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A characterisation of all feasible solutions to an integer program

By H. Paul Williams

Abstract

It is shown how the dual of Fourier–Motzkin elimination can be applied to eliminating the constraints of an Integer Linear Program. The result will, in general, be to reduce the Integer Program to a single Diophantine equation together with a series of Linear homogeneous congruences. Extreme continuous solutions to the Diophantine equation give extreme solutions to the Linear Programming relaxation. Integral solutions to the Diophantine equation which also satisfy the congruences give all the solutions to the Integer Program

Topics: QA Mathematics
Publisher: Elsevier
Year: 1983
DOI identifier: 10.1016/0166-218X(83)90024-0
OAI identifier: oai:eprints.lse.ac.uk:31609
Provided by: LSE Research Online
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