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On the exact solution of the multi-depot open vehicle routing problem

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Abstract

The multi-depot open vehicle routing problem (MDOVRP) is a variant of the classical capacitated vehicle routing problem, where the vehicles can depart from different depots and they do not need to go back to the depot at the end of the route. This paper presents an exact branch-cut-and-price algorithm for the problem that is coded within the VRPSolver framework. In order to prove the robustness of the proposed method, we present several computational experiments over 24 MDOVRP benchmark instances. The results allow us to draw two important conclusions. The first one is that the proposed algorithm solves to the optimality all literature instances including eight that were open so far while the second one is that our algorithm outperforms the former state-of-art. Besides, we propose 440 MDOVRP instances with up to 200 nodes, where 418 of them are solved to the optimality by the proposed method. Another contribution of this paper is to show how to adapt the proposed method for the MDOVRP variant with time windows constraints (MDOVRPTW). We also apply our approach to MDOVRP and MDOVRPTW variants with a single depot. The results for all variants show that our method find the optimal solution for almost all tested instances in reasonable computational times.

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References

  1. Bezerra, S.N., de Souza, S.R., Souza, M.J.F.: A general vns for the multi-depot open vehicle routing problem with time windows. Optim. Lett. (2023). https://doi.org/10.1007/s11590-023-01990-1

    Article  MathSciNet  Google Scholar 

  2. Brandão, J.: A memory-based iterated local search algorithm for the multi-depot open vehicle routing problem. Eur. J. Oper. Res. 284(2), 559–571 (2020)

    Article  MathSciNet  Google Scholar 

  3. Cordeau, J.F., Gendreau, M., Laporte, G.: A tabu search heuristic for periodic and multi-depot vehicle routing problems. Netw. Int. J. 30(2), 105–119 (1997)

    Google Scholar 

  4. Cordeau, J.F., Laporte, G., Mercier, A.: A unified tabu search heuristic for vehicle routing problems with time windows. J. Op. Res soc. 52(8), 928–936 (2001)

    Article  Google Scholar 

  5. Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manage. Sci. 6(1), 80–91 (1959)

    Article  MathSciNet  Google Scholar 

  6. Lahyani, R., Gouguenheim, A.L., Coelho, L.C.: A hybrid adaptive large neighbourhood search for multi-depot open vehicle routing problems. Int. J. Prod. Res. 57(22), 6963–6976 (2019)

    Article  Google Scholar 

  7. Lalla-Ruiz, E., Expósito-Izquierdo, C., Taheripour, S., Voß, S.: An improved formulation for the multi-depot open vehicle routing problem. OR Spectr. 38(1), 175–187 (2016)

    Article  MathSciNet  Google Scholar 

  8. Lalla-Ruiz, E., Mes, M.: Mathematical formulations and improvements for the multi-depot open vehicle routing problem. Optim. Lett. 15(1), 271–286 (2021)

    Article  MathSciNet  Google Scholar 

  9. Letchford, A.N., Lysgaard, J., Eglese, R.W.: A branch-and-cut algorithm for the capacitated open vehicle routing problem. J. Op. Res. Soc. 58(12), 1642–1651 (2007)

    Article  Google Scholar 

  10. Liu, R., Jiang, Z., Geng, N.: A hybrid genetic algorithm for the multi-depot open vehicle routing problem. OR Spectr. 36(2), 401–421 (2014)

    Article  MathSciNet  Google Scholar 

  11. Pessoa, A., Sadykov, R., Uchoa, E., Vanderbeck, F.: A generic exact solver for vehicle routing and related problems. Math. Progr. 183(1), 483–523 (2020)

    Article  MathSciNet  Google Scholar 

  12. Ruiz, E., Soto-Mendoza, V., Barbosa, A.E.R., Reyes, R.: Solving the open vehicle routing problem with capacity and distance constraints with a biased random key genetic algorithm. Comput. Ind. Eng. 133, 207–219 (2019)

    Article  Google Scholar 

  13. Sadati, M.E.H., Çatay, B., Aksen, D.: An efficient variable neighborhood search with tabu shaking for a class of multi-depot vehicle routing problems. Comput. Op. Res. 133, 105269 (2021)

    Article  MathSciNet  Google Scholar 

  14. Solomon, M.M.: Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper. Res. 35(2), 254–265 (1987)

    Article  MathSciNet  Google Scholar 

  15. Soto, M., Sevaux, M., Rossi, A., Reinholz, A.: Multiple neighborhood search, tabu search and ejection chains for the multi-depot open vehicle routing problem. Comput. Ind. Eng. 107, 211–222 (2017)

    Article  Google Scholar 

  16. Subramanian, A., Uchoa, E., Ochi, L.S.: A hybrid algorithm for a class of vehicle routing problems. Comput. Op. Res. 40(10), 2519–2531 (2013)

    Article  Google Scholar 

  17. Tarantilis, C., Kiranoudis, C.: Distribution of fresh meat. J. Food Eng. 51(1), 85–91 (2002)

    Article  Google Scholar 

  18. Uchoa, E., Pecin, D., Pessoa, A., Poggi, M., Vidal, T., Subramanian, A.: New benchmark instances for the capacitated vehicle routing problem. Eur. J. Oper. Res. 257(3), 845–858 (2017)

    Article  MathSciNet  Google Scholar 

  19. Yao, B., Hu, P., Zhang, M., Tian, X.: Improved ant colony optimization for seafood product delivery routing problem. Promet-Traffic Transp. 26(1), 1–10 (2014)

    Google Scholar 

  20. Yu, N., Qian, B., Hu, R., Chen, Y., Wang, L.: Solving open vehicle problem with time window by hybrid column generation algorithm. J. Syst. Eng. Electron. 33(4), 997–1009 (2022)

    Article  Google Scholar 

  21. Zachariadis, E.E., Kiranoudis, C.T.: An open vehicle routing problem metaheuristic for examining wide solution neighborhoods. Comput. Op. Res. 37(4), 712–723 (2010)

    Article  Google Scholar 

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Authors and Affiliations

  1. Pós-Graduação em Engenharia de Produção, Universidade Federal Fluminense, Niterói, Brazil

    Vinícius Carvalho Soares

  2. Departamento de Engenharia de Produção, Universidade Federal Fluminense, Niterói, Brazil

    Marcos Roboredo

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  1. Vinícius Carvalho Soares
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  2. Marcos Roboredo
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Correspondence to Marcos Roboredo.

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Soares, V.C., Roboredo, M. On the exact solution of the multi-depot open vehicle routing problem. Optim Lett 18, 1053–1069 (2024). https://doi.org/10.1007/s11590-023-02072-y

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