Title: Computing Pareto set in the criterion space for bicriteria linear programs using a single criterion software

Authors: François Dubeau; Marie Emmanuel Ntigura Habingabwa

Addresses: Department of Mathematics, Sherbrooke University, Sherbrooke (Qc), J1K 2R1, Canada ' Department of Mathematics, Sherbrooke University, Sherbrooke (Qc), J1K 2R1, Canada

Abstract: In case of a mathematical programming problem with conflicting criteria, the Pareto set is a useful tool for a decision-maker. Based on the geometric properties of the Pareto set for a bicriteria linear program, we present a simple method to compute this set in the criterion space. We describe completely the algorithm and analyse its complexity. We illustrate the method by solving in details two simple examples. It is important to observe that the method requires only a basic linear program solver.

Keywords: bicriteria linear program; efficient set; Pareto set; criterion space; weighted-sum.

DOI: 10.1504/IJOR.2022.122810

International Journal of Operational Research, 2022 Vol.43 No.4, pp.437 - 450

Accepted: 31 May 2019
Published online: 13 May 2022 *

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