A LINEAR PROGRAMMING APPROACH TO OPEN SYSTEM TOTAL ENTERPRISE SIMULATIONS Developments In Business Simulation & Experiential Exercises, Volume 20, 1993 86 A LINEAR PROGRAMMING APPROACH TO OPEN SYSTEM TOTAL ENTERPRISE SIMULATIONS Alan L. Patz, University of Southern California ABSTRACT The promise of open system simulations is no longer a promise. One method of devising them is to use the goal oriented version of linear programming with a focus on the reverse assumption of the standard economic theory of industrial organization. That is, the Structure→Process→Performance model of economic theory needs to be reversed, at east, to Process→Structure→Performance. Doing this eliminates the need for and fixed algorithms that drive current total enterprise (TE) simulations. More important, this sort of logic suggests an even more general approach characterized by a completely interactive structure, process, and performance model. INTRODUCTION Without exception, all popular total enterprise (TE) simulations adhere to the economic theory of industrial organization. The authors of these games pay particular attention to the basic assumptions that (a) the structure of an industry determines the processes that occur in that industry, and (b) the processes in an industry determine its resource allocation efficiency or performance (Patz, 1981). In symbols, these two premises may be represented by a simple linear heuristic: Structure→ Process→ Performance. Key structural factors such as concentration, product differentiation, scale economies, price elasticity of demand, entry conditions, and demand growth and decay are determined a priori, before any competition begins in the classroom. For example, one question is paramount when an administrator configures a TE competition: How many firms are in the industry? The answer given to this question, along with the overall demand growth and decay function determines total market size. Some simulations permit market entry for additional firms as well as exit and mergers, but the overall effect is to create an oligopoly with a limited range of market share possibilities. Individual firms have fixed demand functions that depend upon such factors as price, advertising and R & D expenses, number of salespeople and distribution centers, and so forth-- usually with a highly imaginative set of lead, lag, average, and cumulative effects. The point is that these a priori, overall, and fixed functions remain the same throughout the competition, more or less stabilizing the price elasticity of demand. Likewise, scale economies are fixed, once again, by usually creative production functions, and the net effect is a closed system (Patz, 1990). Indeed, these closed systems follow standard economic theory. However, it is not necessary to do so, and the twofold purpose of this paper is to show that routine linear programming theory can (a) generate open system TE simulations, and (b) stimulate further research on the nature of microeconomic activity. REVERSING STANDARD ECONOMIC THEORY Closed systems must result from standard economic theory. Once the structure of a market is fixed, everything else has to occur within its basic framework. Structure→Process→Performance does not leave much room for the “imperfections” exhibited in real markets. Economists and financial theorists attribute these quirks to systemic failures, that is, practice should conform to theory rather than vice versa. But, if the standard theory is reversed, then some of these so-called imperfections may not be abnormal at all. Beginning with the reverse assumption that Process→Structure→Performance leads to an entirely different way of looking at markets and TE simulations. There is evidence for taking this position (Winsor, 1989) and five representative processes will be used in this paper: pricing, promotion, quality, training, and automation represented as PR, PM, QY, TR, and AT. The Price Constraint For purposes of brevity, only the result of this linear programming approach will be presented. The meandering path that led its development is not worth recounting in such a brief presentation. Therefore, take the pricing process and write a typical linear programming constraint (Dantzig, 1963) such as: a11PR1 + ... + a1n,PRn ≤ b1 (1) where a1j = a variable coefficient j = (1, …n) n = a variable number of firms in the industry PRj = firm j’s pricing decision for the current period, and b1 = a variable stipulation. Notice that price times quantity in equation (2) for b1 is total market revenue. Likewise, making the appropriate substitutions from system (4) definitions into constraint (1): b1 = PRavQ (2) where PRav = some sort of average price, and Q = total market demand. Elaborating further on Q, it could be a fairly complex function such as Q = F(1/ Prav, PMav, QYav, TRav, ATav) (3) where the various process averages, such as QYav, may take many forms. In short, the immediate purpose is not to argue specific forms but to