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Path Preferences and Optimal Paths in Probabilistic Networks

Author

Listed:
  • Amir Eiger

    (Rensselaer Polytechnic Institute, Troy, New York)

  • Pitu B. Mirchandani

    (Rensselaer Polytechnic Institute, Troy, New York)

  • Hossein Soroush

    (Rensselaer Polytechnic Institute, Troy, New York)

Abstract

The classical shortest route problem in networks assumes deterministic link weights, and route evaluation by a utility (or cost) function that is linear over path weights. When the environment is stochastic and the “traveler’s” utility function for travel attributes is nonlinear, we define “optimal paths” that maximize the expected utility. In this setting, the concept of temporary and permanent preferences for route choices is introduced. It is shown that when the utility function is linear or exponential (constant risk averseness), permanent preferences prevail and an efficient Dijkstra-type algorithm can be used.

Suggested Citation

  • Amir Eiger & Pitu B. Mirchandani & Hossein Soroush, 1985. "Path Preferences and Optimal Paths in Probabilistic Networks," Transportation Science, INFORMS, vol. 19(1), pages 75-84, February.
    • Handle: RePEc:inm:ortrsc:v:19:y:1985:i:1:p:75-84
    DOI: 10.1287/trsc.19.1.75
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    Cited by:

    1. Thomas, Barrett W. & White III, Chelsea C., 2007. "The dynamic shortest path problem with anticipation," European Journal of Operational Research, Elsevier, vol. 176(2), pages 836-854, January.
    2. Elise D. Miller-Hooks & Hani S. Mahmassani, 2000. "Least Expected Time Paths in Stochastic, Time-Varying Transportation Networks," Transportation Science, INFORMS, vol. 34(2), pages 198-215, May.
    3. Nie, Yu (Marco) & Wu, Xing & Dillenburg, John F. & Nelson, Peter C., 2012. "Reliable route guidance: A case study from Chicago," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(2), pages 403-419.
    4. Pramesh Kumar & Alireza Khani, 2021. "Adaptive Park-and-ride Choice on Time-dependent Stochastic Multimodal Transportation Network," Networks and Spatial Economics, Springer, vol. 21(4), pages 771-800, December.
    5. Huang, He & Gao, Song, 2012. "Optimal paths in dynamic networks with dependent random link travel times," Transportation Research Part B: Methodological, Elsevier, vol. 46(5), pages 579-598.
    6. Yannick Kergosien & Antoine Giret & Emmanuel Néron & Gaël Sauvanet, 2022. "An Efficient Label-Correcting Algorithm for the Multiobjective Shortest Path Problem," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 76-92, January.
    7. Nielsen, Lars Relund & Pretolani, Daniele & Andersen, Kim Allan, 2004. "K shortest paths in stochastic time-dependent networks," CORAL Working Papers L-2004-05, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    8. Daniel Reich & Leo Lopes, 2011. "Preprocessing Stochastic Shortest-Path Problems with Application to PERT Activity Networks," INFORMS Journal on Computing, INFORMS, vol. 23(3), pages 460-469, August.
    9. Wang, Li & Yang, Lixing & Gao, Ziyou, 2016. "The constrained shortest path problem with stochastic correlated link travel times," European Journal of Operational Research, Elsevier, vol. 255(1), pages 43-57.
    10. Roberto Tadei & Guido Perboli & Francesca Perfetti, 2017. "The multi-path Traveling Salesman Problem with stochastic travel costs," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 3-23, March.
    11. Leilei Zhang & Tito Homem-de-Mello, 2017. "An Optimal Path Model for the Risk-Averse Traveler," Transportation Science, INFORMS, vol. 51(2), pages 518-535, May.
    12. Opasanon, Sathaporn & Miller-Hooks, Elise, 2006. "Multicriteria adaptive paths in stochastic, time-varying networks," European Journal of Operational Research, Elsevier, vol. 173(1), pages 72-91, August.
    13. Qi, Jin & Sim, Melvyn & Sun, Defeng & Yuan, Xiaoming, 2016. "Preferences for travel time under risk and ambiguity: Implications in path selection and network equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 264-284.
    14. Axel Parmentier, 2019. "Algorithms for non-linear and stochastic resource constrained shortest path," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(2), pages 281-317, April.
    15. Yueyue Fan & Yu Nie, 2006. "Optimal Routing for Maximizing the Travel Time Reliability," Networks and Spatial Economics, Springer, vol. 6(3), pages 333-344, September.
    16. Shahabi, Mehrdad & Unnikrishnan, Avinash & Boyles, Stephen D., 2013. "An outer approximation algorithm for the robust shortest path problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 58(C), pages 52-66.
    17. James L. Bander & Chelsea C. White, 2002. "A Heuristic Search Approach for a Nonstationary Stochastic Shortest Path Problem with Terminal Cost," Transportation Science, INFORMS, vol. 36(2), pages 218-230, May.
    18. Miller-Hooks, Elise & Mahmassani, Hani, 2003. "Path comparisons for a priori and time-adaptive decisions in stochastic, time-varying networks," European Journal of Operational Research, Elsevier, vol. 146(1), pages 67-82, April.
    19. Yu Nie & Xing Wu & Tito Homem-de-Mello, 2012. "Optimal Path Problems with Second-Order Stochastic Dominance Constraints," Networks and Spatial Economics, Springer, vol. 12(4), pages 561-587, December.
    20. Nie, Yu (Marco) & Wu, Xing, 2009. "Shortest path problem considering on-time arrival probability," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 597-613, July.

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