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Tailoring Benders decomposition for uncapacitated network design

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Netflow at Pisa

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 26))

Abstract

Because of its imbedded network flow structure, the generic network design problem is an attractive candidate for integer programming decomposition. This paper studies the application and acceleration of Benders decomposition for uncapacitated models from this problem class and illustrates the potential flexibility of the Benders solution strategy. In particular, it (i) shows that several lower bounding inequalities from the literature can be derived as Benders cuts; and (ii) introduces new Benders cuts for the network design problem.

The paper also reports on computational experience in using Benders decomposition with a dual ascent and variable elimination preprocessing procedure to solve uncapacitated network design problems with up to 90 binary variables and 15 080 continuous variables, or 45 binary variables and 105 600 continuous variables.

Supported in part by grants ECS-792-6225 and ECS-831-6224 from the national Science Foundation’s Program on Systems Theory and Operations Research.

Supported in part by grants ECS-811-7876 and ECS-831-6224 from the National Science Foundation’s Program on Systems Theory and Operations Research.

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Authors and Affiliations

  1. Sloan School of Management, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    T. L. Magnanti

  2. Ecole des Hautes Etudes Commerciales, University of Montréal, H3T 1V6, Québec, Canada

    P. Mireault

  3. Krannert Graduate School of Management, Purdue University, 47907, West Lafayette, IN, USA

    R. T. Wong

Authors
  1. T. L. Magnanti
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  2. P. Mireault
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  3. R. T. Wong
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Giorgio Gallo Claudio Sandi

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© 1986 The Mathematical Programming Society, Inc.

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Magnanti, T.L., Mireault, P., Wong, R.T. (1986). Tailoring Benders decomposition for uncapacitated network design. In: Gallo, G., Sandi, C. (eds) Netflow at Pisa. Mathematical Programming Studies, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121090

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  • DOI: https://doi.org/10.1007/BFb0121090

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  • Print ISBN: 978-3-642-00922-8

  • Online ISBN: 978-3-642-00923-5

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