Transformation of a multi-choice linear programming problem

摘要

The aim of this paper is to transform a multi-choice linear programming problem to a standard mathematical programming problem where the right hand side goals of some constraints are ‘multi-choice’ in nature. For each of the constraint there may exist multiple number of goals, out of which exactly one is to be chosen. The selection of goals should be in such a manner that the combination of choices for each constraint should provide an optimal solution to the objective function. There may be more than one combination which will provide an optimal solution. However the problem cannot be solved by standard linear programming techniques. In order to solve the present multi-choice linear programming problem, this paper proposes a new transformation technique. Binary variables are introduced in the transformation technique to formulate a non-linear mixed integer programming model. Using standard 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.