Title: Solving mixed integer linear programming problems with bounded variables by the adaptive method

Authors: Houria Boussouira; Mohand Ouamer Bibi

Addresses: Research Unit LaMOS, Department of Operations Research, Faculty of the Exact Sciences University of Bejaia, 06000, Bejaia, Algeria ' Research Unit LaMOS, Department of Operations Research, Faculty of the Exact Sciences University of Bejaia, 06000, Bejaia, Algeria

Abstract: In this paper, we elaborate a new cut for mixed integer linear programming (MIP) with upper and lower bounded variables. The obtained problems are solved by the adaptive method developed by Gabasov and Kirillova (1980) for solving linear programming problems. This algorithm allows solving directly the considered problem, without modifying it and avoids the drawbacks of the increase in the number of the variables and the constraints. In order to compare our method with the intlinprog method of the MATLAB optimisation toolbox, numerical experiments on randomly generated test problems are presented, that involve the CPU time.

Keywords: mixed integer linear programming; MIP; generating valid inequalities; adaptive method.

DOI: 10.1504/IJMOR.2025.150904

International Journal of Mathematics in Operational Research, 2025 Vol.32 No.4, pp.491 - 510

Received: 25 Dec 2023
Accepted: 05 Jan 2024
Published online: 05 Jan 2026 *

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