The problem of optimizing a real valued function over the efficient set of a multiple objective linear program has some applications in multiple objective decision making. The main difficulty of this problem arises from the fact that its feasible domain, in general, is nonconvex and not given explicitly. In this paper we formulate this problem as a linearly constrained convex-concave program where the number of “nonconvex variables” is just equal to the number of independent criteria. We propose inner and outer procedures to constructing an initial set allowing convex-concave programming decomposition methods to be applied.