Multilevel Facility Location Optimization: A Novel Integer Programming Formulation and Approaches to Heuristic Solutions

Abstract: We attack the 4-level facility location problem (4L-FLP), a critical component in supply chains. Foundational tasks here involve selecting markets, plants, warehouses, and distribution centers to maximize profits while considering related constraints. Based on a variation of the quadratic assignment problem, we propose a novel integer programming formula that significantly reduces the variables. Our model incorporates several realistic features, including transportation costs and upper bounds on facilities at each level. It accounts for one-time fixed costs associated with selecting each facility. To solve this complex problem, we develop and experimentally test two solution procedures: a multi-start greedy heuristic and a multi-start tabu search. We conduct extensive sensitivity analyses on the results to assess the reliability of proposed algorithms. This study contributes to improved solution methods for large-scale 4L-FLPs, providing a valuable tool for supply chain maturity.