0 to 5. For equation 3, g1 is preestablished so that industry demand is equal to around 6000 units. The other parameters for both the industry and firm-level demand calculations are presented below: These starting values and elasticities are used to calculate the industry parameters (g2. .g7) using equations 4 to 6; and the firm parameters (kl..k6) using equations 8 to 10. The resulting market level demand for each segment (j) and weight equations for each firm i n segment j are: For this simple demonstration, the elasticities and the starting values are assumed to be identical over each segment. Exponential smoothing is ignored and simple arithmetic averages is employed. The firms starting economic decisions and attribute location values are presented below. The value of the elasticities and parameters are presented below: The Demand Results - Base Case In tins simple illustration the variability in industry and firm- level demand will be solely based on the gravity flow distances. 137 Developments In Business Simulation & Experiential Learning, Volume 24, 1997 Interpreting The Results As would be expected the demand potential for segment 3 is considerably greater than that of the other two segments. In this example this is due to the smaller distance calculation for the attributes. The higher total demand in segment 3 of 2495 (as compared to segments 1 and 2) is due to the firms’ coming closer to the ideal in that segment. Firm 1 gained 66% of the segment demand for segment 2 because its attribute distance value (.42) is much lower than that of firm 2 or firm 3. Firm 3 has the (east demand potential for both segments 1 and 2 because its distance from the idea! attribute levels is much greater than that of the other firms. Selecting the “Ideal” Attribute Mix What would happen if say, Firm I with product I, hit the ideal attribute mix in Segment 1?1 With the old attributes, Firm 1 only has a 40% share of segment 1, with shares of 66% in segment 2 and 22% in segment 3. 138 Developments In Business Simulation & Experiential Learning, Volume 24, 1997 Depending on the elasticities, the firm should capture most of the segment demand if it is the only firm to have the ideal attributes. In this example Firm 1 (P1) increases its market share from 39% to 93%. It also benefits in Segment 3 as its attributes move closer to the ideal in that market. As would be expected the market grows as the firm comes closer to meeting customer requirements. The absolute amount of the total increase in market demand is controlled by the distance elasticities set at the industry level. Adding a Shadow Attribute One of the most important contributions of the gravity flow model is the possibility of adding a “shadow attribute” such as a new technology, or a new customer interest, say, in multicolors of the product. In a simulation gaming environment, the astute firms would receive customer data during game play on the need for this new attribute. The firm(s) may include this new shadow attribute in their decision scheme and possibly improve their performance in a specified segment. To demonstrate, let’s assume there is a shadow attribute, call it A3, for segment 3 with an ideal value of 5. All firms initially have a value set at 0. 139 Developments In Business Simulation & Experiential Learning, Volume 24, 1997 A major strength of this system is that it allows for different elasticities to vary across segments. One Segment may be characterized as price sensitive with low prices; whereas another segment may command a higher price and be more sensitive to product features, service or quality. Including product attributes allows for a number of significant enrichments to a single-product simulation with standard attributes. Segment Diversity By using the system described above in each market segments, significantly different scenarios can be simulated in each segment. One segment can be price elastic; another can be relatively inelastic. Each segment can have different price ranges, different elasticities and different segment sizes. This system allows for multiproduct marketing concepts to be addressed in a single product simulation. Different segments may be affected by economic and seasonal factors in different ways. One segment may be extremely seasonal; whereas, another may be immune to seasonality. If more than one firm focuses on a small segment, the level of competition prevents a competitive advantage. The beauty of the system is that many different scenarios can be arranged to be consistent with modern economic and strategic management theory. Segments can easily be altered semester to semester, thus eliminating the conventional wisdom that often happens at university-level play. Changing Market Preferences Just as process capability requires continuous attention to customer requirements, the game can have moving attributes as the games proceeds. The game administrator can "tighten" or move the ideal locations, thus simulating that customer requirements are changing or getting more difficult to satisfy. Target Marketing In most single product games, the economic variables such as advertising, service and product R&D are generally continuous variables and are applied to a single-product industry demand Function. With the segmentation approach, firms can direct a percentage of these economic variables toward a specific attribute and/or segment. Firms would then need to specify the amount and the targeted customer in their decision process. Total Quality and Customer Satisfaction Total Quality issues can readily be integrated into the system. If the simulation tracks bad products or failures these can be normalized into an attribute ranging from, say, - 3 to + 3. Segments wanting exceptional quality could carry + 3 attribute value. Customer surveys and other forms of market research can be added, giving teams feedback on how well they are meeting the segment customer requirements - through the attributes and/or the economic variables The customer surveys can also suggest the need for additional attributes. Simulations have improved dramatically in recent years due to improved demand and cost modeling algorithms. Designing product attributes in the demand function of computerized business simulations will enhance their pedagogical effectiveness and further research is recommended into the scenarios suggested above. 140 Developments In Business Simulation & Experiential Learning, Volume 24, 1997 REFERENCES Gold, S. and Pray, F. (1984) “Modeling Market and Firm Level Demand Functions in Computerized Business Simulations” Simulation and Gaming, Vol.15 (3),pp. 346- 363. Teach, Richard D.