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An Exact Solution Framework for Multitrip Vehicle-Routing Problems with Time Windows

Author

Listed:
  • Rosario Paradiso

    (Department of Mathematics and Computer Science, University of Calabria, 87036 Arcavacata di Rende CS, Italy)

  • Roberto Roberti

    (Department of Supply Chain Analytics, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands)

  • Demetrio Laganá

    (Department of Mechanical, Energy and Management Engineering, University of Calabria, 87036 Arcavacata di Rende CS, Italy)

  • Wout Dullaert

    (Department of Supply Chain Analytics, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands)

Abstract

Multitrip vehicle - routing problems (MTVRPs) generalize the well-known VRP by allowing vehicles to perform multiple trips per day. MTVRPs have received a lot of attention lately because of their relevance in real-life applications—for example, in city logistics and last-mile delivery. Several variants of the MTVRP have been investigated in the literature, and a number of exact methods have been proposed. Nevertheless, the computational results currently available suggest that MTVRPs with different side constraints require ad hoc formulations and solution methods to be solved. Moreover, solving instances with just 25 customers can be out of reach for such solution methods. In this paper, we proposed an exact solution framework to address four different MTVRPs proposed in the literature. The exact solution framework is based on a novel formulation that has an exponential number of variables and constraints. It relies on column generation, column enumeration, and cutting plane. We show that this solution framework can solve instances with up to 50 customers of four MTVRP variants and outperforms the state-of-the-art methods from the literature.

Suggested Citation

  • Rosario Paradiso & Roberto Roberti & Demetrio Laganá & Wout Dullaert, 2020. "An Exact Solution Framework for Multitrip Vehicle-Routing Problems with Time Windows," Operations Research, INFORMS, vol. 68(1), pages 180-198, January.
  • Handle: RePEc:inm:oropre:v:68:y:2020:i:1:p:180-198
    DOI: 10.1287/opre.2019.1874
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    References listed on IDEAS

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    1. Azi, Nabila & Gendreau, Michel & Potvin, Jean-Yves, 2010. "An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles," European Journal of Operational Research, Elsevier, vol. 202(3), pages 756-763, May.
    2. Roberto Baldacci & Aristide Mingozzi & Roberto Roberti, 2011. "New Route Relaxation and Pricing Strategies for the Vehicle Routing Problem," Operations Research, INFORMS, vol. 59(5), pages 1269-1283, October.
    3. Christian Tilk & Stefan Irnich, 2017. "Dynamic Programming for the Minimum Tour Duration Problem," Transportation Science, INFORMS, vol. 51(2), pages 549-565, May.
    4. Roberto Baldacci & Aristide Mingozzi & Roberto Roberti, 2012. "New State-Space Relaxations for Solving the Traveling Salesman Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 356-371, August.
    5. Azi, Nabila & Gendreau, Michel & Potvin, Jean-Yves, 2007. "An exact algorithm for a single-vehicle routing problem with time windows and multiple routes," European Journal of Operational Research, Elsevier, vol. 178(3), pages 755-766, May.
    6. Hernandez, Florent & Feillet, Dominique & Giroudeau, Rodolphe & Naud, Olivier, 2016. "Branch-and-price algorithms for the solution of the multi-trip vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 249(2), pages 551-559.
    7. Mads Jepsen & Bjørn Petersen & Simon Spoorendonk & David Pisinger, 2008. "Subset-Row Inequalities Applied to the Vehicle-Routing Problem with Time Windows," Operations Research, INFORMS, vol. 56(2), pages 497-511, April.
    8. Marius M. Solomon, 1987. "Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints," Operations Research, INFORMS, vol. 35(2), pages 254-265, April.
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