demonstrate the feasibility of a linear programming formulation. Now, looking at the variables on the left-hand side of equation (1), let a11 = f11Q = Firm 1 unit sales (4) a1n = f1nQ = Firm n unitsales such that Σ1j ≤ 1, (5) and f1j ≥ 0. Only if Σ1j = 1 does the first constraint (1) equality condtion hold that a11PR1 + ... + a1n,PRn = b1. Notice that price times quantity in equation (2) for b1 is total market revenue. Likewise, making the appropriate substitutions from system (4) definitions into constraint (1): f11(Q)PR1 + ... + f1n(Q)PRn ≤ PRav(Q) (6) where f1n (Q)PR11 is Firm l’s revenue and so forth. Canceling Q in (6) yields Developments In Business Simulation & Experiential Exercises, Volume 20, 1993 87 f11PR1 + … + f1nPRn ≤ Prav (7) with the condition (5) still holding that Σf1i < 1. Since the PRj’s are constant in any given period, the constraint (7) can be rewritten in the usual fashion: PR1f11+ … + PRnf1n ≤ Prav (8) Other Process Constraints and Relative Attractiveness A similar development would lead to parallel constraints for the other four process variables--PM, QY, TR, and AT. For example, the promotion constraint would be PM1g11+ … + PMng1n ≤ PMav (9) Where it is not necessarily true that f1j = g1j (10) But, assuming for the moment that the equality (10) holds, then the following system results: PR1f11+ … + PRnf1n ≤ Prav PM1g11+ … + PMng1n ≤ PMav QY1f11+ … + QYnf1n ≤ QYav (11) TR1f11+ … + TRnf1n ≤ TRav AT1f11+ … + ATnf1n ≤ ATav Obviously, the second subscript on each f1j is superfluous. Therefore, rewrite (11) as PR1r1+ … + PRnrn ≤ Prav PM1r1+ … + PMnrn ≤ PMav QY1r1+ … + QYnrn ≤ QYav (12) TR1r1+ … + TRnrn ≤ TRav AT1r1+ … + ATnrn ≤ ATav where the determination of each element in the (PRav,.. .,ATav)T constraint vector, with T as the transpose notation, is similar to the problem posed by equation (3) for Q. That is, feasibility is the issue--not a final design. Now, without immediate explanation, let rj = the relative attractiveness of firm j to consumers k = the number of competing TE simulation teams, say, in one section of a business policy course, where k < n. Then, as before, with n = a variable number of firms in the industry (n > k), x = n - k is the number of firms under administrator control. The variable x, unknown to the participating teams, can vary from zero to (n-k) in any period at the discretion of the administrator. The first key result of this development is that the administrator sets the relative attractiveness of x = n - k firms by adding further constraints to the system (12). This can be done in many ways, but one overall constraint will hold. That is, r1+ … + rn ≤ 1 (13) since whatever initial values are assigned to the they can always be normalized such that (13) holds. Then, for the x = n - k administrator firms, some other constraint where a 1 will be needed. Again, the number of administrator firms may vary from period to period. Rk + 1+ … + rn ≤ α (13) Where α ≤ 1 will be needed. Again, the number of the administrator firms may vary from period to period. Relative Attractiveness Revisited However, back to relative attractiveness, rj. What does this mean? What concepts support this notion? System (12), actually, is the basic answer to these questions. Its proposition is that a firm j’s Process vector, represented simply here as (PRj, …,ATj) 2 (14) determines its appeal to consumers based upon the process vectors of all other firms. These appeals noted as rj, in turn, are equal to f1j in system (11), where f1j(Q) = Firm j’s unit sales in system (4). The main reason, of course, that each process vector determines firm j’s appeal to consumers, based upon the process vectors of all other is that they are dependent upon each other through system (12) and constraints (13) and (14). System (12) and constraints (13) and (14), in addition, make possible an open system TE simulation with (a) a variable number of firms in the industry, (b) relative attractiveness variations made possible through the goal programming extension of linear programming (ljiri, 1965), and (c) a new and empirically useful way to view the imperfections of standard economic theory. A GOAL PROGRAMMING SOLUTION The variable number of firms has already been established in equations (13) and (14). What is needed is some sort of analytical solution to this “relative- attractiveness” concept. The new, empirical approach to standard economic theory will be considered in a subsequent section. Stated in another way, regarding relative attractiveness, the problem focus is now on how to optimize something associated with system (12) and equations (13) and (14). Therefore, taking another look at this formulation, PR1r1 + … + PRnrn ≤ Prav PM1r1 + … + PMnrn ≤ PMav QY1r1 + … + QYnrn ≤ Qyav AT1r1+ … + ATnrn ≤ ATav (16) r1 + … + rn ≤ 1 rk + 1 + … + rn ≤ α it is clear that other constraints on linear combinations of the rj’s could be added at the administrator’s discretion. For example, specific values could be