Abstract.
We examine progress over the last fifteen years in finding strong valid inequalities and tight extended formulations for simple mixed integer sets lying both on the ``easy'' and ``hard'' sides of the complexity frontier. Most progress has been made in studying sets arising from knapsack and single node flow sets, and a variety of sets motivated by different lot-sizing models. We conclude by citing briefly some of the more intriguing new avenues of research.
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Received: January 15, 2003 / Accepted: April 10, 2003 Published online: May 28, 2003
Key words. mixed integer programming – strong valid inequalities – convex hull – extended formulations – single node flow sets – lot-sizing
This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister's Office, Science Policy Programming. The scientific responsibility is assumed by the authors.
Research carried out with financial support of the project TMR-DONET nr. ERB FMRX–CT98–0202 of the European Union.
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Wolsey, L. Strong formulations for mixed integer programs: valid inequalities and extended formulations. Math. Program., Ser. B 97, 423–447 (2003). https://doi.org/10.1007/s10107-003-0450-2
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DOI: https://doi.org/10.1007/s10107-003-0450-2