Computation of a multi-choice goal programming problem

The standard goal programming problem allows decision maker to assign an aspiration level to an objective function. In real life decision making problems, the decision maker always seeks for suitable aspiration level i.e. “the more suitable the better”. Therefore, a decision maker is allowed to assign multiple number of aspiration levels to an objective function. The aim of the decision maker is to select an appropriate aspiration level for an objective function that minimizes the deviations between the achievement of goal and the aspiration levels. The traditional goal programming techniques cannot be used for solving such type of multi-choice goal programming problem. This paper presents an equivalent model of the multi-choice goal programming problem by using Vandermonde’s interpolating polynomial, binary variables and least square approximation method. The equivalent model is solved by existing method/software. Two illustrative examples are presented in support of the proposed methodology.