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Dynamic Shortest Paths Minimizing Travel Times And Costs

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  • Ahuja, Ravindra
  • Orlin, James
  • Pallottino, Stefano
  • Scutella, Maria

Abstract

In this paper, we study dynamic shortest path problems that determine a shortest path from a specified source node to every other node in the network where arc travel times change dynamically. We consider two problems: the minimum time walk problem and the minimum cost walk problem. The minimum time walk problem is to find a walk with the minimum travel time. The minimum cost walk problem is to find a walk with the minimum weighted sum of the travel time and the excess travel time (over the minimum possible travel time). The minimum time walk problem is known to be polynomially solvable for a class of networks called FIFO networks. In this paper: (i) we show that the minimum cost walk problem is an NP-hard problem; (ii) we develop a pseudopolynomial-time algorithm to solve the minimum cost walk problem (for integer travel times); and (iii) we develop a polynomial-time algorithm for the minimum time walk problem arising in road networks with traffic light

Suggested Citation

  • Ahuja, Ravindra & Orlin, James & Pallottino, Stefano & Scutella, Maria, 2003. "Dynamic Shortest Paths Minimizing Travel Times And Costs," Working papers 4390-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    • Handle: RePEc:mit:sloanp:1798
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    File URL: http://hdl.handle.net/1721.1/1798
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    References listed on IDEAS

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    1. Stuart E. Dreyfus, 1969. "An Appraisal of Some Shortest-Path Algorithms," Operations Research, INFORMS, vol. 17(3), pages 395-412, June.
    2. Ravindra K. Ahuja & James B. Orlin & Stefano Pallottino & Maria Grazia Scutellà, 2002. "Minimum Time and Minimum Cost-Path Problems in Street Networks with Periodic Traffic Lights," Transportation Science, INFORMS, vol. 36(3), pages 326-336, August.
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    Cited by:

    1. Ziliaskopoulos, Athanasios K. & Mandanas, Fotios D. & Mahmassani, Hani S., 2009. "An extension of labeling techniques for finding shortest path trees," European Journal of Operational Research, Elsevier, vol. 198(1), pages 63-72, October.
    2. Giacomo Nannicini & Philippe Baptiste & Gilles Barbier & Daniel Krob & Leo Liberti, 2010. "Fast paths in large-scale dynamic road networks," Computational Optimization and Applications, Springer, vol. 45(1), pages 143-158, January.
    3. Jean-François Cordeau & Gianpaolo Ghiani & Emanuela Guerriero, 2014. "Analysis and Branch-and-Cut Algorithm for the Time-Dependent Travelling Salesman Problem," Transportation Science, INFORMS, vol. 48(1), pages 46-58, February.
    4. Lunce Fu & Maged Dessouky, 2018. "Algorithms for a special class of state-dependent shortest path problems with an application to the train routing problem," Journal of Scheduling, Springer, vol. 21(3), pages 367-386, June.
    5. Hu, Xiao-Bing & Zhang, Ming-Kong & Zhang, Qi & Liao, Jian-Qin, 2017. "Co-Evolutionary path optimization by Ripple-Spreading algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 411-432.
    6. Antonio Polimeni & Antonino Vitetta, 2013. "Optimising Waiting at Nodes in Time-Dependent Networks: Cost Functions and Applications," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 805-818, March.
    7. Bozhenyuk Alexander & Gerasimenko Evgeniya, 2013. "Algorithm for Monitoring Minimum Cost in Fuzzy Dynamic Networks," Information Technology and Management Science, Sciendo, vol. 16(1), pages 53-59, December.

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