Incorporation of regional preferences in facility location: Insights into efficiency and satisfaction trade-offs

This paper studies a regional demand continuous multifacility location problems whose main goal is to locate a given number of facilities and service 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 facilities to the service 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.