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Journal of the Operational Research Society

, Volume 65, Issue 1, pp 37–48 | Cite as

A metaheuristic based on a pool of routes for the vehicle routing problem with multiple trips and time windows

  • Z Wang
  • W Liang
  • X Hu
General Paper

Abstract

This paper studies the vehicle routing problem with multiple trips and time windows, in which vehicles are allowed to perform multiple trips during a scheduling period and each customer must be served within a given time interval. The problem is of particular importance for planning fleets of hired vehicles in common practices, such as e-grocery distributions, but this problem has received little attention in the literature. As a result of the multi-layered structure characteristic of the problem solution, we propose a pool-based metaheuristic in which various routes are first constructed to fill a pool, following which some of the routes are selected and combined to form vehicle working schedules. Finally, we conduct a series of experiments over a set of benchmark instances to evaluate and demonstrate the effectiveness of the proposed metaheuristic.

Keywords

vehicle routing multiple trips time windows a metaheuristic based on a pool of routes 

Notes

Acknowledgements

This work is partially supported by the grants from the National Natural Science Foundation of China (Nos. 70801008, 71271037, 90924006), the Fundamental Research Funds for the Central Universities (No. DUT12JR09) and the National Science Foundation of China for Distinguished Young Scholars (No. 70725004). Those supports are gratefully acknowledged. The authors thank the editor and the referees for their valuable comments and suggestions that have greatly improved the quality of this paper.

Supplementary material

41274_2014_BFjors20134_MOESM1_ESM.pdf (55 kb)
Online Appendix B and C

References

  1. Alonso F, Alvarez MJ and Beasley JE (2008). A tabu search algorithm for the periodic vehicle routing problem with multiple vehicle trips and accessibility restrictions. Journal of the Operational Research Society 59 (7): 963–976.CrossRefGoogle Scholar
  2. Avella P, Boccia M and Sforza A (2004). Solving a fuel delivery problem by heuristic and exact approaches. European Journal of Operational Research 152 (1): 170–179.CrossRefGoogle Scholar
  3. Azi N, Gendreau M and Potvin JY (2007). An exact algorithm for a single-vehicle routing problem with time windows and multiple routes. European Journal of Operational Research 178 (3): 755–766.CrossRefGoogle Scholar
  4. Azi N, Gendreau M and Potvin JY (2010a). An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles. European Journal of Operational Research 202 (3): 756–763.CrossRefGoogle Scholar
  5. Azi N, Gendreau M and Potvin JY (2010b). An adaptive large neighborhood search for a vehicle routing problem with multiple trips. Technical report CIRRELT-2010-08: Montreal.Google Scholar
  6. Battarra M, Moncaci M and Vigo D (2008). An adaptive guidance approach for the heuristic solution of a minimum multiple trip vehicle routing problem. Computers & Operation Research 36 (11): 3041–3050.CrossRefGoogle Scholar
  7. Brandão J and Mercer A (1997). A tabu search algorithm for the multi-trip vehicle routing and scheduling problem. European Journal of Operational Research 100 (1): 180–191.CrossRefGoogle Scholar
  8. Brandão J and Mercer A (1998). The multi-trip vehicle routing problem. Journal of the Operational Research Society 49 (8): 799–805.CrossRefGoogle Scholar
  9. Campbell AM and Savelsbergh M (2004). Efficient insertion heuristics for vehicle routing and scheduling problems. Transportation Science 38 (3): 369–378.CrossRefGoogle Scholar
  10. Chbichib A, Mellouli R and Chabchoub H (2011). Profitable vehicle routing problem with multiple trips: Modeling and constructive heuristics. Logistics (LOGISTIQUA), 2011 4th, International Conference, pp 500–507.Google Scholar
  11. Cornillier F, Laporte G, Boctor FF and Renaud J (2009). The petrol station replenishment problem with time windows. Computers & Operations Research 36 (3): 919–935.CrossRefGoogle Scholar
  12. Fleischmann B (1990). The vehicle routing problem with multiple use of vehicles. Working paper, Fachbereich Wirtschaftswissenschaften, Universität Hamburg.Google Scholar
  13. Gehring H and Homberger J (1999). A parallel hybrid evolutionary metaheuristic for the vehicle routing problem with time windows. In: Proceedings of EUROGEN, 30 May–3 June, University of Jyväskylä, Finland. Vol. 99, pp 57–64.Google Scholar
  14. Golden B, Laporte G and Taillard E (1997). An adaptive memory heuristic for a class of vehicle routing problems with minmax objective. Computers & Operations Research 24 (5): 445–452.CrossRefGoogle Scholar
  15. Jeon G, Leep HR and Shim JY (2007). A vehicle routing problem solved by using a hybrid genetic algorithm. Computers & Industrial Engineering 53 (4): 680–692.CrossRefGoogle Scholar
  16. Lenstra JK and Rinnooy Kan AHG (1981). Complexity of vehicle and scheduling problems. Networks 11 (2): 221–227.CrossRefGoogle Scholar
  17. Olivera A and Viera O (2007). Adaptive memory programming for the vehicle routing problem with multiple trips. Computers & Operations Research 34 (1): 28–47.CrossRefGoogle Scholar
  18. Petch RJ and Salhi S (2003). A multi-phase constructive heuristic for the vehicle routing problem with multiple trips. Discrete Applied Mathematics 133 (1): 69–92.CrossRefGoogle Scholar
  19. Petch RJ and Salhi S (2007). A GA based heuristic for the vehicle routing problem with multiple trips. Journal of Mathematical Modelling and Algorithms 6 (4): 591–613.CrossRefGoogle Scholar
  20. Prins C (2004). A simple and effective evolutionary algorithm for the vehicle routing problem. Computers and Operations Research 31 (12): 1985–2002.CrossRefGoogle Scholar
  21. Rochat Y and Taillard E (1995). Probabilistic diversification and intensification in local search for vehicle routing. Journal of Heuristics 1 (1): 147–167.CrossRefGoogle Scholar
  22. Savelsbergh MWP (1992). The vehicle routing problem with time windows: Minimizing route duration. Journal on Computing 4 (2): 146–154.Google Scholar
  23. Solomon MM (1987). Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research 35 (2): 254–265.CrossRefGoogle Scholar
  24. Taillard ED, Laporte G and Gendreau M (1996). Vehicle routing with multiple use of vehicles. Journal of the Operational Research Society 47 (8): 1065–1070.CrossRefGoogle Scholar

Copyright information

© Operational Research Society 2013

Authors and Affiliations

  • Z Wang
    • 1
  • W Liang
    • 1
  • X Hu
    • 1
  1. 1.Dalian University of TechnologyLiaoningChina

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