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Constructing the value function for an Integer Linear Programme over a Cone

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Abstract

The value function of an Integer Programme is the optimal objective value expressed as a function of the right-hand-side coefficients. For an Integer Programme over a Cone (ILPC) this takes the form of a Chvátal Function which is built up from the operations of taking non-negative linear combinations and integer round-up.

A doubly recursive procedure for calculating such a value function is given. This is illustrated by a small numerical example.

It is also shown how the optimal solution of an ILPC can be obtained as a function of the right-hand-side through this recursion. The connection with the Group optimization representation of an ILPC is also given together with a discussion of the difficulty of calculating the value function for a general Integer Programme.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Southampton, 5017 1BJ, Southampton, Britain

    H. P. Williams

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  1. H. P. Williams
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Williams, H.P. Constructing the value function for an Integer Linear Programme over a Cone. Comput Optim Applic 6, 15–26 (1996). https://doi.org/10.1007/BF00248007

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  • DOI: https://doi.org/10.1007/BF00248007

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