IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v65y2018i1p184-199.html
   My bibliography  Save this article

The Travelers Route Choice Problem Under Uncertainty: Dominance Relations Between Strategies

Author

Listed:
  • Marie Schmidt

    (Rotterdam School of Management, Erasmus University Rotterdam, NL-3000 DR, Rotterdam, The Netherlands)

  • Leo Kroon

    (Deceased, formerly at Rotterdam School of Management, Erasmus University)

  • Anita Schöbel

    (Institute for Numerical and Applied Mathematics, Georg-August University, D-37083, Göttingen, Germany)

  • Paul Bouman

    (Econometric Institute, Erasmus University Rotterdam, NL-3000 DR, Rotterdam, The Netherlands)

Abstract

In this paper we describe the Traveler’s Route Choice Problem (TRCP). This is the problem of a traveler in a railway system who plans to take the fastest route to a destination but is faced with a disruption of unknown length on this route. In that case, he can wait until the disruption is over or take a detour route as an alternative. Since the duration of the disruption is not known in advance, he is left with a decision problem under uncertainty. In this paper we model the problem and describe the strategies that may be used in such a situation. Instead of finding optimal strategies for a specialized quality measure, we consider dominance relations between strategies and show that dominated strategies are nonoptimal for the common quality measures. We then analyze which strategies for the TRCP are dominated. In general, the set of nondominated strategies is strongly reduced. We also show that, under certain assumptions, only a small set of strategies is nondominated and conclude that in this case the TRCP can be solved by enumeration for any of the quality measures.

Suggested Citation

  • Marie Schmidt & Leo Kroon & Anita Schöbel & Paul Bouman, 2017. "The Travelers Route Choice Problem Under Uncertainty: Dominance Relations Between Strategies," Operations Research, INFORMS, vol. 65(1), pages 184-199, February.
    • Handle: RePEc:inm:oropre:v:65:y:2018:i:1:p:184-199
    DOI: 10.287/opre.2016.1564
    as

