Metaheuristics and a matheuristic for solving the facility layout problem in the presence of alternative process plans and machine redundancy

¹ Department of Logistics, Tourism, and Services Management, German University of Technology in Oman, P. O. Box 1816, PC 130, Muscat, Oman
² Faculty of Engineering, Urmia University, Urmia, Iran
³ Department of Economics and Management, University of Brescia, Brescia, Italy

^* Corresponding author: mehdi.kamran@gutech.edu.om

Received: 10 May 2024
Accepted: 20 July 2025

Abstract

This research tackles a crucial aspect of manufacturing system design: optimizing the Facility Layout Problem (FLP). We address a specific scenario involving multiple products with flexible processing plans on various machines in a job-shop environment. Redundant machines of each type exist, with known acquisition costs and capacities. Processing times and production volumes for each product are also pre-determined. An integer non-linear mathematical model is formulated to represent the problem. While a linearization technique is applied, the inherent NP-hardness renders exact solution methods impractical for medium to large-scale problems. To address this, three algorithms are proposed: a matheuristic, Iterated Local Search (ILS), and a Genetic Algorithm (GA). These are evaluated based on solution quality, runtime, and robustness across diverse problem instances. Results demonstrate the superiority of the ILS algorithm in terms of solution quality, robustness, and overall effectiveness. These findings offer valuable guidance for decision-makers seeking optimization tools for FLPs. The ILS’s consistent delivery of high-quality solutions with minimal variation makes it a reliable choice. Additionally, as many facility layout decisions are tactical or strategic – where computational time is less critical – the matheuristic demonstrates acceptable performance and holds promise for handling problems of varying sizes and complexities. To further validate the effectiveness and demonstrate the practical applicability of our proposed solution methodology, the ILS and matheuristic algorithms were applied to a real-world layout design case adapted from the literature. The results once again confirm the strong performance of both methods in terms of solution quality, computational efficiency, and robustness.