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The dependency diagram of a mixed integer linear programme

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  • H Paul Williams

    (London School of Economics and Political Science)

Abstract

The Dependency Diagram of a Linear Programme (LP) shows how the successive inequalities of an LP depend on former inequalities, when variables are projected out by Fourier-Motzkin Elimination. This is explained in a paper referenced below. The paper, given here, extends the results to the Mixed Integer case (MILP). It is shown how projection of a MILP leads to a finite disjunction of polytopes. This is expressed as a set of inequalities (mirroring those in the LP case) augmented by correction terms with finite domains which are subject to linear congruences.

Suggested Citation

  • H Paul Williams, 2017. "The dependency diagram of a mixed integer linear programme," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(7), pages 829-833, July.
    • Handle: RePEc:pal:jorsoc:v:68:y:2017:i:7:d:10.1057_jors.2016.45
    DOI: 10.1057/jors.2016.45
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    References listed on IDEAS

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    1. Williams, H. Paul, 2013. "The general solution of a mixed integer linear programme over a cone," LSE Research Online Documents on Economics 49681, London School of Economics and Political Science, LSE Library.
    2. H Paul Williams, 2016. "The dependency diagram of a linear programme," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(3), pages 450-456, March.
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    Cited by:

    1. Maximilian Merkert & Galina Orlinskaya & Dieter Weninger, 2022. "An exact projection-based algorithm for bilevel mixed-integer problems with nonlinearities," Journal of Global Optimization, Springer, vol. 84(3), pages 607-650, November.

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    1. Williams, H. Paul, 2013. "The dependency diagram of a mixed integer linear programme," LSE Research Online Documents on Economics 49680, London School of Economics and Political Science, LSE Library.
    2. Williams, H. Paul & Hooker, J. N., 2014. "Integer programming as projection," LSE Research Online Documents on Economics 55426, London School of Economics and Political Science, LSE Library.

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