    Download full text from publisher

    File URL: https://doi.org/10.287/opre.2016.1564
    Download Restriction: no
    File URL: https://libkey.io/10.287/opre.2016.1564?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Lam, Terence C. & Small, Kenneth A., 0. "The value of time and reliability: measurement from a value pricing experiment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 37(2-3), pages 231-251, April.
    2. Loomes, Graham & Sugden, Robert, 1982. "Regret Theory: An Alternative Theory of Rational Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 92(368), pages 805-824, December.
    3. Hites, R. & De Smet, Y. & Risse, N. & Salazar-Neumann, M. & Vincke, P., 2006. "About the applicability of MCDA to some robustness problems," European Journal of Operational Research, Elsevier, vol. 174(1), pages 322-332, October.
    4. Jean-Philippe Chancelier & Michel Lara & André Palma, 2009. "Risk aversion in expected intertemporal discounted utilities bandit problems," Theory and Decision, Springer, vol. 67(4), pages 433-440, October.
    5. André de Palma & Robin Lindsey & Nathalie Picard, 2012. "Risk Aversion, the Value of Information, and Traffic Equilibrium," Transportation Science, INFORMS, vol. 46(1), pages 1-26, February.
    6. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    7. Small, Kenneth A., 2001. "The Value of Pricing," University of California Transportation Center, Working Papers qt0rm449sx, University of California Transportation Center.
    8. David E. Bell, 1982. "Regret in Decision Making under Uncertainty," Operations Research, INFORMS, vol. 30(5), pages 961-981, October.
    9. Dan A. Iancu & Nikolaos Trichakis, 2014. "Pareto Efficiency in Robust Optimization," Management Science, INFORMS, vol. 60(1), pages 130-147, January.
    10. Dias, Luis C. & Climaco, Joao N., 2000. "Shortest path problems with partial information: Models and algorithms for detecting dominance," European Journal of Operational Research, Elsevier, vol. 121(1), pages 16-31, February.
    11. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    12. C. Elliott Sigal & A. Alan B. Pritsker & James J. Solberg, 1980. "The Stochastic Shortest Route Problem," Operations Research, INFORMS, vol. 28(5), pages 1122-1129, October.
    13. Panos Kouvelis & Serpil Sayın, 2006. "Algorithm robust for the bicriteria discrete optimization problem," Annals of Operations Research, Springer, vol. 147(1), pages 71-85, October.
    14. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gang Lin & Honglei Xu & Shaoli Wang & Conghua Lin & Fan Zhang & Junxiang Zhu, 2024. "Navigating Uncertainty: A Framework for Optimising Public Transport Networks’ Performance," Sustainability, MDPI, vol. 16(3), pages 1-23, February.
    2. König, Eva & Schön, Cornelia, 2021. "Railway delay management with passenger rerouting considering train capacity constraints," European Journal of Operational Research, Elsevier, vol. 288(2), pages 450-465.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marie Schmidt & Leo Kroon & Anita Schöbel & Paul Bouman, 2017. "The Travelers Route Choice Problem Under Uncertainty: Dominance Relations Between Strategies," Operations Research, INFORMS, vol. 65(1), pages 184-199, February.
    2. Chorus, Caspar G. & Arentze, Theo A. & Molin, Eric J.E. & Timmermans, Harry J.P. & Van Wee, Bert, 2006. "The value of travel information: Decision strategy-specific conceptualizations and numerical examples," Transportation Research Part B: Methodological, Elsevier, vol. 40(6), pages 504-519, July.
    3. Phillips Peter J. & Pohl Gabriela, 2018. "The Deferral of Attacks: SP/A Theory as a Model of Terrorist Choice when Losses Are Inevitable," Open Economics, De Gruyter, vol. 1(1), pages 71-85, February.
    4. Tan, Zhijia & Yang, Hai & Guo, Renyong, 2014. "Pareto efficiency of reliability-based traffic equilibria and risk-taking behavior of travelers," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 16-31.
    5. Martín Egozcue & Xu Guo & Wing-Keung Wong, 2015. "Optimal output for the regret-averse competitive firm under price uncertainty," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 5(2), pages 279-295, December.
    6. Colson, Gérard, 1993. "Prenons-nous assez de risque dans les théories du risque?," L'Actualité Economique, Société Canadienne de Science Economique, vol. 69(1), pages 111-141, mars.
    7. Qin, Jie, 2015. "A model of regret, investor behavior, and market turbulence," Journal of Economic Theory, Elsevier, vol. 160(C), pages 150-174.
    8. Sugden, Robert & Wang, Mengjie & Zizzo, Daniel John, 2019. "Take it or leave it: Experimental evidence on the effect of time-limited offers on consumer behaviour," Journal of Economic Behavior & Organization, Elsevier, vol. 168(C), pages 1-23.
    9. Enrico G. De Giorgi & Thierry Post, 2011. "Loss Aversion with a State-Dependent Reference Point," Management Science, INFORMS, vol. 57(6), pages 1094-1110, June.
    10. Ulrich Schmidt & Stefan Traub, 2009. "An Experimental Investigation of the Disparity Between WTA and WTP for Lotteries," Theory and Decision, Springer, vol. 66(3), pages 229-262, March.
    11. Soora Rasouli & Harry Timmermans, 2017. "Specification of regret-based models of choice behaviour: formal analyses and experimental design based evidence," Transportation, Springer, vol. 44(6), pages 1555-1576, November.
    12. George Wu, 1999. "Anxiety and Decision Making with Delayed Resolution of Uncertainty," Theory and Decision, Springer, vol. 46(2), pages 159-199, April.
    13. Pedro Bordalo & Nicola Gennaioli & Andrei Shleifer, 2013. "Salience and Consumer Choice," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 803-843.
    14. Raquel M. Gaspar & Paulo M. Silva, 2023. "Investors’ perspective on portfolio insurance," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 22(1), pages 49-79, January.
    15. Yuval Rottenstreich & Alex Markle & Johannes Müller-Trede, 2023. "Risky Sure Things," Management Science, INFORMS, vol. 69(8), pages 4707-4720, August.
    16. Ulrich Schmidt & Horst Zank, 2012. "A genuine foundation for prospect theory," Journal of Risk and Uncertainty, Springer, vol. 45(2), pages 97-113, October.
    17. Ronald Bosman & Frans Van Winden, 2010. "Global Risk, Investment and Emotions," Economica, London School of Economics and Political Science, vol. 77(307), pages 451-471, July.
    18. Aluma Dembo & Shachar Kariv & Matthew Polisson & John Quah, 2021. "Ever since Allais," IFS Working Papers W21/15, Institute for Fiscal Studies.
    19. Serge Blondel & Louis Lévy-garboua, 2011. "Can non-expected utility theories explain the paradox of not voting?," Economics Bulletin, AccessEcon, vol. 31(4), pages 3158-3168.
    20. Ivan Barreda-Tarrazona & Ainhoa Jaramillo-Gutierrez & Daniel Navarro-Martinez & Gerardo Sabater-Grande, 2014. "The role of forgone opportunities in decision making under risk," Journal of Risk and Uncertainty, Springer, vol. 49(2), pages 167-188, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:65:y:2018:i:1:p:184-199. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.