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The transportation problem with conflicts

Author

Listed:
  • Annette M. C. Ficker

    (KU Leuven)

  • Frits C. R. Spieksma

    (Eindhoven University of Technology)

  • Gerhard J. Woeginger

    (RWTH Aachen)

Abstract

The transportation problem is a fundamental problem in operations research, where items need to be transported from supply nodes (each with a given supply) to demand nodes (each with a given demand) in the cheapest possible way. Here, we are interested in a generalization of the transportation problem where, each supply node has a (possibly empty) set of conflicting pairs of demand nodes, and each demand node a (possibly empty) set of conflicting pairs of supply nodes. Each supply node may only send supply to at most one demand node of each conflicting pair. Likewise, each demand node may only receive supply from at most one supply node of each conflicting pair. We call the resulting problem the transportation problem with conflicts (TPC). We show that the complexity of TPC depends upon the structure of the so-called conflict graph that follows from the conflicting pairs. More concrete, we show that for many graph-classes the corresponding TPC remains NP-hard, and for some special cases we derive constant factor approximation algorithms.

Suggested Citation

  • Annette M. C. Ficker & Frits C. R. Spieksma & Gerhard J. Woeginger, 2021. "The transportation problem with conflicts," Annals of Operations Research, Springer, vol. 298(1), pages 207-227, March.
    • Handle: RePEc:spr:annopr:v:298:y:2021:i:1:d:10.1007_s10479-018-3004-y
    DOI: 10.1007/s10479-018-3004-y
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    References listed on IDEAS

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    1. Ulrich Pferschy & Joachim Schauer, 2013. "The maximum flow problem with disjunctive constraints," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 109-119, July.
    2. Lisa Fleischer & Michel X. Goemans & Vahab S. Mirrokni & Maxim Sviridenko, 2011. "Tight Approximation Algorithms for Maximum Separable Assignment Problems," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 416-431, August.
    3. Sun, Minghe, 2002. "The transportation problem with exclusionary side constraints and two branch-and-bound algorithms," European Journal of Operational Research, Elsevier, vol. 140(3), pages 629-647, August.
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