Path cover and path pack inequalities for the capacitated fixed-charge network flow problem

Alper Atamtürk, Simge Küçükyavuz, Birce Tezel

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Capacitated fixed-charge network flows are used to model a variety of problems in telecommunication, facility location, production planning, and supply chain management. In this paper, we investigate capacitated path substructures and derive strong and easy-to-compute path cover and path pack inequalities. These inequalities are based on an explicit characterization of the submodular inequalities through a fast computation of parametric minimum cuts on a path, and they generalize the well-known flow cover and flow pack inequalities for the single-node relaxations of fixed-charge flow models. We provide necessary and sufficient facet conditions. Computational results demonstrate the effectiveness of the inequalities when used as cuts in a branch-and-cut algorithm.

Original languageEnglish (US)
Pages (from-to)1943-1976
Number of pages34
JournalSIAM Journal on Optimization
Volume27
Issue number3
DOIs
StatePublished - Sep 6 2017

Keywords

  • Covers
  • Fixed-charge networks
  • Mixed-integer programming
  • Packs
  • Submodular functions
  • Valid inequalities

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science

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