Stable formulations for the Capacitated Facility Location Problem with Customer Preferences

TL;DR

This paper introduces new stable allocation models for the Capacitated Facility Location Problem with Customer Preferences, providing formulations that maximize global preferences and Pareto optimality, supported by extensive computational experiments.

Contribution

It develops three new types of stable allocation formulations for the CFLCP, including Pareto optimal cyclic-coalition stable formulations, and compares their effectiveness through computational experiments.

Findings

Cyclic-coalition stable formulations are Pareto optimal.

New mixed-integer linear formulations improve allocation stability.

Computational results show enhanced allocation quality.

Abstract

In the Simple Plant Location Problem with Order (SPLPO), the aim is to open a subset of plants to assign every customer taking into account their preferences. Customers rank the plants in strict order and are assigned to their favorite open plant, and the objective is to minimize the location plus allocation costs. Here, we study a generalization of the SPLPO named the Capacitated Facility Location Problem with Customer Preferences (CFLCP) where a limited number of customers can be allocated to each facility. We consider the global preference maximization setting, where the customers preferences are globally maximized. For this setting, we define three new types of stable allocations, namely customer stable, pairwise stable and cyclic-coalition stable allocations, and we provide two mixed-integer linear formulations for each setting. In particular, our cyclic-coalition stable formulations are Pareto optimal in a global-preference maximization setting, in the sense that no customer can improve their allocation without making another one worse off. We provide extensive computational experiments and compare the quality of our allocations with previous ones defined in the literature. As an additional result, we present a novel formulation that provides Pareto optimal matchings in the Capacitated House Allocation problem of maximum cardinality.