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A Comparison of Three Real-Time Shortest Path Models in Dynamic Interval Graph

Author

Listed:
  • Bo Xu

    (Business School, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Xiaodong Ji

    (School of Management, Shanghai University of Engineering Science, Shanghai 201620, China)

  • Zhengrong Cheng

    (School of Business Information, Shanghai Business School, Shanghai 201499, China)

Abstract

The Dynamic Interval (DI) graph models the updating uncertainty of the arc cost in the graph, which shows great application prospects in unstable-road transportation planning and management. This paper studies the Real-time Shortest Path (RTSP) problems in the DI graph. First, the RTSP problem is defined in mathematical equations. Second, three models for RTSP are proposed, which are the Dynamic Robust Shortest Path (DRSP) model, the Dynamic Greedy Robust Shortest Path (DGRSP) model and the Dynamic Mean Shortest Path (DMSP) model. Then, three solution methods are designed. Finally, a numerical study is conducted to compare the efficiency of the models and corresponding solution methods. It shows that the DGRSP model and DMSP model generally present better results than the others. In the real road network test, they have the minimum average-regret-ratio of DGSP 7.8% and DMSP 7.1%; while in the generated network test, they both have a minimum average-regret-ratio of 0.5%.

Suggested Citation

  • Bo Xu & Xiaodong Ji & Zhengrong Cheng, 2025. "A Comparison of Three Real-Time Shortest Path Models in Dynamic Interval Graph," Mathematics, MDPI, vol. 13(1), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:1:p:134-:d:1558377
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    References listed on IDEAS

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    1. Dimitris J. Bertsimas & Garrett van Ryzin, 1991. "A Stochastic and Dynamic Vehicle Routing Problem in the Euclidean Plane," Operations Research, INFORMS, vol. 39(4), pages 601-615, August.
    2. Bertsimas, Dimitris & Van Ryzin, Garrett., 1991. "A stochastic and dynamic vehicle routing problem in the Euclidean plane," Working papers 3286-91., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Dimitris J. Bertsimas & Garrett van Ryzin, 1993. "Stochastic and Dynamic Vehicle Routing in the Euclidean Plane with Multiple Capacitated Vehicles," Operations Research, INFORMS, vol. 41(1), pages 60-76, February.
    4. Azaron, Amir & Kianfar, Farhad, 2003. "Dynamic shortest path in stochastic dynamic networks: Ship routing problem," European Journal of Operational Research, Elsevier, vol. 144(1), pages 138-156, January.
    5. Zielinski, Pawel, 2004. "The computational complexity of the relative robust shortest path problem with interval data," European Journal of Operational Research, Elsevier, vol. 158(3), pages 570-576, November.
    6. Luciana S. Buriol & Mauricio G. C. Resende & Mikkel Thorup, 2008. "Speeding Up Dynamic Shortest-Path Algorithms," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 191-204, May.
    7. 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.
    8. Refael Hassin & Eitan Zemel, 1985. "On Shortest Paths in Graphs with Random Weights," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 557-564, November.
    9. H. Frank, 1969. "Shortest Paths in Probabilistic Graphs," Operations Research, INFORMS, vol. 17(4), pages 583-599, August.
    10. Randolph W. Hall, 1986. "The Fastest Path through a Network with Random Time-Dependent Travel Times," Transportation Science, INFORMS, vol. 20(3), pages 182-188, August.
    11. 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.
    12. J. J. Martin, 1965. "Distribution of the Time Through a Directed, Acyclic Network," Operations Research, INFORMS, vol. 13(1), pages 46-66, February.
    13. Harilaos N. Psaraftis & John N. Tsitsiklis, 1993. "Dynamic Shortest Paths in Acyclic Networks with Markovian Arc Costs," Operations Research, INFORMS, vol. 41(1), pages 91-101, February.
    14. Chassein, André & Dokka, Trivikram & Goerigk, Marc, 2019. "Algorithms and uncertainty sets for data-driven robust shortest path problems," European Journal of Operational Research, Elsevier, vol. 274(2), pages 671-686.
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