assigned for the relative attractiveness of each administrator firm in such a fashion that their sum equals a. In fact, imagination is the only limit on the variations of system (16) that may be attained by adding or removing constraints on the terms. The key issues are how to how to solve the resulting system, whatever it is, and how to modify a system that has no solutions. Solvable Systems Assuming that system (16) is solvable in the form chosen by the administrator, the simplest solution procedure is the one provided by goal programming. That is, rewrite (16) as: where the ym+’s and ym’s, for m = PR, PM, QY, TR, and AT, are overages and underages respectively for each process constraint. For example, continuing the assumption that (17) has a solution and using the price constraint PR1 r1 + ... + PRn r n-ypr + + yPR = PRav, ypR + measures the amount by which PR1 r1 + .. + PRn r n exceeds PRay in that solution. Likewise, yPR measures the amount by which it falls short. Furthermore, when viewing (1 7) as a matrix, the columns for ypr + and ypr are linearly dependent. One is simply the negative of the other. Therefore, only one can have a value different from zero in any Developments In Business Simulation & Experiential Exercises, Volume 20, 1993 88 solution. A similar interpretation holds for every other process constraint in this example, or for any other process constraint that a TE simulation designer chooses to include. In short, the procedure is to minimize deviations from the augmented constraint vector (PRav ATav,, 1 ,a)T, and it has two basic advantages. First, it does not impose a predefined structure on the market. Each firm’s pricing, promotion, and so forth decisions do that. Second, it’s simple. There is no need to classify unusual results as imperfections. What happens simply happens. Unsolvable Systems But, when system (17) does not have a solution, the routine simplex algorithm for solving linear programming problems will not suffice. An extended one is needed that halts execution when a problem is encountered alerts the administrator regarding which constraint is incompatible with a solution, and in more elaborate models, suggests modifications to the original problem. This sort of extended simplex algorithm is entirely possible (Cooper, 1991), and its implementation involves basically a more complex computer routine. The theoretical Point of such a routine is that whatever the administrator does to resolve an unsolvable system the market. These market-clearing corrections, in turn, suggest new avenues of empirical research. STRUCTURE VS. PROCESS: ONE MORE TIME Dorfman, Samuelson and Solow (1958), of course, were among the first to note the advantages of linear programming over conventional mathematics in the development of economic theory. The preceding argument is just another example of their basic approach, but it adds several new dimensions by reversing the traditional notion of Structure→ Process. First, by focusing on process, a TE simulation of an industry becomes an open system. Any number of firms may enter or leave at the discretion of the administrator. Second, a firm’s relative attractiveness to consumers is a composite of all its processes in relation to the processes of all competitors. This is also the case in traditional TE simulations, but the linear programming model allows for additional constraints on relative attractiveness per se. Third, the process focus in the linear programming system (17) is infinitely expandable. Unlike the a priori, and fixed algorithms in TE simulations, an administrator can vary the number and type of constraints in system (1 7) at will. Fourth, and most important, this approach adds at least two new research directions--market models and expert systems. Market Models As noted above in the case of unsolvable systems, whatever an administrator does to resolve the issue clears the market. In other words, imperfections are no longer imperfections when viewed in this manner. Markets simply clear one way or another. As constraints are modified in order to reach a solution, the inner workings of the market being created by process decisions become apparent. The question to be answered is straightforward: What had to be done in any period in order to clear the market, solve the system? In fact, competing teams in a classroom are not required to answer this question. They would not qualify as a controlled experiment. Instead, specific decision patterns would have to be tested on plausible versions of system (17) in order to determine fundamental answers to the preceding question. System (1 7) by itself, however, has to be expanded to include issues of production or service capacity, inventories, distribution, balance sheets, income statements, cash flows, and so forth. The five processes used for expository purposes in this paper are only a beginning. In fact, the assumption in equation (10) that equated the coefficients for each process variable is