Abstract
The problem (P) of optimizing a linear function $d^Tx$ over the set of efficient points for a multiple objective linear program (M) is difficult because the efficient set is nonconvex. There are some interesting properties between the objective linear vector d and the matrix of multiple objectives C and those properties lead us to establish criteria to solve (P) with a linear program. In this paper we investigate a system of the linear equations $C^T{\alpha}$ = d and construct two linearly independent positive vectors u, v such that ${\alpha}$ = u - v. From those vectors u, v, solving an weighted sum linear program for finding an efficient extreme point for the (M) is a way of getting an optimal solution of the problem (P). Therefore the theorems presented in this paper provided us an easy way of solving nonconvex program (P) with a weighted sum linear program.
