Journal
MATHEMATICAL PROGRAMMING
Volume 98, Issue 1-3, Pages 73-88Publisher
SPRINGER
DOI: 10.1007/s10107-003-0397-3
Keywords
mixed integer programming; valid inequalities; extended formulations
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We study the polyhedral structure of simple mixed integer sets that generalize the two variable set {(s,z) is an element of R(+)(1)x(1):sgreater than or equal toz-b}. These sets form basic building blocks that can be used to derive tight formulations for more complicated mixed integer programs. For four such sets we give a complete description by valid inequalities and/or an integral extended formulation, and we also indicate what constraints can be added without destroying integrality. We apply these results to provide tight formulations for certain piecewise-linear convex objective integer programs, and in a companion paper we exploit them to provide polyhedral descriptions and computationally effective mixed integer programming formulations for discrete lot-sizing problems.
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