Optimization over the efficient set of a parametric multiple objective linear programming problem

Abstract

In this paper we consider the problem ( P) for optimizing a function over the efficient set of a multiple objective linear programming (MOLP) problem with parameters in the right hand side vector. Three solution algorithms in a most general case of problem ( P) and improvements of them in some special cases are presented. In the case when the objective function of problem ( P) is linear, it can be solved based on | T 2| linear programming problems with mixed one-zero integer variables if the parametric set is finite and based on | T 2| linear programming problems if the right hand side vector of the MOLP problem is a linear function of the parameters and the parametric set is a polyhedron, where | T 2| is, in general, the number of maximal efficient faces of the MOLP problem corresponding to a value of the parameters. A numerical example is given to illustrate the working of the algorithms.