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The general solution of a mixed integer linear programme over a cone

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  • Williams, H. Paul

Abstract

We give a general method of finding the optimal objective, and solution, values of a Mixed Integer Linear Programme over a Cone (MILPC) as a function of the coefficients (objective, matrix and right- hand side). In order to do this we first convert the matrix of constraint coefficients to a Normal Form (Modified Hermite Normal Form (MHNF)). Then we project out all the variables leaving an (attainable) bound on the optimal objective value. For (M)IPs, including MILPC, projection is more complex, than in the Linear programming (LP) case, yielding the optimal objective value as a finite disjunction of inequalities The method can also be interpreted as finding the 'minimal' strengthening of the constraints of the LP relaxation which yields an integer solution to the associated LP.

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:49681
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    File URL: http://eprints.lse.ac.uk/49681/
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    Cited by:

    1. 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.
    2. 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.
    3. 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.

    More about this item

    JEL classification:

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

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