Title: On efficient solutions to bi-objective max-linear programming problems

Authors: Abdulhadi Aminu; Sunday E. Olowo; Salisu Usaini

Addresses: Department of Mathematics, Aliko Dangote University of Science and Technology, Wudil, PMB 3244, Kano, Nigeria ' Department of Computer Sciences and Statistics, Federal College of Agricultural Produce Technology, Plot 54-56, Hotoro CBN Quarter, Kano, Nigeria ' Department of Mathematics, Aliko Dangote University of Science and Technology, Wudil, PMB 3244, Kano, Nigeria

Abstract: A number of methods for determining solutions to max-linear programming problems with one objective function have been developed. In this work, we introduce the concept of a bi-objective max-linear programming problem subject to two sided constraints (BOMLP) for both minimisation and maximisation cases, then we proposed two methods for determining efficient solutions to the problem and developed improved algorithms based on an alternating and bisecting method of solving two sided max-linear system. Performance of the methods were compared based on effectiveness, user friendliness and task time, in fact the second method is found to be faster than the first method, some numerical examples were considered to test the problems using MATLAB software.

Keywords: bi-objective max-linear programming; two-sided system; optimal solution; efficient solution; pseudo-polynomial algorithms.

DOI: 10.1504/IJMOR.2025.147859

International Journal of Mathematics in Operational Research, 2025 Vol.31 No.3, pp.339 - 371

Received: 27 Aug 2023
Accepted: 31 Aug 2023
Published online: 05 Aug 2025 *

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