MODELING THE HUMAN COMPONENT OF COMPUTERIZED BUSINESS SIMULATIONS Developments in Business Simulation & Experiential Exercises, Volume 16, 1989 37 MODELING THE HUMAN COMPONENT OF COMPUTERIZED BUSINESS SIMULATIONS Precha Thavikulwat, Towson State University ABSTRACT The effects of recruitment, benefits, training, and labor cost on the human component of production can be modeled plausibly by the concave exponential, convex exponential, logistic, and cusp catastrophic functions, respectively. When continuous mathematical functions such as these are used in computerized business simulations, the student who researches the algorithms of the simulation will develop a deep understanding of the mathematics. This deep understanding may be more valuable than the surface understanding of business that such simulations nominally teach. INTRODUCTION Since Pray and Gold’s (1982) analysis of the demand functions of published computerized business simulations, a lively discussion has ensued on the problem of modeling demand (Decker, LaBarre, & Adler , 1987; Frazer, 1983; Gold & Pray, 1983, 1984; Golden, 1987; Goodsen, 1986; Lambert & Lambert, 1988; Thavikulwat, 1988). The problem of modeling supply, however, has tended to be neglected. Yet, the supply side of modeling presents issues that are at least as involved as those of the demand side. In particular, how best to incorporate the human component of the supply side is an interesting problem in the design of such simulations. This problem can be approached in four ways: First, the human aspect of the human resources can be ignored. Thus, human resources would be modeled linearly, as if they were another kind of material resource. Second, the human aspect could be inserted by the administrator. Thus, the administrator would change worker productivity, cause workers to quit, or call strikes (Dickson & Kinney, 1982). Third, ad hoc algorithms based on ‘research findings, conventional wisdom, common sense, and . supposition" (Estes, 1986) could be incorporated. Fourth, continuous nonlinear functions could be utilized. The first approach of using Linear models is expedient, but it gives rise to implausible results. The second approach of administrative intervention is flexible, but it makes the simulation difficult to administer. The third approach of using ad hoc algorithms suffers because ad hoc rules have no generality. Thus, the fourth approach would be ideal, provided suitable functions can be found. This paper proposes that the concave exponential, covex exponential, logistic, and cusp catastrophic (Thom, 1975) functions constitute a set of continuous nonlinear functions that can plausibly model the effects, respectively, of recruitment, benefits, training, and labor cost on the human component of production. THE MODELS Recruitment Recruitment serves primarily to raise the productivity of new hires. As recruitment cost rises, the productivity of new hires should rise also, but at a diminishing rate until it finally levels off. These characteristics can be captured by a concave exponential function moderated by three parameters: base productivity, recruitment asymptote, and recruitment reaction. The function is graphed in Figure 1, and is defined as follows Benefits Benefits serve primarily to lower attrition. As benefits cost rises, the rate of attrition should decrease, but at a diminishing rate until it finally levels off. These characteristics can be captured by a convex exponential function moderated by three parameters: attrition asymptote, attrition reaction, and attrition base. The function is graphed in Figure 2, and is defined as follows: Developments in Business Simulation & Experiential Exercises, Volume 16, 1989 38 Training Training serves primarily to raise the productivity of trained employees who remain with the firm following the period of training. As training cost rises, the productivity of trained employees should rise also. Because training cost directly affects training quality and because fatigue limits people’s ability to benefit from training, the effectiveness of training should be most sensitive to training cost when the training cost is moderate, and it should eventually level off at higher levels of training cost. These characteristics can be captured by a logistic function moderated by four parameters: training asymptote, training base, training reaction, and training inflection. This S-shaped function is graphed in Figure 3, and Is defined as follows: Labor Cost Labor cost, combining salaries and wages, directly affect the size of the labor pool. The effect of labor cost, however, is contingent upon the productivity of labor. The more productive the labor, the