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Increasing the Capacity of a Network: The Parametric Budget Problem

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  • D. R. Fulkerson

    (The RAND Corporation)

Abstract

The problem considered in this paper is that of allocating a budget of resources among the links of a network for the purpose of increasing its flow capacity relative to given sources and sinks. On the assumption that the cost of increasing each link capacity is linear, a labeling algorithm is described that permits rapid calculation of optimal allocations for all budgets.

Suggested Citation

  • D. R. Fulkerson, 1959. "Increasing the Capacity of a Network: The Parametric Budget Problem," Management Science, INFORMS, vol. 5(4), pages 472-483, July.
    • Handle: RePEc:inm:ormnsc:v:5:y:1959:i:4:p:472-483
    DOI: 10.1287/mnsc.5.4.472
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    Cited by:

    1. Ahuja, Ravindra K., 1956- & Kanpur, I. I. T. & Orlin, James B., 1953-, 1993. "A capacity scaling algorithm for the constrained maximum flow problem," Working papers 3587-93., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Burkard, Rainer E. & Lin, Yixun & Zhang, Jianzhong, 2004. "Weight reduction problems with certain bottleneck objectives," European Journal of Operational Research, Elsevier, vol. 153(1), pages 191-199, February.
    3. Majid Taghavi & Kai Huang, 2016. "A multi‐stage stochastic programming approach for network capacity expansion with multiple sources of capacity," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(8), pages 600-614, December.
    4. Dangalchev, Chavdar A., 2000. "Optimization of the transportation expense of a firm with contractual supplies," Transportation Research Part B: Methodological, Elsevier, vol. 34(3), pages 203-217, April.
    5. Ahuja, R. K. & Batra, J. L. & Gupta, S. K. & Punnen, A. P., 1996. "Optimal expansion of capacitated transshipment networks," European Journal of Operational Research, Elsevier, vol. 89(1), pages 176-184, February.
    6. Majid Taghavi & Kai Huang, 2020. "A Lagrangian relaxation approach for stochastic network capacity expansion with budget constraints," Annals of Operations Research, Springer, vol. 284(2), pages 605-621, January.
    7. 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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