An enhanced conversion scheme for lexicographic, multiobjective integer programs

Abstract

A number of approaches have been proposed (and several implemented) for the solution of lexicographic, multiobjective programming problems. These approaches may be divided into two classes. The first encompasses the development of algorithms specifically designed to deal directly with the initial model while the second attempts to transform, efficiently, the lexicographic, multiobjective model into an equivalent, single objective programming problem. This second approach would appear particularly attractive since it permits the use of conventional, readily available, mathematical programming software. In this paper we address a particular form of the lexicographic, multiobjective model; specifically one in which all functions are linear and all variables integer. It is then shown how a recently developed scheme for the transformation of this model may be substantially improved. As a result, lexicographic, multiobjective integer linear programs may be easily converted into conventional linear integer programs wherein the magnitude of the objective function coefficients are minimized.