(A) modified benders' decomposition for multiple choice mixed integer programming problems

Abstract

When applied to Mixed Integer Programming (MIP) problems, Benders`` iterative scheme considers two types of problem ; (1) an LP subproblem determined by fixing integer variables iteratively to a solution, (2) the relaxed pure integer program for solving the equivalent version of the original MIP problem. From the computational point of view, one major drawback of this method is that is requires solving (2) at each iteration. But when the integer part of MIP is of multiple choice type, (2) can be solved efficiently by sum-ranking method. This ranking-based modification is exploited in this paper. It assigns the priorities to the integer variables, which are determined by the amount of possible contribution to the objective value and it also defines another LP subproblem which calculates the decrease in the objective value due to the change in the righthand side. The modification is explained in comparison with the original Benders`` Decomposition and finally an illustrative example and limited computational results are given.