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<p>In the context of increasing industrial complexity and competitive manufacturing environments, the efficient design of facility layouts has become a key factor for improving material handling performance and reducing operational costs. This paper addresses the Multi-Row Facility Layout Problem (MRFLP), a challenging combinatorial optimization problem characterized by complex spatial, operational, and economic constraints. A comprehensive mixed-integer linear programming (MILP) model is proposed to determine the optimal assignment and positioning of machines across multiple rows while minimizing material flow distances and row utilization costs. To analyze model effectiveness, three alternative single-objective configurations are first evaluated on a single small-scale instance using the CPLEX solver: minimizing material flow distance, minimizing row utilization costs, and minimizing an aggregated objective combining both criteria. Based on these preliminary experiments, the aggregated objective is subsequently tested on multiple instances to assess the robustness and computational limits of CPLEX as problem size increases. The results show that CPLEX provides optimal solutions for small and medium-sized instances, but its performance deteriorates significantly as problem size increases. To address this limitation, a Genetic Algorithm (GA) is developed to efficiently solve large-scale instances. The proposed GA is validated on eight benchmark instances, achieving a gap below 3% and reaching optimal solutions in most cases. A scalability analysis further demonstrates the ability of the model to automatically identify the cost-efficient number of active rows. In addition, a sensitivity analysis highlights the influence of key parameters, including clearance distances, row cost coefficients, and layout width, on solution quality and layout compactness. Overall, the results indicate that the proposed framework is effective and scalable, making it suitable for practical multi-row facility layout design.</p>

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MILP based–genetic algorithm framework for multi-row facility layout optimization under spatial and cost constraints

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Sara Fatima Zohra Megaiz,
  • Fouad Maliki,
  • Mehdi Souier,
  • Mohammed Dahane

摘要

In the context of increasing industrial complexity and competitive manufacturing environments, the efficient design of facility layouts has become a key factor for improving material handling performance and reducing operational costs. This paper addresses the Multi-Row Facility Layout Problem (MRFLP), a challenging combinatorial optimization problem characterized by complex spatial, operational, and economic constraints. A comprehensive mixed-integer linear programming (MILP) model is proposed to determine the optimal assignment and positioning of machines across multiple rows while minimizing material flow distances and row utilization costs. To analyze model effectiveness, three alternative single-objective configurations are first evaluated on a single small-scale instance using the CPLEX solver: minimizing material flow distance, minimizing row utilization costs, and minimizing an aggregated objective combining both criteria. Based on these preliminary experiments, the aggregated objective is subsequently tested on multiple instances to assess the robustness and computational limits of CPLEX as problem size increases. The results show that CPLEX provides optimal solutions for small and medium-sized instances, but its performance deteriorates significantly as problem size increases. To address this limitation, a Genetic Algorithm (GA) is developed to efficiently solve large-scale instances. The proposed GA is validated on eight benchmark instances, achieving a gap below 3% and reaching optimal solutions in most cases. A scalability analysis further demonstrates the ability of the model to automatically identify the cost-efficient number of active rows. In addition, a sensitivity analysis highlights the influence of key parameters, including clearance distances, row cost coefficients, and layout width, on solution quality and layout compactness. Overall, the results indicate that the proposed framework is effective and scalable, making it suitable for practical multi-row facility layout design.