(1985), “Demand Equations Which Include Product Attributes,” Developments in Business Simulations, Vol.12,-pp.161-156. Teach. Richard D. (1984), "Using Spatial Relationships to Estimate Demand in Business Simulations,” Developments in Business Simulations Vol. 11, pp. 244-246 141 Table of Contents Volume 24, 1997 Incorporating Computer Telephony into the MIS Course A Learner Oriented Infrastructure for videoconferencing Based Distance Education Courses The Identification of Temporally Related Structural Elements of the Experiential Component of Electronic Spreadsheet Tasks Does Involvement Influence Learning from Simulation Participation? Some Relationships with Helpfulness and Performance Outcomes Musings on Business Garne Performance Evaluation Performance on a TE Simulation: What does it represent? The Business Policy Game: An International Simulation - An Assessment Tool Students in Free Enterprise as Experiential Learning The Role of Computer Models in Wargames: A Practitioner's view Using Focus Groups as a Tool to Research Learning: A Demonstration and a Discussion Using Medical Simulations to Teach Multi-Cultural Diversity Using the World Game to Internationalize International Exchange Game Community Services Needs Assessment: An Innovative Approach Introducing Students to Potential Total Quality Management Ethical Dilemmas Privacy in the Workplace: A Situational Analysis Antecedents of Learning in Simulations Demonstrating the Learning Effectiveness of Simulation: Where we are and Where we need to go The Use of Computer Simulations as a Pedagogical Aid in Teaching Management Information Systems Evaluating Simulation Learning in a Distant Learning Instructional Model Financial Engineering of Global Investments The Labor History Game: Playing with the Past Perks Participation Assessing Negotiator's Proficiency with a Negotiation role-play The Art of Negotiating Enhancing Learning and Employee Development through the Assessment of Learning Pedagogy Preferences across selected Dimensions of Culture: A Preliminary Investigation Cooperative Learning: What are we Learning? Effective Use of Mastery Based Experiential learning in a Project Course to improve skills in system analysis and Design Simulations and Learning: Can we prove a relationship? (Seminar) Predicting and Reviewing NYSE Stock Prices by use of Basic Statistical Analysis and Logic Toy Car Depreciation Exercise ABSEL as Home Community: An Interactive Exploration Service Learning: Linking Academic Study to Community Development and Business Enhancement Ability of Efficient Evaluation of Knowledge-Based Management Strategies Corporate Ethics Training Programs Modeling Attributes in Demand Functions of Computerized Business Simulations: An Extension of Teach's Gravity Flow Algorithm Expert Systems Combined with Neutral Networks: Tools to Benefit the Marketing Researcher Computer Game Design: New Directions for Intercultural Simulation Game Designers Consistency in Simulation Performance over Time and Across Simulation Games The Impact of an Artificial Market Leader on Simulation Competitor's Strategies Business Plans, Case Studies, and Total Enterprise Simulations: A Natural Co-existence An Exploration into the Non-Use of Business Simulations The Market Game: Interactive Learning Through Market Simulation Plotting Brand Trajectories with the COMPLETE PPM package: A Market Segmentation Analysis and Positioning Tool Me and Mine Inc: An Exercise in Management Theory Learning to Differentiate Leadership from Managerial Position Business Ethics Survey: A Perspective from the Retail Industry Experiential Learning in Demand Analysis for an Agricultural Commodity Marketing on the Internet: A Pedagogical Exercise College Students Need Simple Computer Simulations, Especially for International Business Courses An Analysis of Student Attitudes, Performance, and Strategies in a Simulation Competition Based on a Controlled Product-Market-Entry Game Structure The Crystal Enterprise: Application of a Non-Computerized Simulation Model in a Process of Organizational Change Threshold: A Windows-Based Behaviorally Oriented Total Enterprise Simulation Coaching Business Game Teams Using a Decision Variable Optimizer Rock and Roll is here to Stay: Enhancing Experiential Pedagogy with Musical Exercises An Example of Business Process Analysis Simulation for Customer Software Support The Use of Business Gaming in Hong Kong Academic Institutions Using the Integrative International Simulation INTOPIA Mark 2000 in a Concentrated MBA Curriculum A Group Experience as an Integrated Part of the Core Management Course Empowered Learning in the Classroom The Inter-Group Interaction: An Innovative Approach to Cooperative Learning Courses that Utilize Student Team: An Approach to enhancing their Effectiveness Thoughts about the Measurement of Learning: The Case for Guided Learning and Associated Measurement Issues Measuring Student Learning Using Business Simulations: A Theory Based Perspective On the Use of PC Fingame in an Undergraduate Finance Course How Managers get Things Done: A Virtual Soundbite Internet Experiential learning in the Principals of Marketing Classroom: A Pedagogical Approach Current Student Perceptions Relative to Business Simulations Beyond Capitalism: Designing Business Policy and Social Justice The Use of Boards of Directors to Evaluate Reports and Presentations in an Undergraduate Business Policy Course Beacon Lumber: An Experiential Introduction to Financial Accounting The Application of Organizational Motivation Principles: The Experiential Business Simulation Motus Manufacturing Avoiding a Bogey: Grading Case Discussions Scientifically Communicating Consumer Behavior II: A Modified Exercise Using Personal Consumption Journals in Condensed Courses Designing Instruments for Assessing the Effectiveness of Simulations, (Seminar) 360º Performance Feedback: Appraisal vs. Assessment The Cafeteria Approach to Managing an Academic Career: Remaining Non-Perishable while Doing Your Own Thing An Experiential Exercise Related to Person-Organization Fit and it's Consequences For Today's Dynamic and Changing World, Business Simulations need to be expanded to encompass Much Greater Complexity: A Demonstration The Incident Process: A Case in Reverse Contextually-Anchored Business Simulations The Energy Factor: Building Motivation in the Simulation Gaming Environment The Design of an Internet Game