Williams, H. Paul
(1996)
*Constructing the value function for an Integer Linear Programme over a Cone.*
Computational Optimization and Applications, 6 (1).
pp. 15-26.
ISSN 0926-6003

## 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.

Item Type: | Article |
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Official URL: | http://www.springer.com/mathematics/journal/10589 |

Additional Information: | © 1996 Kluwer Academic Publishers |

Subjects: | Q Science > QA Mathematics |

Sets: | Research centres and groups > Management Science Group Departments > Management |

Date Deposited: | 24 Jan 2011 10:57 |

Last Modified: | 06 Jun 2012 17:17 |

URI: | http://eprints.lse.ac.uk/id/eprint/31595 |

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