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Nonadditive Shortest Paths: Subproblems in Multi-Agent Competitive Network Models

Author

Listed:
  • Steven A. Gabriel

    (The George Washington University and ICF Consulting)

  • David Bernstein

    (James Madison University)

Abstract

A variety of different multi-agent (competitive) network models have been described in the literature. Computational techniques for solving such models often involve the iterative solution of “shortest” path subproblems. Unfortunately, the most theoretically interesting models involve nonlinear cost or utility functions and they give rise to nonadditive “shortest” path subproblems. This paper both describes some basic existence and uniqueness results for these subproblems and develops a heuristic for solving them.

Suggested Citation

  • Steven A. Gabriel & David Bernstein, 2000. "Nonadditive Shortest Paths: Subproblems in Multi-Agent Competitive Network Models," Computational and Mathematical Organization Theory, Springer, vol. 6(1), pages 29-45, May.
    • Handle: RePEc:spr:comaot:v:6:y:2000:i:1:d:10.1023_a:1009621108971
    DOI: 10.1023/A:1009621108971
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    References listed on IDEAS

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    1. Dial, Robert B., 1979. "A model and algorithm for multicriteria route-mode choice," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 311-316, December.
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    Cited by:

    1. Xing, Tao & Zhou, Xuesong, 2011. "Finding the most reliable path with and without link travel time correlation: A Lagrangian substitution based approach," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1660-1679.
    2. Zhang, Yuli & Shen, Zuo-Jun Max & Song, Shiji, 2016. "Parametric search for the bi-attribute concave shortest path problem," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 150-168.
    3. Maruyama, Takuya & Sumalee, Agachai, 2007. "Efficiency and equity comparison of cordon- and area-based road pricing schemes using a trip-chain equilibrium model," Transportation Research Part A: Policy and Practice, Elsevier, vol. 41(7), pages 655-671, August.

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