What is OR

Role of Mathematical Models

G. D. Eppen, F. J. Gould, C. P. Schmidt, J. H. Moore, and L. R. Weatherford, Introductory Management Science, 5th edition (Upper Saddle River, NJ: Prentice Hall, 1998), 2-24.

At the center of operations research practice and theory is a diverse set of mathematical models that are used to capture and explore a wide-range of real-world settings. An operations research model is a mathematical abstraction or simplification of reality. The degree of simplification is a function of data availability, time and resources available to develop the model and the situational issues and decisions that the model is designed to address. With a mathematical model in hand, the operations researcher can work with managers and decision makers to evaluate decision alternatives or system redesign. These analyses are typically carried out in a computer implementation of the model that enables the decision makers and managers to explore changes in the mathematical representation without changing the actual system. Eppen and others (1998) discuss the role of a mathematical model in decision making
  • Make objectives explicit
  • Identify decisions that influence objectives
  • Clarify tradeoffs amongst decisions and objectives
  • Require identification and definition of quantifiable variables
  • Explore the interaction between variables
  • Help identify critical data elements and their role as model inputs
  • Assist in recognizing and clarifying constraints on decisions and operations
  • Facilitate communication
One drawback of mathematical modeling is by definition the emphasis on quantifiable measures. As a result a decision maker may ignore critical organizational issues and concerns that may be difficult to quantify. In addition, the word "optimization" is an integral part of the vocabulary of the operations researcher. This term may lead the unsophisticated model user to expect more from the model than it is really able to deliver and to rely on the model's results more than he should. Ideally, a model should be used as J. D. C. Little suggested, "to update the intuition of a decision maker". Also the term optimal should be viewed as " model-related rather than a real-world concept. One optimizes models, but rarely, if ever, real-world situations." (Eppen et al. 1998)

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