A PARAMETRIC SIMPLEX METHOD FOR OPTIMIZING A LINEAR FUNCTION OVER THE EFFICIENT SET OF A BICRITERIA LINEAR PROBLEM

The problem of optimizing a linear function over the e-cient set of a multiple objective problem has many applications in multiple crite- ria decision making. The main di-culty of this problem is that its feasible region, in general, is a nonconvex set. In this paper we develop a fast algorithm for optimizing a linear function over the e-cient set of a bicri- teria linear programming problem. The method is a parametric simplex procedure using one parameter in the objective function.