Insights into Efficiency and Satisfaction Trade-offs in Facility Location Problems with Regional Preferences

TL;DR

This paper develops a mathematical framework for regional multifacility location problems that balances transportation costs with customer satisfaction, using optimization models and extensive computational analysis.

Contribution

It introduces a novel optimization framework incorporating preference functions and provides scalable models for complex regional facility location problems.

Findings

Optimal solutions for up to 500 regions in single-facility cases

Statistical significance of preferences in improving satisfaction levels

Effective mixed-integer second order cone models for various cost and preference scenarios

Abstract

This paper studies a practical regional demand continuous multifacility location problems whose main goal is to locate a given number of services and entry points in each region to distribute certain products to the users at minimum transportation cost. Additionally, a minimum satisfaction level is required for the customers in each region. This satisfaction is measured through continuous preference functions that reflect the satisfaction degree of each location in the region. We provide a mathematical optimization-based framework for the problem and derive suitable Mixed Integer Second Order Cone optimization models for some interesting situations: norm-based transportation costs for the services to the entry points, and different families of preference functions. Among these preference functions, we highlight those derived from economic production models and distance-based preferences. We conduct an extensive computational study along two main lines: a computational approach, where we provide optimal solutions for up to 500 demand regions in the single-facility case and up to $50$ for the p-facility case; and a qualitative approach, where we analyze whether the incorporation of preferences is statistically significant compared to the case without preferences.