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Multi-trip pickup and delivery problem with time windows and synchronization

Abstract

In this paper, we consider two-tiered city logistics systems accounting for both the inbound and outbound traffic, that have not been taken into account in models and algorithms for vehicle routing research. The problem under study, called the Multi-trip Pickup and Delivery Problem with Time Windows and Synchronization, has two sets of intertwined decisions: the routing decisions which determine the sequence of customers visited by each vehicle route, the scheduling decisions which plan movements of vehicles between facilities within time synchronization restrictions. We propose a tabu search algorithm integrating multiple neighborhoods targeted to the decision sets of the problem. To assess the proposed algorithm, tests have been conducted on the first benchmark instances of the problem which have up to 72 facilities and 7200 customer demands. As no previous results are available in the literature for the problem, we also evaluate the performance of the method through comparisons with published results on two simplified problems: the Multi-zone multi-trip vehicle routing problem with separate delivery and collection, and the Vehicle routing problem with backhauls. The proposed algorithm is competitive with existing exact and meta-heuristic methods for these two problems.

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References

  1. Berbeglia, G., Cordeau, J.-F., Gribkovskaia, I., & Laporte, G. (2007). Static pickup and delivery problems: A classification scheme and survey. TOP, 15, 1–31.

    Article  Google Scholar 

  2. Berbeglia, G., Cordeau, J.-F., & Laporte, G. (2010). Dynamic pickup and delivery problems. European Journal of Operational Research, 202, 8–15.

    Article  Google Scholar 

  3. Bettinelli, A., Crainic, T.G., & Vigo, D. (2015). The multi-zone multi-trip vehicle routing problem with separate delivery and collection. Publication, Centre interuniversitaire de recherche sur les réseaux d’entreprise, la logistique et le transport, Université de Montréal, Montréal, QC, Canada. forthcoming.

  4. Brandão, J. (2006). A new tabu search algorithm for the Vehicle Routing Problem with backhauls. European Journal of Operational Research, 173(2), 540–555.

    Article  Google Scholar 

  5. Cordeau, J.-F., Laporte, G., & Mercier, A. (2001). A unified Tabu Search heuristic for vehicle routing problems with time windows. Journal of the Operational Research Society, 52, 928–936.

    Article  Google Scholar 

  6. Crainic, T. G., Ricciardi, N., & Storchi, G. (2009). Models for evaluating and planning city logistics systems. Transportation Science, 43(4), 432–454.

    Article  Google Scholar 

  7. Crainic, T. G., Errico, F., Rei, W., & Ricciardi, N. (2012). Integrating c2e and c2c Traffic into City logistics planning. Procedia Social and Behavioral Sciences, 39, 47–60.

    Article  Google Scholar 

  8. Dell’Amico, M., Righini, G., & Salani, M. (2006). A branch-and-price approach to the vehicle routing problem with simultaneous distribution and collection. Transportation Science, 40(2), 235–247.

    Article  Google Scholar 

  9. Dethloff, J. (2002). Relation between vehicle routing problems: An insertion heuristic for the vehicle routing problem with simultaneous delivery and pick-up applied to the vehicle routing problem with backhauls. Journal of the Operational Research Society, 53(1), 115–118.

    Article  Google Scholar 

  10. Dongarra, J.J. (2014). Performance of various computers using standard linear equations software. Technical report, University of Tennessee.

  11. Gélinas, S., Desrochers, M., Desrosiers, J., & Solomon, M. (1995). A new branching strategy for time constrained routing problems with application to backhauling. Annals of Operations Research, 61(1), 91–109.

    Article  Google Scholar 

  12. Goetschalckx, M., & Jacobs-Blecha, C. (1989). The Vehicle Routing Problem with backhauls. European Journal of Operational Research, 42(1), 39–51.

    Article  Google Scholar 

  13. Gribkovskaia, I., Halskau, O., Myklebost, K. (2001). Models for pick-up and deliveries from depots with Lasso solutions. In Proceedings of the 13th annual conference on logistics research (pp. 279–293). NOFOMA 2001, Collaboration in logistics: Connecting Islands using Information Technology.

  14. Lee, Y. H., Jung, J. W., & Lee, K. M. (2006). Vehicle routing scheduling for cross-docking in the supply chain. Computers & Industrial Engineering, 51(2), 247–256.

    Article  Google Scholar 

  15. Liao, C.-J., Lin, Y., & Shih, S. C. (2010). Vehicle routing with cross-docking in the supply chain. Expert Systems with Applications, 37(10), 6868–6873.

    Article  Google Scholar 

  16. Lin, S. (1965). Computer solutions of the traveling salesman problem. Bell System Technical Journal, 44, 2245–2269.

    Article  Google Scholar 

  17. Nagy, G., & Salhi, S. (2005). Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries. European Journal of Operational Research, 162(1), 126–141.

    Article  Google Scholar 

  18. Nguyen, P. K., Crainic, T. G., & Toulouse, M. (2013). A tabu search for time-dependent multi-zone multi-trip vehicle routing problem with time windows. European Journal of Operational Research, 231(1), 43–56.

    Article  Google Scholar 

  19. Or, I. (1976). Traveling salesman-type combinatorial problems and their relation to the logistics of blood banking. PhD thesis, Department of Industrial Engineering and Management Science, Northwestern University, Evanston, IL.

