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Finding Equivalent Network Formulations for Constrained Network Problems

Author

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  • Darwin Klingman

    (University of Texas at Austin)

Abstract

This paper describes a procedure for determining if constrained network problems (i.e., network problems with additional linear constraints) can be transformed into equivalent pure network problems by a linear transformation involving the node constraints and the extra constraints. These results extend procedures for problems in which the extra constraints consist of bounding certain partial sums of variables. This has proved to be an effective managerial technique for a major automobile manufacturer and a major energy modeling company.

Suggested Citation

  • Darwin Klingman, 1977. "Finding Equivalent Network Formulations for Constrained Network Problems," Management Science, INFORMS, vol. 23(7), pages 737-744, March.
    • Handle: RePEc:inm:ormnsc:v:23:y:1977:i:7:p:737-744
    DOI: 10.1287/mnsc.23.7.737
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    Cited by:

    1. Nalân Gülpinar & Gautam Mitra & Istvan Maros, 1998. "Detecting embedded pure network structures in LP problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 67-95, June.
    2. Mohammad Ali Raayatpanah & Salman Khodayifar & Thomas Weise & Panos Pardalos, 2022. "A novel approach to subgraph selection with multiple weights on arcs," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 242-268, August.
    3. ÇalIskan, Cenk, 2011. "A specialized network simplex algorithm for the constrained maximum flow problem," European Journal of Operational Research, Elsevier, vol. 210(2), pages 137-147, April.

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