Inverse Linear Goal Programming Problem

Abstract

This paper considers the inverse linear goal programming problem of multi-objective function in case the change in coefficient of the objective function. Let denote the set of feasible solutions points of linear goal programming problem of a multi-objective function, and let be the positive and negative deviation variables of the maximum and minimum goals respectively, be a specified cost vector, be given feasible solution vector, and be given tow vectors denoted the feasible positive deviation and the feasible negative deviation points of the max or min goals, respectively. The inverse linear goal programming problem of multi-objective function is as follows: Consider the change of the cost vectors as less as possible such that the vectors feasible solution becomes an optimal solution of LGP of multi-objective function under the new cost vectors and is minimal, where is some selected -norm. In this paper, we consider the inverse version ILGP of LGMP. under the -norm where the objective is to minimize , with denoting the index set of variables . We show that the inverse version of the considered under -norm reduces to solving a problem for the same kind; that is, an inverse multi-objective assignment problem reduces to an assignment problem.