Publication: Stable formulations for the Capacitated Facility Location Problem with Customer Preferences
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Date
2026
Authors
Domínguez Sánchez, Concepción ; Jaime Alcántara, Juan de Dios
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Facultades de la UMU::Facultad de Matemáticas
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info:eu-repo/semantics/preprint
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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 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. 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 assess the performance of the proposed formulations and the quality of the resulting stable allocations through extensive computational experiments. As an additional contribution, we present a novel formulation that provides maximum-cardinality Pareto-optimal matchings for the Capacitated House Allocation problem.
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