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Sequence Independent Lifting for Mixed Integer Programs with Variable Upper Bounds

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Abstract

We investigate the convex hull of the set defined by a single inequality with continuous and binary variables with variable upper bound constraints. We extend the traditional flow cover inequality, and show that it is valid for a restriction of the set in which some variables are fixed. We also give conditions under which this inequality is facet-defining and, when it is not, we show how it can be lifted to obtain valid inequalities for the entire set using sequence independent lifting. In general, computing the lifting function is NP-hard, but under an additional restriction on the cover we obtain a closed form. Finally, we show how these results imply and extend known results about the single node fixed charge flow polyhedron.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    S. Shebalov

  2. Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    D. Klabjan

Authors
  1. S. Shebalov
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  2. D. Klabjan
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Correspondence to D. Klabjan.

Additional information

This material is based upon work supported by the National Science Foundation under Grant No. 0084826.

Received: April 2004

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Shebalov, S., Klabjan, D. Sequence Independent Lifting for Mixed Integer Programs with Variable Upper Bounds. Math. Program. 105, 523–561 (2006). https://doi.org/10.1007/s10107-005-0664-6

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  • DOI: https://doi.org/10.1007/s10107-005-0664-6

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