Hub location under competition

Hubs are consolidation and dissemination points in many-to-many flow networks. Hub location problem is to locate hubs among available nodes and allocate non-hub nodes to these hubs. The mainstream hub location studies focus on optimal decisions of one decision-maker with respect to some objective(s) even though the markets that benefit hubbing are oligopolies. Therefore, in this paper, we propose a competitive hub location problem where the market is assumed to be a duopoly. Two decision-makers (or firms) sequentially decide locations of their hubs and then customers choose one firm with respect to provided service levels. Each decision-maker aims to maximize his/her own market share. We propose two problems for the leader (former decision-maker) and follower (latter decision-maker): (r|Xp)hub-medianoid and (r|p)hub-centroid problems, respectively. Both problems are proven to be NP-complete. Linear programming models are presented for these problems as well as exact solution algorithms for the (r|p)hub-centroid problem. The performance of models and algorithms are tested by computational analysis conducted on CAB and TR data sets. © 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved

A Branch-Price-and-Cut Procedure for the Discrete Ordered Median Problem

International audienceThe Discrete Ordered Median Problem (DOMP) is formulated as a set partitioning problem using an exponential number of variables. Each variable corresponds to a set of demand points allocated to the same facility with the information of the sorting position of their corresponding costs. We develop a column generation approach to solve the continuous relaxation of this model. Then, we apply a branch-price-and-cut algorithm to solve small to large sized instances of DOMP in competitive computational time

A branch-and-price approach for the continuous multifacility monotone ordered median problem

Acknowledgements The authors of this research acknowledge financial support by the Spanish Ministerio de Ciencia y Tecnología, Agencia Estatal de Investigación and Fondos Europeos de Desarrollo Regional (FEDER) via project PID2020-114594GB-C21. The authors also acknowledge partial support from project B-FQM-322-UGR20. The first, third and fourth authors also acknowledge partial support from projects FEDER-US-1256951, Junta de Andaluca P18-FR-1422, CEI-3-FQM331, FQM-331, and NetmeetData: Ayudas Fundacin BBVA a equipos de investigacin científica 2019. The first and second authors were par- tially supported by research group SEJ-584 (Junta de Andalucía). The first author was also partially supported by the IMAG-Maria de Maeztu grant CEX2020-001105-M/AEI/10.13039/50110 0 011033. The second author was supported by Spanish Ministry of Education and Science grant number PEJ2018-002962-A and the Doctoral Program in Mathematics at the Universidad of Granada. The third author also acknowledges the grant Contratación de Personal Investigador Doctor (Convocatoria 2019) 43 Contratos Capital Humano Línea 2 Paidi 2020, supported by the European Social Fund and Junta de Andalucía.In this paper, we address the Continuous Multifacility Monotone Ordered Median Problem. The goal of this problem is to locate facilities in minimizing a monotone ordered weighted median function of the distances between given demand points and its closest facility. We propose a new branch-and-price procedure for this problem, and three families of matheuristics based on: solving heuristically the pricer problem, aggregating the demand points, and discretizing the decision space. We give detailed discussions of the validity of the exact formulations and also specify the implementation details of all the solution procedures. Besides, we assess their performances in an extensive computational experience that shows the superiority of the branch-and-price approach over the compact formulation in medium-sized instances. To handle larger instances it is advisable to resort to the matheuristics that also report rather good results.Spanish Ministerio de Ciencia y Tecnología, Agencia Estatal de Investigación and Fondos Europeos de Desarrollo Regional (FEDER) via project PID2020-114594GB-C21Partial support from project B-FQM-322-UGR20Partial support from projects FEDER-US-1256951, Junta de Andaluca P18-FR-1422, CEI-3-FQM331, FQM-331, and NetmeetData: Ayudas Fundación BBVA a equipos de investigacin científica 2019Research group SEJ-584 (Junta de Andalucía)Partially supported by the IMAG-Maria de Maeztu grant CEX2020-001105-M/AEI/10.13039/50110 0 011033Spanish Ministry of Education and Science grant number PEJ2018-002962-AEuropean Social Fund and Junta de Andalucí