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

M. Hujter, B. Klinz, G.J. Woeginger

    Research output: Contribution to journalArticleAcademicpeer-review

    6 Citations (Scopus)

    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=(b1,…,bn) 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 bj, j=1,…,n, are large integers. In this note we show that the TP-PD remains strongly NP-hard even for the case where bj]{0,3} for j=1,…,n. As a positive result, we show that the TP-PD becomes strongly polynomial time solvable if bj] {0,1,2} holds for j=1,…,n. This result can be extended to the case where bj]{3,3+1,3+2} for an integer 3.
    Original languageEnglish
    Pages (from-to)9-16
    Number of pages8
    JournalMathematical Methods of Operations Research
    Volume50
    Issue number1
    DOIs
    Publication statusPublished - 1999

    Fingerprint Dive into the research topics of 'A note on the complexity of the transportation problem with a permutable demand vector'. Together they form a unique fingerprint.

  • Cite this