higher the labor cost that should be required to maintain a labor pool of a given size. Because people are capable of collective action, the labor pool should be subject to discontinuities occasioned by strikes and settlements of strikes. These characteristics can be captured by a cusp catastrophic function moderated by eight parameters: asymmetry intercept, asymmetry labor cost, asymmetry productivity, bifurcation intercept, bifurcation labor cost, bifurcation productivity, labor pool midpoint, and labor pool deviation. The cusp catastrophic function is a three-dimensional cubic function, as illustrated in Figure 4. A two-dimensional cross section is shown in Figure 5, and the function is defined as follows: Developments in Business Simulation & Experiential Exercises, Volume 16, 1989 39 The cusp catastrophe is an element of catastrophe theory, which is a relatively recent method of applying topographical mathematics to the modeling of divergent and discontinuous phenomena by the use of continuous functions (Stewart & Peregoy, 1983; Zeeman, 1976). In catastrophe theory, discontinuities are represented by folds. Thus, in the cross-section of Figure 5, the edges of the two folds represent the strike and settlement points. The backward sloping region between the two edges represents a region of instability. Movement along the curve follows Path 1 in the forward direction and Path 2 in the reverse direction. Movement does not take place in the backward sloping region. DISCUSSION The concave exponential, convex exponential, logistic, and cusp catastrophic functions can model the effects of recruitment, benefits, training, and labor cost on the human component of production. Thus, a simulation incorporating these functions should be a useful device for teaching students about them. With the easy availability of sophisticated equation-solving programs, such as MathCAD (Mathsoft, 1987), solving nonlinear functions has become an exercise simple enough for undergraduate college students. Students who work with business simulations often show great interest in the computational algorithms of the simulation, for a very sensible reason--to win. Success in simulation depends on decisions that fit the algorithms. Thus, if the algorithms are ad hoc, the intelligent student will learn ad hoc rules that have no real-world appLication. On the other hand, if the aLgorithms are continuous mathematical functions, the intelligent student will learn about the functions, and wiLl leave the simulation with an understanding of the mathematics. In time, this deep understanding of mathematics, the science of patterns (Steen, 1988), may be more valuable to the student than the surface understanding of business that the simulation nominally taught. Thus, the algorithms of business simulations ought to consist of continuous mathematical functions such as those proposed here. REFERENCES Decker, Ronald, James LaBarre, and Thomas Adler (1987), “The Exponential Logarithm Function as an Algorithm for Business Simulation,” Developments in Business Simulation & Experiential Exercises, 14, 47- 49. Dickson, Elmer C., and Kinney, Paul T. (1982), “A New Generation in Business Simulation,’ Developments in Business Simulation & Experiential Exercises, 9, 256- 259. Estes, James E. (1986), “But What Will the Workers Do?” Simulation and Games, 17, 245-262. Frazer, J. Ronald (1983), “A Deceptively Simple Business Strategy Game,” Developments in Business Simulation & Experiential Exercises, 10, 98-100. Gold, Steven C. and Thomas F. Pray (1983), “Simulating Market and Firm Level Demand--A Robust Demand System,” Developments in Business Simulation and Experiential Exercises, 10, 101-106. Developments in Business Simulation & Experiential Exercises, Volume 16, 1989 40 Gold, Steven C. and Thomas F. Pray (1984), “Modeling Non-Price Factors in the Demand Functions of Computerized Business Simulations,” Developments in Business Simulation and Experiential Exercises, Li, 240-243. Golden, Peggy A. (1987), ”Demand Generation in a Service Industry Simulation: An Algorithmic Paradox,” Developments in Business Simulation and Experiential Exercises, 14, 67-70. Goodsen, Kenneth R. (1981), “A Generalized Algorithm for Designing and Developing Business Simulations,” Developments in Business Simulation and Experiential Exercises, 8, 41-47. Goodsen, Kenneth R. (1986), “An Interpolation Approach to Developing Mathematical Functions for Business Simulations,” Developments in Business Simulation and Experiential Exercises, 13, 248-255. Lambert, Nancy. L. and David R. Lambert (1988), “Advertising Response in the Gold and Pray Algorithm: A Critical Assessment,” Developments in Business