A POPMUSIC approach for the Multi-Depot Cumulative Capacitated Vehicle Routing Problem

  • Eduardo Lalla-RuizEmail author
  • Stefan Voß
Original Paper


The Multi-Depot Cumulative Capacitated Vehicle Routing Problem is a variation of the recently proposed Capacitated Cumulative Vehicle Routing Problem, where several depots can be considered as starting points of routes. Its objective aims at minimizing the sum of arrival times at customers for providing service. Practical considerations imply to address the delivery of customers from multiple depots where the service quality level depends on the customer waiting time and the delivering vehicles may be able to depart from different points. Those scenarios require theoretical models to support the decision-making process as well as for measuring the quality of the solutions provided by approximate approaches. In the present work, we formalize this new problem variant by means of a mathematical formulation and propose a matheuristic approach (POPMUSIC) for solving it.


Multi-Depot Cumulative Vehicle Routing Problem POPMUSIC Matheuristic Disaster logistics Customer-oriented applications 



  1. 1.
    Bertacco, L., Brunetta, L., Fischetti, M.: The linear ordering problem with cumulative costs. Eur. J. Oper. Res. 189(3), 1345–1357 (2008)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Blum, A., Chalasani, P., Coppersmith, D., Pulleyblank, B., Raghavan, P., Sudan, M.: The minimum latency problem. In: Proceedings of the 26th Annual ACM Symposium on Theory of computing, pp. 163–171. ACM (1994)Google Scholar
  3. 3.
    Chen, P., Dong, X., Niu, Y.: An iterated local search algorithm for the cumulative capacitated vehicle routing problem. In: Tan, H. (ed.) Technology for Education and Learning, pp. 575–581. Springer, Berlin (2012)CrossRefGoogle Scholar
  4. 4.
    Cordeau, J.F., Gendreau, M., Laporte, G.: A tabu search heuristic for periodic and multi-depot vehicle routing problems. Networks 30(2), 105–119 (1997)CrossRefGoogle Scholar
  5. 5.
    Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manag. Sci. 6, 80–91 (1959)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Fischetti, M., Laporte, G., Martello, S.: The delivery man problem and cumulative matroids. Oper. Res. 41(6), 1055–1064 (1993)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Fischetti, M., Monaci, M.: Exploiting erraticism in search. Oper. Res. 62(1), 114–122 (2014)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Gouveia, L., Voß, S.: A classification of formulations for the (time-dependent) traveling salesman problem. Eur. J. Oper. Res. 83(1), 69–82 (1995)CrossRefGoogle Scholar
  9. 9.
    Lalla-Ruiz, E., Voß, S.: Improving solver performance through redundancy. J. Syst. Sci. Syst. Eng. 25(3), 303–325 (2016)CrossRefGoogle Scholar
  10. 10.
    Lalla-Ruiz, E., Voß, S.: Popmusic as a matheuristic for the berth allocation problem. Ann. Math. Artif. Intell. 76(1–2), 173–189 (2016)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Lalla-Ruiz, E., Voß, S., Expósito-Izquierdo, C., Melián-Batista, B., Moreno-Vega, J.M.: A POPMUSIC-based approach for the berth allocation problem under time-dependent limitations. Ann. Oper. Res. 253(2), 871–897 (2017)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lalla-Ruiz, E., Schwarze, S., Voß, S.: A matheuristic approach for the p-cable trench problem. In: Festa, P., Sellmann, M., Vanschoren, J. (eds.) Learning and Intelligent Optimization, pp. 247–252. Springer (2016)Google Scholar
  13. 12.
    Lysgaard, J., Wøhlk, S.: A branch-and-cut-and-price algorithm for the cumulative capacitated vehicle routing problem. Eur. J. Oper. Res. 236(3), 800–810 (2014)MathSciNetCrossRefGoogle Scholar
  14. 13.
    Martínez-Salazar, I., Angel-Bello, F., Alvarez, A.: A customer-centric routing problem with multiple trips of a single vehicle. J. Oper. Res. Soc. 66(8), 1312–1323 (2015)CrossRefGoogle Scholar
  15. 14.
    Montoya-Torres, J.R., Franco, J.L., Isaza, S.N., Jiménez, H.F., Herazo-Padilla, N.: A literature review on the vehicle routing problem with multiple depots. Comput. Ind. Eng. 79, 115–129 (2015)CrossRefGoogle Scholar
  16. 15.
    Ngueveu, S., Prins, C., Wolfler-Calvo, R.: An effective memetic algorithm for the cumulative capacitated vehicle routing problem. Comput. Oper. Res. 37(11), 1877–1885 (2010)MathSciNetCrossRefGoogle Scholar
  17. 16.
    Renaud, J., Laporte, G., Boctor, F.: A tabu search heuristic for the multi-depot vehicle routing problem. Comput. Oper. Res. 23(3), 229–235 (1996)CrossRefGoogle Scholar
  18. 17.
    Ribeiro, G., Laporte, G.: An adaptive large neighborhood search heuristic for the cumulative capacitated vehicle routing problem. Comput. Oper. Res. 39(3), 728–735 (2012)MathSciNetCrossRefGoogle Scholar
  19. 18.
    Rivera, J.C., Afsar, H.M., Prins, C.: Mathematical formulations and exact algorithm for the multitrip cumulative capacitated single-vehicle routing problem. Eur. J. Oper. Res. 249(1), 93–104 (2016)MathSciNetCrossRefGoogle Scholar
  20. 19.
    Salehipour, A., Sörensen, K., Goos, P., Bräysy, O.: Efficient GRASP + VND and GRASP + VNS metaheuristics for the traveling repairman problem. 4OR 9(2), 189–209 (2011)MathSciNetCrossRefGoogle Scholar
  21. 20.
    Sumichras, R., Markham, I.: A heuristic and lower bound for a multi-depot routing problem. Comput. Oper. Res. 22(10), 1047–1056 (1995)CrossRefGoogle Scholar
  22. 21.
    Sze, J.F., Salhi, S., Wassan, N.: The cumulative capacitated vehicle routing problem with min–sum and min–max objectives: an effective hybridisation of adaptive variable neighbourhood search and large neighbourhood search. Transp. Res. Part B Methodol. 101, 162–184 (2017)CrossRefGoogle Scholar
  23. 22.
    Taillard, É.D., Voß, S.: POPMUSIC-partial optimization metaheuristic under special intensification conditions. In: Ribeiro, C.C., Hansen, P. (eds.) Essays and Surveys in Metaheuristics, pp. 613–629. Springer, Berlin (2002)CrossRefGoogle Scholar
  24. 23.
    Taillard, É.D., Voß, S.: Popmusic. In: Martí, R., Pardalos, P.M., Resende, M.G.C. (eds.) Handbook of Heuristics, pp. 687–701. Springer, Berlin (2017).
  25. 24.
    Talarico, L., Meisel, F., Sörensen, K.: Ambulance routing for disaster response with patient groups. Comput. Oper. Res. 56, 120–133 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Business Information SystemsUniversity of TwenteEnschedeThe Netherlands
  2. 2.Institute of Information SystemsUniversity of HamburgHamburgGermany
  3. 3.Escuela de Ingeniería IndustrialPontificia Universidad Católica de ValparaísoValparaisoChile

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