only a beginning. There is no reason to continue with this assumption beyond the purposes of brevity in this paper. Nevertheless, experimental trial and error runs of system (17), using a flexible simplex algorithm (Erikson & Hall, 1 99x), have shown that it is a feasible approach. When solutions fail, reasonable guesses on where to begin again produce the needed market share or relative attractiveness answers so crucial to this development (Patz, 1991). Expert Systems Reasonable guesses, however, are not very elegant. What is needed, to repeat, is a simplex algorithm that provides solution suggestions. This is where rule based linear programming, expert systems and TE simulations meet. The process has six steps: 1 - The expert system is the overall control program and begins by asking for decision inputs, as usual. 2. Decision inputs are placed into some version of a model such as system (17). 3. A simplex algorithm is invoked to solve the system. 4. Under no solution conditions, the expert system examines the situation and recommends solutions to the administrator r. 5. The administrator selects a solution based upon research or teaching goals. 6. Results are printed including income statements, balance sheets and cash flows. One of the key challenges in this process is to develop the knowledge base for the expert system that recommends the modifications necessary to achieve a solution to whatever model the administrator chooses. But basic linear programming is so well understood that this should be more of a routine than creative task. In fact, such knowledge bases may already be available. If they are, they pose another interesting research problem. What market result differences do different combinations of rule based expert systems and knowledge bases create when applied to the same TE simulations? Once again, the research potential of open system TE simulations is boundless (Patz, 1987). CONCLUSIONS This last statement, more than anything else summarizes the twofold purpose of this paper. That is, open system TE simulations are possible, using a linear programming framework in this case. Second, they do cause a rethinking of economic theory and market or industry research. In this case, the standard Structure→Process→Performance model has been called into question. The Process→Structure→Performance model relaxes the need for a overall, and fixed algorithms in TE simulations. Moreover, going beyond the arguments in this paper, this model suggests that a more general requirement is for TE simulations based upon the following model: Process Structure Performance The simplicity of standard approaches will not suffice for the complex educational and business practices of international economies. Process, structure, and performance interact. They are not arranged in a simple causal fashion. A simple reversal of this linear model emphasizes the point. REFERENCES Charnes, A., & Cooper, W. W. (1961) Management Models and industrial applications of Linear Programming New York: Wiley. Dantzig, G. B. (1963) Linear Programming and Extensions Princeton, NJ: Princeton University Press. Developments In Business Simulation & Experiential Exercises, Volume 20, 1993 89 Dorfman, R., Samuelson, P. A., & Solow, R. M. (1958) Linear Programming and Economic Analysis New York: McGraw-Hill. Erikson, W. J., & Hall, 0. P. (1989). Computer Models for Management Science. (3rd e.) Reading, MA: Addison-Wesley. Ijiri, Y. (1965). Management Goals and Accounting for Control Chicago: Rand- McNally. Patz, A. L. (1981)- Strategic Decision Analysis: A General Management Framework. Boston: Little, Brown. Patz, A. L. (1987) Open system simulations and simulation based research. Development in Business Simulation & Experiential Exercises, 14, 160-1 65. Patz, A. L. (1990) Open system simulation.. In J. W. Gentry (Ed.), Guide to Business Gaming and Experiential Learning Association for Business Simulation and Experiential Learning (ABSEL). New York: Nichols/GP. Patz, A. L. (1991) [Open system testing using linear programming. Unpublished raw data. Winsor, R. D. (1989) A Biogeographic Theory of Market Structure and Competitive Dynamics Unpublished doctoral dissertation, University of Southern California, Los Angeles. Table of Contents Volume 20, 1993 Dominant Personality Types and Total Enterprise Simulation Performance Shelf Wars: A Grocery Channel Simulation Shared Cultural Perspectives: An Experiential Exercise Utilizing International Students to Globalize the Classroom An Instrument for Investigating the Effectiveness of Teaching Methods in the Business Policy and Strategy Formulation Course Providing Better Trained Graduates for Accounting Employers The Ambition Gradient Approach to Evaluation of Computer Simulation Game Team Performance Alphatec: A Negotiation Exercise with Logrolling and Bridging Potential Using the Ideafisher Idea Generation System as a Decision Support System in Marketing Strategy Courses A Dynamic Market Share