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On the relative strength of families of intersection cuts arising from pairs of tableau constraints in mixed integer programs

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Abstract

We compare the relative strength of valid inequalities for the integer hull of the feasible region of mixed integer linear programs with two equality constraints, two unrestricted integer variables and any number of nonnegative continuous variables. In particular, we prove that the closure of Type 2 triangle (resp. Type 3 triangle; quadrilateral) inequalities, are all within a factor of \(1.5\) of the integer hull, and provide examples showing that the approximation factor is not less than \(1.125\). There is no fixed approximation ratio for split or Type 1 triangle inequalities however.

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Notes

  1. \([k]:=\{1,2,\ldots ,k\}\).

  2. \((a,b)\) denotes the open interval between \(a\) and \(b\).

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Authors and Affiliations

  1. Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Yogesh Awate & Gérard Cornuéjols

  2. Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Ontario, N2L 3G1, Canada

    Bertrand Guenin & Levent Tunçel

Authors
  1. Yogesh Awate
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  2. Gérard Cornuéjols
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  3. Bertrand Guenin
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  4. Levent Tunçel
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Corresponding author

Correspondence to Levent Tunçel.

Additional information

Yogesh Awate: Research of this author was supported in part by a Mellon Fellowship.

Gérard Cornuéjols: Research of this author was supported in part by NSF grant CMMI1024554 and ONR grant N00014-09-1-0033.

Bertrand Guenin: Research of this author was supported in part by a Discovery Grant from NSERC and ONR grant N00014-12-1-0049.

Levent Tunçel: Research of this author was supported in part by a Discovery Grant from NSERC and ONR grant N00014-12-1-0049.

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Awate, Y., Cornuéjols, G., Guenin, B. et al. On the relative strength of families of intersection cuts arising from pairs of tableau constraints in mixed integer programs. Math. Program. 150, 459–489 (2015). https://doi.org/10.1007/s10107-014-0775-z

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  • DOI: https://doi.org/10.1007/s10107-014-0775-z

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