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The dependency diagram of a mixed integer linear programme

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  • Williams, H. P.

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.

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  • Williams, H. P., 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.
    • Handle: RePEc:ehl:lserod:49680
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    File URL: http://eprints.lse.ac.uk/49680/
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    References listed on IDEAS

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    1. Williams, H. P., 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.
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    1. 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.
    2. 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.

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    JEL classification:

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

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