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

TL;DR

This paper introduces a new integer programming model for the complex 4-level facility location problem, incorporating realistic features and proposing heuristic algorithms to efficiently find solutions for large-scale supply chain design.

Contribution

A novel integer programming formulation for 4L-FLP that reduces variables and includes realistic constraints, along with two heuristic algorithms for practical solution finding.

Findings

The new model significantly reduces problem complexity.

Heuristic algorithms perform reliably in extensive sensitivity tests.

Proposed methods improve solution efficiency for large-scale problems.

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.