An exact method for optimizing two linear fractional functions over the efficient set of a Multiobjective Integer Linear Fractional Program

TL;DR

This paper introduces an exact Branch and Bound method combined with cutting planes to efficiently optimize two fractional linear functions over the efficient set of a multiobjective integer linear fractional program, avoiding exhaustive enumeration.

Contribution

It presents a novel exact solution approach for bi-criteria fractional multiobjective integer linear programs using combined Branch and Bound and cutting plane techniques.

Findings

The method effectively finds optimal solutions without enumerating all efficient solutions.

Computational results demonstrate the efficiency of the proposed approach.

An illustrative example validates the method's applicability.

Abstract

In this paper, an exact method is proposed to optimize two fractional linear functions over the efficient set of a fractional multiobjective linear problem (MOILFP). This type of problems is encountered when there are two decision makers and each has his own utility function that he wants to optimize over the efficient set of multiobjective problem. The proposed method uses Branch and Bound method combined with a cutting plane technique to find the efficient solutions for both utility functions and (MOILFP) without going through all the efficient solutions of the two problems. An illustrative example and a computational study are reported.