A Heuristic Framework of Variable Neighborhood Descent Methods for the Large-Scale Multi-Level Facility Location Problem in Supply Chain Networks

TL;DR

This paper introduces a heuristic framework based on Variable Neighborhood Descent for solving large-scale multi-level facility location problems in supply chains, demonstrating effectiveness on instances with thousands of nodes.

Contribution

It develops and compares four variants of VND heuristics with multi-start strategies for large-scale multi-level facility location problems, filling a gap in scalable solutions.

Findings

All variants effectively solve large instances with up to 10,000 customers.

Each algorithm exhibits unique computational times and performance.

Sensitivity analyses confirm the robustness of the proposed heuristics.

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.