Allocation Model For Computerized Business Simulations Multi-Cultural Adaptability Using Experiential Learning in a Graduate Course Development of Experiential Applications in HRM: Practicing What Preach and Preaching for Practice Linking Students and Business Leaders Through Portfolios Debriefing International Experiential Learning Exercises: Road Signs for Effectiveness Sales Manager: A Simulation Modeling Interactive Effects in Mathematical Functions for Business Simulations: A Critique of Goosen's Interpolation Reducing the Complexity of Interactive Variable Modeling in Business Simulations Through Interpolation Antecedent Biases of Experiential Learners: Trainee Occupation and Subgroup Diversity Pax in Terra Sancta: Simulating the Middle East Peace Negotiations A Multiple Regression Case In Experiential Learning Changes in Ethnocentric/Geocentric Orientation by Business Students after Exposure to a One Summer Course in International Marketing's A Systematic Approach to the Development and Evaluation of Experiential Exercises Entrepreneurs Evaluate Experiential Education A Linear Programming Approach to Open System Total Enterprise Simulations Reflecting Leader Behavior from the Looking Glass, Inc. Simulation Linking Cognitive Styles, Teaching Methods, Educational Objectives and Assessment: A Decision Tree Approach Restructuring Management Education in Post-Communist Countries: How Western Experts Can Help Managerial and Cultural Pre-Conditions for Superior Performance in a Global Setting: An Experimental Study with the Aid of Business Games Multiple Industries in Computerized Business Gaming Simulations Content or Process? - Content and Process! Some Observations and Reflections About Management Education in Central Europe Out-of-Class Experiences to Promote Volunteerism Enacting the Linguistic Consciousness of the Modern Managerial Mind: Post-Modernism and Experiential Learning Intergrating Experiential Exercises into the College Curriculum: The Case of Internationalizing the Business Curriculum Simulation Marketing Oversights Incorporating Advertising Creative Strategy into Computer-Based Business Simulations The Dynamics of a Partnership Between Business and Education Collaborative Education Done Globally Experiential Systems Analysis CADPLAN: A Simulation for Comparative Advertising A Doctoral Symposium: Preparing Students for Conference Behavior Comparing the Simulation with the Case Approach: Again! Total Quality Management: A Model for Continuous Quality Improvement The Quality Audit: An Experiential Exercise for Business Students Extending the Reach of Simulations: DECIDE Heads for the Inner City Lessons Learned from a Customized Management Development Simulation The Foreign Exchange Spot Trading Simulation Using Lotus 1-2-3 to complete a Triple Play in a Simulated Competition International Business Education: Is Enough Being Done? Matching of Student-Teacher Cognitive Style as a Factor in Student Success in an Introduction to Information Systems Course Breathing (More) Life into the Case Approach Lord of the Flies: A Live Case Approach to Leadership Cooperative Case Studies: Experiential Tools for Teaching Business Problem Solving Tools Strategy Simulations in Context: An Evaluation of Key Dimensions The Distribution Channel Game Evaluation of a Simulation Game as an Education Tool for Utility Professionals The Relationship Between Total Enterprise Simulation Performance and Learning Total Quality Management does not Happen by Magic, but it can be Taught Using a Pedagogical Methodology that Utilizes Magic Effectively Preparing Students for Careers in a Global Environment by Integrating Total Quality Management Thoughout the Business Curriculum An Empirical Investigation of Cognitive and Performance Consistency in a Marketing Simulation Game Environment Using MARSGAP with LAPTOP: (A Marketing Simulation Game Analysis Program) with LAPTOP: A Marketing Simulation Adapting TQM Implementation to Organizational Level An MBA Business Simulation: Executive Interaction Experiential Exercises and Pedagogy Track Workshop: Experiencing Cultural Diversity in the Classroom (and the Hotel Meeting Room) Closing the Gap between Corporate and National Culture The Dynamic Manufacturing Company The Use of Experiential Techniques in Corporate Training The State of Simulation Gaming in Easter European Countries- Principally Russia An Experiential Exercise in Cross-Cultural Training Valuing Differences: A Conceptual Framework Demonstration of an Experiential Exercise Effectively Using Experiential Learning to Impart TQM Concepts in a High Technology Environment The Older Worker Questionnaire: An Exercise Concerning Older Worker Stereotypes and Behaviors The Crime Fighting Task Force: An Exercise in Organizational Politics Welcome to the Party! An Expression of Vocational Preference Experiential Exercise for Imparting Cross-Cultural Appreciation Six Swift Simulations on Globalization Overview of BASF Delegate Program