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A cutting plane algorithm for the Capacitated Connected Facility Location Problem

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Abstract

We consider a network design problem that arises in the cost-optimal design of last mile telecommunication networks. It extends the Connected Facility Location problem by introducing capacities on the facilities and links of the networks. It combines aspects of the capacitated network design problem and the single-source capacitated facility location problem. We refer to it as the Capacitated Connected Facility Location Problem. We develop a basic integer programming model based on single-commodity flows. Based on valid inequalities for the capacitated network design problem and the single-source capacitated facility location problem we derive several (new) classes of valid inequalities for the Capacitated Connected Facility Location Problem including cut set inequalities, cover inequalities and combinations thereof. We use them in a branch-and-cut framework and show their applicability and efficacy on a set of real-world instances.

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Acknowledgements

The authors thank the two anonymous referees for their valuable comments and suggestions to improve the paper.

Stefan Gollowitzer was supported by the Fonds de recherche du Québec—Nature et technologies under grant 163879 within the Programme de Stages Internationaux. Ivana Ljubić was supported by an APART Fellowship of the Austrian Academy of Sciences (OEAW). This support is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, Faculty of Business, Economics, and Statistics, University of Vienna, Brünner Straße 72, 1210, Vienna, Austria

    Stefan Gollowitzer & Ivana Ljubić

  2. Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), and Department of Computer Science and Operations Research, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montreal, H3C 3J7, Canada

    Bernard Gendron

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  1. Stefan Gollowitzer
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Correspondence to Stefan Gollowitzer.

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Gollowitzer, S., Gendron, B. & Ljubić, I. A cutting plane algorithm for the Capacitated Connected Facility Location Problem. Comput Optim Appl 55, 647–674 (2013). https://doi.org/10.1007/s10589-013-9544-9

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