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Optimal Flows in Networks with Multiple Sources and Sinks, with Applications to Oil and Gas Lease Investment Programs

Author

Listed:
  • Awi Federgruen

    (Columbia University, New York, New York)

  • Henry Groenevelt

    (University of Rochester, Rochester, New York)

Abstract

In the classical maximal flow problem, the objective is to maximize the supply to a single sink in a capacitated network. In this paper we consider general capacitated networks with multiple sinks: the objective is to optimize a general “concave” preference relation on the set of feasible supply vectors. We show that an optimal solution can be obtained by a marginal allocation procedure. An efficient implementation results in an adaptation of the augmenting path algorithm. We also discuss an application of the procedure for an investment company that deals in oil and gas ventures.

Suggested Citation

  • Awi Federgruen & Henry Groenevelt, 1986. "Optimal Flows in Networks with Multiple Sources and Sinks, with Applications to Oil and Gas Lease Investment Programs," Operations Research, INFORMS, vol. 34(2), pages 218-225, April.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:2:p:218-225
    DOI: 10.1287/opre.34.2.218
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    Cited by:

    1. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    2. Paul Dütting & Thomas Kesselheim & Éva Tardos, 2021. "Algorithms as Mechanisms: The Price of Anarchy of Relax and Round," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 317-335, February.
    3. Gerard M. Campbell, 1999. "Cross-Utilization of Workers Whose Capabilities Differ," Management Science, INFORMS, vol. 45(5), pages 722-732, May.
    4. Dorit Hochbaum, 2007. "Complexity and algorithms for nonlinear optimization problems," Annals of Operations Research, Springer, vol. 153(1), pages 257-296, September.
    5. Zeyang Wu & Kameng Nip & Qie He, 2021. "A New Combinatorial Algorithm for Separable Convex Resource Allocation with Nested Bound Constraints," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1197-1212, July.
    6. Sushil Bikhchandani & Sven de Vries & James Schummer & Rakesh V. Vohra, 2011. "An Ascending Vickrey Auction for Selling Bases of a Matroid," Operations Research, INFORMS, vol. 59(2), pages 400-413, April.

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