Optimizing a linear fractional function over the integer efficient set

Abstract

In this article, a new exact method is proposed to solve a problem, say \((ILFP)_E\), of maximizing a linear fractional function over the integer efficient set of multi-objective integer linear programming problem (MOILP). The method is developed through the branch and cut technique and the continuous linear fractional programming, to come up with an integer optimal solution for problem \((ILFP)_E\) without having to explicitly list all efficient solutions of problem (MOILP). The branching process is strengthened by an efficient cut as well as an efficiency test so that a large number of non-efficient feasible solutions can be avoided. Illustrative example and an experimental study are reported to show the merit of this new approach.