Generalized transformation techniques for multi-choice linear programming problems

Abstract

The multi-choice programming allows the decision maker to consider multiple number ofresources for each constraint or goal. Multi-choice linear programming problem can not be solveddirectly using the traditional linear programming technique. However, to deal with the multi-choiceparameters, multiplicative terms of binary variables may be used in the transformed mathematicalmodel. Recently, Biswal and Acharya [2] have proposed a methodology to transform the multi-choicelinear programming problem to an equivalent mathematical programming model, which can accommodate a maximum of eight goals on the right hand side of any constraint. In this paper we present twomodels as generalized transformation the multi-choice linear programming problem. Using any one ofthe transformation techniques a decision maker can handle a parameter with finite number of choices.Binary variables are introduced to formulate a non-linear mixed integer programming model. Using anon-linear programming software optimal solution of the proposed model can be obtained. Finally, anumerical example is presented to illustrate the transformation technique and the solution procedure.