Mathematical Modeling with Multidisciplinary Applications

CHAPTER 16

THE GOAL PROGRAMMING MODEL: THEORY AND APPLICATIONS

BELAID AOUNI¹, CINZIA COLAPINTO² AND DAVIDE LA TORRE³

¹School of Commerce and Administration, Laurentian University, Canada

²Department of Management, Ca’ Foscari University of Venice, Italy

³Department of Economics, Management and Quantitative Methods, University of Milan, Italy

16.1 MULTI-CRITERIA DECISION AID

In any kind of organization, managers are frequently challenged with complex decision making situations which involve several, and often conflicting, objectives and priorities. In fact, the decision setting is unstable because of corporate politics, market conditions or regulations’ changes. The decision-making is central within organizations, and managers have to make the best choices, substituting objective issues for casual judgments. The classical and easiest formulation of a decision-making model usually involves an objective function f, which has to be optimized, depending on a set of decision variables and subject to some constraints. The model can be mathematically stated as

(16.1)

subject to

(16.2)

where the set D describes in compact form the set of all possible constraints. D is called the feasible set and, in general, it is a subset of R^m (that is the set of all m-tuples of real numbers). For instance, ...