On the Efficiency of Feasible Solutions of a Multicriteria Assignment Problem

The particular structure of the assignment problem made of it a very popular subject of study and an important research tool in operations research and management science. In addition to the importance that the assignment problem represents in its own, it can appear as a relaxation of more complex combinatorial optimization problems. That is why the assignment problem has received great attention from the operations research community. The assignment problem may appear as an optimization problem with multiple objectives. In this paper, we address the problem of efficiency of feasible solutions of a multicriteria assignment problem. It is done in two steps. In the first step, we determine whether or not a given feasible solution of a multicriteria assignment problem is efficient. In a second step, if the feasible solution is not efficient, we provide an efficient solution that dominates it. The proposed method consists of transforming the original problem into an assignment problem with side constraints for which solution techniques already exist.