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Parallel algorithms for the maximum flow problem with minimum lot sizes

In: Operations Research Proceedings 2011

Author

Listed:
  • Mujahed Eleyat

    (Miriam AS, Halden, Norway & IDI, NTNU)

  • Dag Haugland

    (University of Bergen)

  • Magnus Lie Hetland

    (Norwegian University of Science and Technology (NTNU))

  • Lasse Natvig

    (Norwegian University of Science and Technology (NTNU))

Abstract

In many transportation systems, the shipment quantities are subject to minimum lot sizes in addition to regular capacity constraints. This means that either the quantity must be zero, or it must be between the two bounds. In this work, we prove that the maximum flow problem with minimum lot-size constraints on the arcs is strongly NP-hard, and we enhance the performance of a previously suggested heuristic. Profiling the serial implementation shows that most of the execution time is spent on solving a series of regular max flow problems. Therefore, we develop a parallel augmenting path algorithm that accelerates the heuristic by an average factor of 1.25.

Suggested Citation

  • Mujahed Eleyat & Dag Haugland & Magnus Lie Hetland & Lasse Natvig, 2012. "Parallel algorithms for the maximum flow problem with minimum lot sizes," Operations Research Proceedings, in: Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), Operations Research Proceedings 2011, edition 127, pages 83-88, Springer.
    • Handle: RePEc:spr:oprchp:978-3-642-29210-1_14
    DOI: 10.1007/978-3-642-29210-1_14
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