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An Implicit Enumeration Algorithm for the Concave Cost Network Flow Problem

Author

Listed:
  • M. Florian

    (University of Montreal)

  • P. Robillard

    (University of Montreal)

Abstract

The objective of this paper is the construction of a branch-and-bound algorithm for computing minimum cost flows in capacitated networks when the cost of passing a flow over an are is concave. The method is based on the equivalence of the general network flow problem to a network flow problem in a bipartite network of a special form. An optimal flow is found by implicit enumeration of the set of extremal flows in that network.

Suggested Citation

  • M. Florian & P. Robillard, 1971. "An Implicit Enumeration Algorithm for the Concave Cost Network Flow Problem," Management Science, INFORMS, vol. 18(3), pages 184-193, November.
    • Handle: RePEc:inm:ormnsc:v:18:y:1971:i:3:p:184-193
    DOI: 10.1287/mnsc.18.3.184
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    Cited by:

    1. Vasilios I. Manousiouthakis & Neil Thomas & Ahmad M. Justanieah, 2011. "On a Finite Branch and Bound Algorithm for the Global Minimization of a Concave Power Law Over a Polytope," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 121-134, October.
    2. Vedat Verter & M. Cemal Dincer, 1995. "Facility location and capacity acquisition: An integrated approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(8), pages 1141-1160, December.

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