  20. Osman, I. H. (1993). Metastrategy simulated annealing and tabu search algorithms for the Vehicle Routing Problem. Annals of Operations Research, 41, 421–452.

    Article  Google Scholar 

  21. Osman, I. H., & Wassan, N. (2002). A reactive tabu search meta-heuristic for the vehicle routing problem with back-hauls. Journal of Scheduling, 5(4), 263–285.

    Article  Google Scholar 

  22. Parragh, S., Doerner, K., & Hartl, R. (2008a). A survey on pickup and delivery problems. Part I: Transportation between customers and depot. Journal für Betriebswirtschaft, 58, 21–51.

    Article  Google Scholar 

  23. Parragh, S., Doerner, K., & Hartl, R. (2008b). A survey on pickup and delivery problems. Part II Transportation between pickup and delivery locations. Journal für Betriebswirtschaft, 58, 81–117.

    Article  Google Scholar 

  24. Potvin, J.-Y., Duhamel, C., & Guertin, F. (1996). A genetic algorithm for vehicle routing with backhauling. Applied Intelligence, 6(4), 345–355.

    Article  Google Scholar 

  25. Reimann, M., & Ulrich, H. (2006). Comparing backhauling strategies in vehicle routing using ant colony optimization. Central European Journal of Operations Research, 14(2), 105–123.

    Article  Google Scholar 

  26. Reimann, M., Doerner, K., & Hartl, R. (2002). Insertion based ants for vehicle routing problems with backhauls and time windows. In M. Dorigo, G. Caro, & M. Sampels (Eds.), Ant algorithms volume 2463 of lecture notes in computer science (pp. 135–148). Berlin: Springer.

  27. Ropke, S., & Pisinger, D. (2006). A unified heuristic for a large class of vehicle routing problems with backhauls. European Journal of Operational Research, 2004, 750–775.

    Article  Google Scholar 

  28. Salhi, S., & Nagy, G. (1999). A cluster insertion heuristic for single and multiple depot vehicle routing problems with backhauling. Journal of the Operational Research Society, 50(10), 1034–1042.

    Article  Google Scholar 

  29. Savelsbergh, M. W. P., & Solomon, M. M. (1995). The general pickup and delivery problem. Transportation Science, 29, 17–29.

    Article  Google Scholar 

  30. Solomon, M. M. (1987). Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research, 35, 254–265.

    Article  Google Scholar 

  31. Taillard, E. D., Badeau, P., Gendreau, M., Guertin, F., & Potvin, J.-Y. (1997). A tabu search heuristic for the vehicle routing problem with soft time windows. Transportation Science, 31, 170–186.

    Article  Google Scholar 

  32. Thangiah, S. R., Potvin, J.-Y., & Sun, T. (1996). Heuristic approaches to vehicle routing with backhauls and time windows. Computers & Operations Research, 23(11), 1043–1057.

    Article  Google Scholar 

  33. Toth, P., & Vigo, D. (1997). An exact algorithm for the vehicle routing problem with backhauls. Transportation Science, 31(4), 372–385.

    Article  Google Scholar 

  34. Toth, P., & Vigo, D. (2002). The vehicle routing problem. Philadelphia, PA: Society for Industrial and Applied Mathematics.

    Book  Google Scholar 

  35. Vidal, T., Crainic, T. G., Gendreau, M., & Prins, C. (2014). A unified solution framework for multi-attribute vehicle routing problems. European Journal of Operational Research, 234(3), 658–673.

    Article  Google Scholar 

  36. Wassan, N. (2007). Reactive tabu adaptive memory programming search for the vehicle routing problem with backhauls. Journal of the Operational Research Society, 58(12), 1630–1641.

    Article  Google Scholar 

  37. Wen, M., Larsen, J., Clausen, J., Cordeau, J.-F., & Laporte, G. (2008). Vehicle routing with cross-docking. Journal of the Operational Research Society, 60, 1708–1718.

    Article  Google Scholar 

  38. Zhong, Y., & Cole, M. H. (2005). A vehicle routing problem with backhauls and time windows: A guided local search solution. Transportation Research Part E: Logistics and Transportation Review, 41(2), 131–144.

    Article  Google Scholar 

Download references

Acknowledgments

While working on this project, the first author was doctoral student with the Computer Science and Operations Research Department, Université de Montréal, and the second author was Adjuct Professor with the same department. The authors thank Professor Daniel Vigo and Dr. Andrea Bettinelli for their great kindness, cooperation and efforts to adjust their code and perform the exact-resolution part of the comparison experiments. Partial funding for this project comes from the Discovery Grant and the Discovery Accelerator Supplements Programs of the Natural Science and Engineering Research Council of Canada, and the Strategic Clusters program of the Fonds québécois de la recherche sur la nature et les technologies. The authors thank the two institutions for supporting this research.

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Correspondence to Teodor Gabriel Crainic.

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Nguyen, P.K., Crainic, T.G. & Toulouse, M. Multi-trip pickup and delivery problem with time windows and synchronization. Ann Oper Res 253, 899–934 (2017). https://doi.org/10.1007/s10479-015-2001-7

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Keywords

  • Multi-trip pickup and delivery problem with time windows
  • Synchronization
  • Tabu search
  • Multiple neighborhoods