Mathematical Programming

, Volume 163, Issue 1–2, pp 411–444 | Cite as

A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method

  • Jordi CastroEmail author
  • Stefano Nasini
  • Francisco Saldanha-da-Gama
Full Length Paper Series A


We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either exact or inexact) efficient solution of large instances. The consequences of different modeling conditions and problem specifications on the computational performance are also investigated both theoretically and empirically, providing a deeper understanding of the significant factors influencing the overall efficiency of the cutting-plane method. The methodology proposed allowed the solution of instances of up to 200 potential locations, one million customers and three periods, resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables. Those problems were solved by the specialized approach in less than one hour and a half, outperforming other state-of-the-art methods, which exhausted the (144 GB of) available memory in the largest instances.


Mixed integer linear optimization Interior-point methods Multi-period facility location Cutting planes Benders decomposition Large-scale optimization 

Mathematics Subject Classification

90C06 90C11 90C51 90B80 



The first author has been supported by MINECO/FEDER Grants MTM2012-31440 and MTM2015-65362-R of the Spanish Ministry of Economy and Competitiveness; the second author has been supported by the European Research Council-ref. ERC-2011-StG 283300-REACTOPS; the third author has been supported by the Portuguese Science Foundation (FCT-Fundação para a Ciência e Tecnologia) under the Project UID/MAT/04561/2013 (CMAF-CIO/FCUL). The authors would like to thank the two anonymous reviewers for their valuable comments, suggestions and insights that helped improving the manuscript.


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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2016

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Department of MarketingIESEG School of Management (LEM-CNRS 9221)LilleFrance
  3. 3.Department of Statistics and Operations Research/Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Faculdade de CiênciasUniversidade de LisboaLisbonPortugal

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