Generalized Transformation Techniques for Multi-Choice Linear Programming Problems
DOI:
https://doi.org/10.11121/ijocta.01.2013.00132Keywords:
Linear programming, mixed integer programming, multi-choice programming, non-linear programming, transformation technique.Abstract
The multi-choice programming allows the decision maker to consider multiple number of resources for each constraint or goal. Multi-choice linear programming problem can not be solved directly using the traditional linear programming technique. However, to deal with the multi-choice parameters, multiplicative terms of binary variables may be used in the transformed mathematical model. Recently, Biswal and Acharya (2009) have proposed a methodology to transform the multi-choice linear programming problem to an equivalent mathematical programming model, which can accommodate a maximum of eight goals in righthand side of any constraint. In this paper we present two models as generalized transformation of the multi-choice linear programming problem. Using any one of the transformation techniques a decision maker can handle a parameter with nite number of choices. Binary variables are introduced to formulate a non-linear mixed integer programming model. Using a non-linear programming software optimal solution of the proposed model can be obtained. Finally, a numerical example is presented to illustrate the transformation technique and the solution procedure.
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