145725 20260217205604.0 doi 10.3390/math12223459 sideral 140649 ART-2024-140649 eng Calvete, Herminia I. Universidad de Zaragoza (orcid)0000-0001-7603-9380 A Bilevel Approach to the Facility Location Problem with Customer Preferences Under a Mill Pricing Policy 2024 Access copy available to the general public Unrestricted This paper addresses the facility location problem under a mill pricing policy, integrating customers’ behavior through the concept of preferences. The problem is modeled as a bilevel optimization problem, where the existence of ties in customers’ preferences can lead to an ill-posed bilevel problem due to the possible existence of multiple optima to the lower-level problem. As the commonly employed optimistic and pessimistic strategies are inadequate for this problem, a specific approach is proposed bearing in mind the customers’ rational behavior. In this work, we propose a novel formulation of the problem as a bilevel model in which each customer faces a lexicographic biobjective problem in which the preference is maximized and the total cost of accessing the selected facility is minimized. This allows for a more accurate representation of customer preferences and the resulting decisions regarding facility location and pricing. To address the complexities of this model, we apply duality theory to the lower-level problems and, ultimately, reformulate the bilevel problem as a single-level mixed-integer optimization problem. This reformulation incorporates big-M constants, for which we provide valid bounds to ensure computational tractability and solution quality. The computational study conducted allows us to assess, on the one hand, the effectiveness of the proposed reformulation to address the bilevel model and, on the other hand, the impact of the length of the customer preference lists and fixed opening cost for facilities on the computational time and the optimal solution. info:eu-repo/grantAgreement/ES/DGA/E41-23R info:eu-repo/grantAgreement/ES/MICINN/PID2022-139543OB-C43 info:eu-repo/grantAgreement/EUR/MICINN/TED2021-130961B-I00 info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es 2.2 2024 MATHEMATICS 30 / 492 = 0.061 2024 Q1 T1 0.498 2024 Computer Science (miscellaneous) 2024 Q2 Mathematics (miscellaneous) 2024 Q2 Engineering (miscellaneous) 2024 Q2 4.6 2024 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Galé, Carmen Universidad de Zaragoza (orcid)0000-0002-5630-3719 Hernández, Aitor Universidad de Zaragoza (orcid)0000-0003-4420-7567 Iranzo, José A. Universidad de Zaragoza (orcid)0000-0001-9993-9816 2007 265 Universidad de Zaragoza Dpto. Métodos Estadísticos Área Estadís. Investig. Opera. 12, 22 (2024), 3459 [25 pp.] Mathematics (Basel) Mathematics 2227-7390 398721 http://zaguan.unizar.es/record/145725/files/texto_completo.pdf Versión publicada 2635340 http://zaguan.unizar.es/record/145725/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:145725 articulos driver 2026-02-17-20:46:22 ARTICLE