A branch-and-cut algorithm for the hub location and routing problem |
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| Affiliation: | 1. Department of Industrial Engineering, Federal University of Minas Gerais, Brazil;2. Department of Mechanical and Industrial Engineering, Concordia University, Canada;3. Department of Logistics and Operations Management, HEC Montréal, Canada;1. Department of Applied Social Sciences, Federal Center of Technological Education of Minas Gerais, 30510-000 Belo Horizonte, Brazil;2. Department of Industrial Engineering, Federal University of São Carlos, 13565-905 São Carlos, Brazil;3. Department of Industrial Engineering, Federal University of Minas Gerais, 31270-921 Belo Horizonte, Brazil;1. Faculty of Enginering, Department of Industrial Engineering, Abdullah Gul University, Kayseri 38080, Turkey,;2. Department of Industrial Engineering, Bilkent University, Ankara, Turkey;1. Department of Industrial Engineering, Universidade Federal de Minas Gerais, MG, Brazil;2. Department of Applied Mathematics, Universidade Federal do Espírito Santo, ES, Brazil;3. Department of Geography, Ohio State University, OH, USA;4. College of Business Administration, University of Missouri, St. Louis, MO, USA |
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| Abstract: | We study the hub location and routing problem where we decide on the location of hubs, the allocation of nodes to hubs, and the routing among the nodes allocated to the same hubs, with the aim of minimizing the total transportation cost. Each hub has one vehicle that visits all the nodes assigned to it on a cycle. We propose a mixed integer programming formulation for this problem and strengthen it with valid inequalities. We devise separation routines for these inequalities and develop a branch-and-cut algorithm which is tested on CAB and AP instances from the literature. The results show that the formulation is strong and the branch-and-cut algorithm is able to solve instances with up to 50 nodes. |
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| Keywords: | Hub location Routing Valid inequalities Branch-and-cut |
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