Facets of two-dimensional infinite group problems

• 成果类型: Article
• 署名作者: Dey, Santanu S.; Richard, Jean-Philippe P.
• 署名单位: Purdue University System; Purdue University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1070.0283
• 发表日期: 2008
• 页码: 140-166
• 关键词: cutting planes; integer; cuts

摘要

In this paper, we lay the foundation for the study of the two-dimensional mixed integer infinite group problem (2DMIIGP). We introduce tools to determine if a given continuous and piecewise linear function over the two-dimensional infinite group is subadditive and to determine whether it defines a facet of 2DMIIGP. We then present two different constructions that yield the first known families of facet-defining inequalities for 2DMIIGP. The first construction uses valid inequalities of the one-dimensional integer infinite group problem (1DIIGP) as building blocks for creating inequalities for the two-dimensional integer infinite group problem (2DIIGP). We prove that this construction yields all continuous piecewise linear facets of the two-dimensional group problem that have exactly two gradients. The second construction we present has three gradients and yields facet-defining inequalities of 2DMIIGP whose continuous coefficients are not dominated by those of facets of the one-dimensional mixed integer infinite group problem (1DMIIGP).