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The dependency diagram of a mixed integer linear programme

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  • Williams, H. Paul

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

  • Williams, H. Paul, 2017. "The dependency diagram of a mixed integer linear programme," LSE Research Online Documents on Economics 66311, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:66311
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    File URL: http://eprints.lse.ac.uk/66311/
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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.

    More about this item

    Keywords

    linear programming; projection; fourier–motzkin elimination;
    All these keywords.

    JEL classification:

    • J50 - Labor and Demographic Economics - - Labor-Management Relations, Trade Unions, and Collective Bargaining - - - General

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