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Mathematical formulations for consistent travelling salesman problems

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  • Díaz-Ríos, Daniel
  • Salazar-González, Juan-José

Abstract

The consistent travelling salesman problem looks for a minimum-cost set of Hamiltonian routes, one for every day of a given time period. When a customer requires service in several days, the service times on different days must differ by no more than a given threshold (for example, one hour). We analyze two variants of the problem, depending on whether the vehicle is allowed to wait or not at a customer location before its service starts. There are three mathematical models in the literature for the problem without waiting times, and this paper describes a new model appropriated to be solved with a branch-and-cut algorithm. The new model is a multi-commodity flow formulation on which Benders’ Decomposition helps manage a large number of flow variables. There were no mathematical models in the literature for the variant with waiting times, and this paper adapts the four mathematical models to it. We analyze the computational results of the formulations on instances from the literature with up to 100 customers and three days.

Suggested Citation

  • Díaz-Ríos, Daniel & Salazar-González, Juan-José, 2024. "Mathematical formulations for consistent travelling salesman problems," European Journal of Operational Research, Elsevier, vol. 313(2), pages 465-477.
    • Handle: RePEc:eee:ejores:v:313:y:2024:i:2:p:465-477
    DOI: 10.1016/j.ejor.2023.08.021
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    References listed on IDEAS

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    1. Yao, Yu & Van Woensel, Tom & Veelenturf, Lucas P. & Mo, Pengli, 2021. "The consistent vehicle routing problem considering path consistency in a road network," Transportation Research Part B: Methodological, Elsevier, vol. 153(C), pages 21-44.
    2. Dominik Goeke & Roberto Roberti & Michael Schneider, 2019. "Exact and Heuristic Solution of the Consistent Vehicle-Routing Problem," Transportation Science, INFORMS, vol. 53(4), pages 1023-1042, July.
    3. Lu Zhen & Wenya Lv & Kai Wang & Chengle Ma & Ziheng Xu, 2020. "Consistent vehicle routing problem with simultaneous distribution and collection," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(5), pages 813-830, May.
    4. Anirudh Subramanyam & Chrysanthos E. Gounaris, 2018. "A Decomposition Algorithm for the Consistent Traveling Salesman Problem with Vehicle Idling," Transportation Science, INFORMS, vol. 52(2), pages 386-401, March.
    5. Luo, Zhixing & Qin, Hu & Che, ChanHou & Lim, Andrew, 2015. "On service consistency in multi-period vehicle routing," European Journal of Operational Research, Elsevier, vol. 243(3), pages 731-744.
    6. John W. Chinneck, 1997. "Finding a Useful Subset of Constraints for Analysis in an Infeasible Linear Program," INFORMS Journal on Computing, INFORMS, vol. 9(2), pages 164-174, May.
    7. Braekers, Kris & Kovacs, Attila A., 2016. "A multi-period dial-a-ride problem with driver consistency," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 355-377.
    8. Chris Groër & Bruce Golden & Edward Wasil, 2009. "The Consistent Vehicle Routing Problem," Manufacturing & Service Operations Management, INFORMS, vol. 11(4), pages 630-643, February.
    9. T. L. Magnanti & R. T. Wong, 1981. "Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria," Operations Research, INFORMS, vol. 29(3), pages 464-484, June.
    10. Nolz, Pamela C. & Absi, Nabil & Feillet, Dominique & Seragiotto, Clóvis, 2022. "The consistent electric-Vehicle routing problem with backhauls and charging management," European Journal of Operational Research, Elsevier, vol. 302(2), pages 700-716.
    11. Subramanyam, Anirudh & Gounaris, Chrysanthos E., 2016. "A branch-and-cut framework for the consistent traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 248(2), pages 384-395.
    12. Campelo, Pedro & Neves-Moreira, Fábio & Amorim, Pedro & Almada-Lobo, Bernardo, 2019. "Consistent vehicle routing problem with service level agreements: A case study in the pharmaceutical distribution sector," European Journal of Operational Research, Elsevier, vol. 273(1), pages 131-145.
    13. Bektaş, Tolga & Gouveia, Luis, 2014. "Requiem for the Miller–Tucker–Zemlin subtour elimination constraints?," European Journal of Operational Research, Elsevier, vol. 236(3), pages 820-832.
    14. Kunlei Lian & Ashlea Bennett Milburn & Ronald L. Rardin, 2016. "An improved multi-directional local search algorithm for the multi-objective consistent vehicle routing problem," IISE Transactions, Taylor & Francis Journals, vol. 48(10), pages 975-992, October.
    15. Stavropoulou, F. & Repoussis, P.P. & Tarantilis, C.D., 2019. "The Vehicle Routing Problem with Profits and consistency constraints," European Journal of Operational Research, Elsevier, vol. 274(1), pages 340-356.
    16. Vansteenwegen, Pieter & Souffriau, Wouter & Oudheusden, Dirk Van, 2011. "The orienteering problem: A survey," European Journal of Operational Research, Elsevier, vol. 209(1), pages 1-10, February.
    17. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
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