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Dynamic journeying under uncertainty

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  • Häme, Lauri
  • Hakula, Harri

Abstract

We introduce a journey planning problem in multi-modal transportation networks under uncertainty. The goal is to find a journey, possibly involving transfers between different transport services, from a given origin to a given destination within a specified time horizon. Due to uncertainty in travel times, the arrival times of transport services at public transport stops are modeled as random variables. If a transfer between two services is rendered unsuccessful, the commuter has to reconsider the remaining path to the destination. The problem is modeled as a Markov decision process in which states are defined as paths in the transport network. The main contribution is a backward induction method that generates an optimal policy for traversing the public transport network in terms of maximizing the probability of reaching the destination in time. By assuming history independence and independence of successful transfers between services we obtain approximate methods for the same problem. Analysis and numerical experiments suggest that while solving the path dependent model requires the enumeration of all paths from the origin to the destination, the proposed approximations may be useful for practical purposes due to their computational simplicity. In addition to on-time arrival probability, we show how travel and overdue costs can be taken into account, making the model applicable to freight transportation problems.

Suggested Citation

  • Häme, Lauri & Hakula, Harri, 2013. "Dynamic journeying under uncertainty," European Journal of Operational Research, Elsevier, vol. 225(3), pages 455-471.
    • Handle: RePEc:eee:ejores:v:225:y:2013:i:3:p:455-471
    DOI: 10.1016/j.ejor.2012.10.027
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    3. 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.
    4. Redmond, Michael & Campbell, Ann Melissa & Ehmke, Jan Fabian, 2022. "Reliability in public transit networks considering backup itineraries," European Journal of Operational Research, Elsevier, vol. 300(3), pages 852-864.
    5. Patrick Jaillet & Jin Qi & Melvyn Sim, 2016. "Routing Optimization Under Uncertainty," Operations Research, INFORMS, vol. 64(1), pages 186-200, February.
    6. Arvind U. Raghunathan & David Bergman & John N. Hooker & Thiago Serra & Shingo Kobori, 2024. "Seamless Multimodal Transportation Scheduling," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 336-358, March.
    7. López, David & Lozano, Angélica, 2020. "Shortest hyperpaths in a multimodal hypergraph with real-time information on some transit lines," Transportation Research Part A: Policy and Practice, Elsevier, vol. 137(C), pages 541-559.
    8. Zhang, Yu & Tang, Jiafu, 2018. "Itinerary planning with time budget for risk-averse travelers," European Journal of Operational Research, Elsevier, vol. 267(1), pages 288-303.

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