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Facets and valid inequalities for the time-dependent travelling salesman problem

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  • Miranda-Bront, Juan José
  • Méndez-Díaz, Isabel
  • Zabala, Paula

Abstract

The Time-Dependent Travelling Salesman Problem (TDTSP) is a generalization of the traditional TSP where the travel cost between two cities depends on the moment of the day the arc is travelled. In this paper, we focus on the case where the travel time between two cities depends not only on the distance between them, but also on the position of the arc in the tour. We consider two formulations proposed in the literature, we analyze the relationship between them and derive several families of valid inequalities and facets. In addition to their theoretical properties, they prove to be very effective in the context of a Branch and Cut algorithm.

Suggested Citation

  • Miranda-Bront, Juan José & Méndez-Díaz, Isabel & Zabala, Paula, 2014. "Facets and valid inequalities for the time-dependent travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 236(3), pages 891-902.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:3:p:891-902
    DOI: 10.1016/j.ejor.2013.05.022
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    References listed on IDEAS

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    1. Gouveia, Luis & Vo[ss], Stefan, 1995. "A classification of formulations for the (time-dependent) traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 83(1), pages 69-82, May.
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    4. Russ J. Vander Wiel & Nikolaos V. Sahinidis, 1995. "Heuristic Bounds and Test Problem Generation for the Time-Dependent Traveling Salesman Problem," Transportation Science, INFORMS, vol. 29(2), pages 167-183, May.
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    Cited by:

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    2. 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.
    3. Kinable, Joris & Cire, Andre A. & van Hoeve, Willem-Jan, 2017. "Hybrid optimization methods for time-dependent sequencing problems," European Journal of Operational Research, Elsevier, vol. 259(3), pages 887-897.
    4. Cacchiani, Valentina & Contreras-Bolton, Carlos & Toth, Paolo, 2020. "Models and algorithms for the Traveling Salesman Problem with Time-dependent Service times," European Journal of Operational Research, Elsevier, vol. 283(3), pages 825-843.
    5. Albert Einstein Fernandes Muritiba & Tibérius O. Bonates & Stênio Oliveira Da Silva & Manuel Iori, 2021. "Branch-and-Cut and Iterated Local Search for the Weighted k -Traveling Repairman Problem: An Application to the Maintenance of Speed Cameras," Transportation Science, INFORMS, vol. 55(1), pages 139-159, 1-2.
    6. Lera-Romero, Gonzalo & Miranda-Bront, Juan José, 2021. "A branch and cut algorithm for the time-dependent profitable tour problem with resource constraints," European Journal of Operational Research, Elsevier, vol. 289(3), pages 879-896.

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