New inequalities for finite and infinite group problems from approximate lifting

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Abstract

In this paper, we derive new families of facet-defining inequalities for the finite group problem and extreme inequalities for the infinite group problem using approximate lifting. The new valid inequalities for the finite group problem include two- and three-slope facet-defining inequalities as well as the first family of four-slope facet-defining inequalities. The new valid inequalities for the infinite group problem include families of two- and three-slope extreme inequalities. These new inequalities not only illustrate the diversity of strong inequalities for the finite and infinite group problems, but also provide a large variety of new cutting planes for solving integer and mixed-integer programming problems.

Original languageEnglish (US)
Pages (from-to)172-191
Number of pages20
JournalNaval Research Logistics
Volume55
Issue number2
DOIs
StatePublished - Mar 2008
Externally publishedYes

Keywords

  • Approximate lifting
  • Group problem
  • Integer programming
  • Polyhedral theory

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