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A note on the complexity of the transportation problem with a permutable demand vector

  • Mihály Hujter
  • Bettina Klinz
  • Gerhard J. Woeginger
  • 48 Downloads

Abstract.

In this note we investigate the computational complexity of the transportation problem with a permutable demand vector, TP-PD for short. In the TP-PD, the goal is to permute the elements of the given integer demand vector b=(b 1,…,b n) in order to minimize the overall transportation costs. Meusel and Burkard [6] recently proved that the TP-PD is strongly NP-hard. In their NP-hardness reduction, the used demand values b j, j=1,…,n, are large integers. In this note we show that the TP-PD remains strongly NP-hard even for the case where b j∈{0,3} for j=1,…,n. As a positive result, we show that the TP-PD becomes strongly polynomial time solvable if b j∈{0,1,2} holds for j=1,…,n. This result can be extended to the case where b j∈{κ,κ+1,κ+2} for an integer κ.

Key words: Transportation problem permutable demand vector computational complexity minimum weight f-factor problem 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Mihály Hujter
    • 1
  • Bettina Klinz
    • 2
  • Gerhard J. Woeginger
    • 2
  1. 1.Department of Applied Mathematics, University of Miskolc, H-3515 Miskolc-Egyetemváros, Hungary (e-mail: mathm@gold.uni-miskolc.hu)HU
  2. 2.Institut für Mathematik B, TU Graz, Steyrergasse 30, A-8010 Graz, Austria (e-mail: klinz@opt.math.tu-graz.at; gwoegi@math.tu-graz.ac.at)AT

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