Simulation and Experiential Exercises, 15, 188-191. Mathsoft, Inc. (1987) MathCAD (Computer program]. Cambridge, MA: Mathsoft, Inc. Pray, Thomas F. and Steven Gold (1982), “Inside the Black F ox: An Analysis of Underlying Demand Functions in Contemporary Business Simulations,” Developments in Business Simulation and Experiential Exercises, 9, 110-116. Steen, Lynn A. (1988), “The Science of Patterns,” Science, 240, 611-616. Stewart, I. N. & Peregoy, P. L. (1983), “Catastrophe Theory Modeling in Psychology,” Psychological Bulletin, 94, 336-362. Teach, Dick D. (1984), ‘Using Spatial Relationships to Estimate Demand in Business Simulations,” Developments in Business Simulation and Experiential Exercises, 11, 244-246. Thavikulwat, Precha (1988), ‘Simulating Demand in an Independent-Across-Firms Management Game,” Developments in Business Simulation and Experiential Exercises, 15, 183-187. Zeeman, E. C. “Catastrophe Theory,” Scientific American, 1976, 234 (4), 65-83. Table of Contents Volume 16, 1989 Quality Control Circles (QC™s): Towards a Computerized Simulation The Canadian Hospital Executive Simulation System (CHESS) The Impact of Using Group Performance Evaluation as an Experiential Exercise The Impact of Leader and Team Member Characteristics Upon Simulation Performance: A Start-Up Study Planning for Career Success: Is Where you are Going Where you Really Want to Be? The Production Frontier: Modeling Production in the Computerized business Simulation A Study of the Need for Valid Business Game Algorithms Modeling the Human Component of Business Simulations A Stimulating Simulation in International Business Business Ethics, Experiential Exercises and Simulation Games Collective Bargaining Simulation: Adding Reality Through Point Scoring The Use of Experiential Teaching Techniques: Creativity vs. Conformity Visualization and Guided Imagery in the Organization Behavior Class: An Experiential Exploratory Approach Arranging an Agenda: An Activity on Running Better Meetings Harried Harry: An Experiential Capstone for Students of Organizational Behavior Coping with Stress: An Experiential Exercise Fairness in the Classroom: An Empirical Extension of the Notion of Organizational Justice A Study of the Relationship Between Student Final Exam Performance and Simulation Game Participation Competency Based Development: A Management Development Exercise Simulation Performance Revisited: The Fit Between Instructor Style and Learning Style An Evaluation and Application of an Instrument for Measuring Pedagogical Effectiveness A Knowledge Based System to Support Reasoning by Analogy for Business Simulation Gaming using Forecasting Accuracy as a Measure of Success in Business Simulations The Development of Algorithmic Functional Business Games Strategy Design, Process and Implementation in an Unstable/Complex Environment: A Second Exploratory Study Simulation Integration Contrasts Between MBAs and Undergraduates in the Capstone Policy Course An Investigation of the Real World Usefulness of a Strategy and Policy Course Using a Business Simulation Framework Duel (sic) Views of Internships, as Experiential Learning The Impact of Decision Support Systems on the Effectiveness of Small Group Decisions - An Exploratory Study An Investigation of the Relationship Between Formal Planning and Simulation Team Performance Under Changing Environmental conditions Sensitivity Analysis with the Complete IFPS/Personal Student Analysis Package: A marketing Decision Support System A New Approach to Teaching Salesmanship using Persona, Microskills, and a Sales Process A Rational Case for Synthetic Experience as a Prime Ingredient in the Marketing Curriculum SalesHire: A Microcomputer-Based Salesperson Selection Exercise TRANSECON: An Interactive Program for Learning Transportation Economics Hypercard as a Construction Tool for Short Instructional Exercises A Game to Introduce Accounting Information Systems Students to Certain Internal Control Concepts "Commitments" - A Demonstration Proposal An Analysis of Popular Games as Experiential Models for Corporate and Collegiate Management Education An Exploratory Study of the Effects of Strategic Emphasis in Management Games on Attitudes, Interest, and learning in the Business Policy Course Predicting Individual Decision Making Performance in a Business Simulation: An Empirical Study Strategic Planning And Organizational Performance In A Business Simulation: An Empirical Study, PAM (Planning Action Management) Simulation of a District Sales Territory Lifelong Learning and ABSEL: An Inquiry on Definitions and Relationships A Review of Salient Trends in Proceedings: A Fifteen year (1974 - 1988) Review of ABSEL Contributorship