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

By H. Paul Williams


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

Topics: QA Mathematics
Publisher: Springer
Year: 1996
DOI identifier: 10.1007/BF00248007
OAI identifier:
Provided by: LSE Research Online
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