Tight formulations for some simple mixed integer programs and convex objective integer programs

Tight formulations for some simple mixed integer programs and convex objective integer programs

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Article ID: iaor20051091
Country: Germany
Volume: 98
Issue: 1/3
Start Page Number: 73
End Page Number: 88
Publication Date: Jan 2003
Journal: Mathematical Programming
Authors: ,
Keywords: programming: integer
Abstract:

We study the polyhedral structure of simple mixed integer sets that generalize the two variable set{(s, z) ∈ ℝ1+ × ℤ1 : s ≥ z − 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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