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The Mixing Set with Divisible Capacities

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Integer Programming and Combinatorial Optimization (IPCO 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5035))

Abstract

Given rational numbers C 0,...,C m and b 0,...,b m , the mixing set with arbitrary capacities is the mixed-integer set defined by conditions

s + C t z t  ≥ b t , 0 ≤ t ≤ m,

s ≥ 0,

z t integer, 0 ≤ t ≤ m.

Such a set has applications in lot-sizing problems. We study the special case of divisible capacities, i.e. C t /C t − 1 is a positive integer for 1 ≤ t ≤ m. Under this assumption, we give an extended formulation for the convex hull of the above set that uses a quadratic number of variables and constraints.

This work was partly carried out within the framework of ADONET, a European network in Algorithmic Discrete Optimization, contract no. MRTN-CT-2003-504438.

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Authors and Affiliations

  1. Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy

    Michele Conforti & Marco Di Summa

  2. Center for Operations Research and Econometrics (CORE), Université catholique de Louvain, 34, Voie du Roman Pays, 1348, Louvain-la-Neuve, Belgium

    Laurence A. Wolsey

Authors
  1. Michele Conforti
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  2. Marco Di Summa
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  3. Laurence A. Wolsey
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Editor information

Andrea Lodi Alessandro Panconesi Giovanni Rinaldi

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© 2008 Springer-Verlag Berlin Heidelberg

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Conforti, M., Di Summa, M., Wolsey, L.A. (2008). The Mixing Set with Divisible Capacities. In: Lodi, A., Panconesi, A., Rinaldi, G. (eds) Integer Programming and Combinatorial Optimization. IPCO 2008. Lecture Notes in Computer Science, vol 5035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68891-4_30

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  • DOI: https://doi.org/10.1007/978-3-540-68891-4_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68886-0

  • Online ISBN: 978-3-540-68891-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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