{"ID":2880009,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.15954","arxiv_id":"2508.15954","title":"A Heuristic Framework of Variable Neighborhood Descent Methods for the Large-Scale Multi-Level Facility Location Problem in Supply Chain Networks","abstract":"This paper addresses the single-assignment, uncapacitated, multi-level facility location (MFL) problem, a strategic decision-making process critical to the design of long-term supply chain networks. Specifically, we examine four- and five-level facility location structures (k-LFL), modeled as a location-allocation problem where demand nodes must be assigned to open facilities across hierarchical levels. Although the MFL has been addressed in the literature, solutions to large-scale, realistic problems involving thousands of nodes are lacking. This paper proposes a heuristic framework based on the Variable Neighborhood Descent (VND) metaheuristic with a multi-start strategy. We develop and compare four variants: Basic Variable Neighborhood Descent (BVND), Pipe Variable Neighborhood Descent (PVND), Cyclic Variable Neighborhood Descent (CVND), and Union Variable Neighborhood Descent (UVND). In each case, a multi-start strategy with strong diversification components is employed. Extensive computational experiments compare the methods on large-scale instances involving up to 10,000 customers, 150 distribution centers, 50 warehouses, and 30 plants. Each algorithm settled into a unique, statistically significant computational time when solving these problems. Sensitivity analyses, supported by non-parametric statistical methods, validate the effectiveness of the proposed heuristic framework.","short_abstract":"This paper addresses the single-assignment, uncapacitated, multi-level facility location (MFL) problem, a strategic decision-making process critical to the design of long-term supply chain networks. Specifically, we examine four- and five-level facility location structures (k-LFL), modeled as a location-allocation prob...","url_abs":"https://arxiv.org/abs/2508.15954","url_pdf":"https://arxiv.org/pdf/2508.15954v2","authors":"[\"Haibo Wang\",\"Bahram Alidaee\"]","published":"2025-08-21T20:46:34Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"stat.AP\"]","methods":"[]","has_code":false}