On the transportation problem with market choice

Pelin Damci-Kurt, Santanu S. Dey, Simge Küçükyavuz*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We study a variant of the classical transportation problem in which suppliers with limited capacities have a choice of which demands (markets) to satisfy. We refer to this problem as the transportation problem with market choice (TPMC). While the classical transportation problem is known to be strongly polynomial-time solvable, we show that its market choice counterpart is strongly NP-complete. For the special case when all potential demands are no greater than two, we show that the problem reduces in polynomial time to minimum weight perfect matching in a general graph, and thus can be solved in polynomial time. We give valid inequalities and coefficient update schemes for general mixed-integer sets that are substructures of TPMC. Finally, we give conditions under which these inequalities define facets, and report our preliminary computational experiments with using them in a branch-and-cut algorithm.

Original languageEnglish (US)
Pages (from-to)54-77
Number of pages24
JournalDiscrete Applied Mathematics
Volume181
DOIs
StatePublished - Jan 30 2015

Keywords

  • Complexity
  • Facet
  • Market choice
  • Transportation problem

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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