Handling capacity constraints in facility location problems with user preferences

H. I. Calvete, C. Galé, A. Hernández, J. A. Iranzo

Facility location problems with users' preferences naturally adopt a bilevel structure, where the upper level handles location decisions while the lower level reflects users' reaction according to their individual preferences. Capacity constraints introduce a significant challenge in this setting: when facilities cannot accommodate all demand, strict adherence to users' preferences may lead to infeasibility. Pricing policies can be adopted as a mechanism to provide flexibility in capacity management. Moreover, we explore an alternative approach to handle infeasibility arising from the interaction between users' preferences and capacity constraints. By enriching the bilevel formulation with new sets of variables, we develop a framework that preserves the hierarchical structure of the problem while offering greater modeling flexibility. Preliminary results suggest that this approach is both effective and computationally tractable.

Keywords: Capacitated facility location problem, User preferences, Bilevel optimization

GT GELOCA V: Location and routing with preferences
September 5, 2026  4:00 PM
Aula B

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