Efficient Solution Methods for Large-Scale 4-Level Facility Location Problems

Proceedings of the 9th International Conference on Advanced Research in Business, Management and Economics

Year: 2025

DOI:

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Efficient Solution Methods for Large-Scale 4-Level Facility Location Problems

Bahram Alidaee, Haibo Wang

ABSTRACT:

This paper addresses the 4-level facility location problem (4L-FLP), a critical component in the design of supply chains. The 4L-FLP involves selecting markets, plants, warehouses, and distribution centers to maximize profits while considering various constraints. We propose a novel integer programming formulation based on a variation of the quadratic assignment problem, significantly reducing the number of variables. Our model incorporates several realistic features, including transportation costs, upper bounds on the number of facilities selected at each level, and one-time fixed costs associated with selecting each facility. 4L-FLP is a complex problem that has received significant attention in the literature. However, existing studies often assume that all customers must be served and that all plants are pre-identified, which is not always true in real-world scenarios. Our approach takes a more holistic and realistic view, where markets, plants, warehouses, and distribution centers are selected from available options. To solve this complex problem, we develop and experimentally test two solution procedures: a multi-start greedy heuristic and a multi-start tabu search. First, we propose a novel integer programming formulation that reduces the number of variables. Second, we develop and test two solution procedures that effectively solve large-scale 4L-FLPs. Our results show that these procedures are effective in solving large-scale 4L-FLPs. Our study contributes to developing efficient solution methods for realistic large-scale 4L-FLPs, providing a valuable tool for supply chain designers and managers.

keywords: Facility Location Problem (FLP), Integer Programming, Large-Scale Optimization, Multi-Level Supply Chain, Quadratic Assignment Problem (QAP)