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A Note on the Ichoua, Gendreau, and Potvin (2003) Travel Time Model

Author

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  • Gianpaolo Ghiani

    (Department of Engineering, Università del Salento Via Monteroni, 73100 Lecce, Italy)

  • Emanuela Guerriero

    (Department of Engineering, Università del Salento Via Monteroni, 73100 Lecce, Italy)

Abstract

In this paper we exploit some properties of the travel time model proposed by Ichoua, Gendreau, and Potvin [Ichoua S, Gendreau M, Potvin J-Y (2003) Vehicle dispatching with time-dependent travel times. Eur. J. Oper. Res. 144:379--396], on which most of the current time-dependent vehicle-routing literature relies. First, we prove that any continuous piecewise-linear travel time model, satisfying the FIFO property, can be generated by an appropriate model. We also show that the model parameters can be obtained by solving a system of linear equations for each arc. Then such parameters are proved to be nonnegative, which allows us to interpret them as (dummy) speeds. Finally, we illustrate the procedure through a numerical example. As a by-product, we are able to link the travel time models of a road graph and the associated complete graph over which vehicle-routing problems are usually formulated.

Suggested Citation

  • Gianpaolo Ghiani & Emanuela Guerriero, 2014. "A Note on the Ichoua, Gendreau, and Potvin (2003) Travel Time Model," Transportation Science, INFORMS, vol. 48(3), pages 458-462, August.
    • Handle: RePEc:inm:ortrsc:v:48:y:2014:i:3:p:458-462
    DOI: 10.1287/trsc.2013.0491
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    References listed on IDEAS

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    1. Bernhard Fleischmann & Martin Gietz & Stefan Gnutzmann, 2004. "Time-Varying Travel Times in Vehicle Routing," Transportation Science, INFORMS, vol. 38(2), pages 160-173, May.
    2. Ichoua, Soumia & Gendreau, Michel & Potvin, Jean-Yves, 2003. "Vehicle dispatching with time-dependent travel times," European Journal of Operational Research, Elsevier, vol. 144(2), pages 379-396, 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.
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    Cited by:

    1. Huang, Yixiao & Zhao, Lei & Van Woensel, Tom & Gross, Jean-Philippe, 2017. "Time-dependent vehicle routing problem with path flexibility," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 169-195.
    2. Hamza Ben Ticha & Nabil Absi & Dominique Feillet & Alain Quilliot & Tom Woensel, 2021. "The Time-Dependent Vehicle Routing Problem with Time Windows and Road-Network Information," SN Operations Research Forum, Springer, vol. 2(1), pages 1-25, March.
    3. Visser, T.R. & Spliet, R., 2017. "Efficient Move Evaluations for Time-Dependent Vehicle Routing Problems," Econometric Institute Research Papers EI2017-23, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Vu, Duc Minh & Hewitt, Mike & Vu, Duc D., 2022. "Solving the time dependent minimum tour duration and delivery man problems with dynamic discretization discovery," European Journal of Operational Research, Elsevier, vol. 302(3), pages 831-846.
    5. E. Angelelli & R. Mansini & M. Vindigni, 2016. "The Stochastic and Dynamic Traveling Purchaser Problem," Transportation Science, INFORMS, vol. 50(2), pages 642-658, May.
    6. Saif Eddin Jabari & Nikolaos M. Freris & Deepthi Mary Dilip, 2020. "Sparse Travel Time Estimation from Streaming Data," Transportation Science, INFORMS, vol. 54(1), pages 1-20, January.
    7. Thibaut Vidal & Rafael Martinelli & Tuan Anh Pham & Minh Hoàng Hà, 2021. "Arc Routing with Time-Dependent Travel Times and Paths," Transportation Science, INFORMS, vol. 55(3), pages 706-724, May.
    8. Thomas R. Visser & Remy Spliet, 2020. "Efficient Move Evaluations for Time-Dependent Vehicle Routing Problems," Transportation Science, INFORMS, vol. 54(4), pages 1091-1112, July.

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    Keywords

    time-varying travel times; vehicle routing;

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