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Variable-Depth Search for the Single-Vehicle Pickup and Delivery Problem with Time Windows

Author

Listed:
  • L. J. J. van der Bruggen

    (Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands)

  • J. K. Lenstra

    (Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands)

  • P. C. Schuur

    (Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands)

Abstract

We consider a single depot and a set of customers with known demands, each of which must be picked up and delivered at specified locations and within given time windows. We seek a route and a schedule for a single vehicle with known capacity, which minimizes the route duration, i.e., the difference between the arrival time and the departure time at the depot. We develop a local search method for this problem based on a variable-depth search, similar to the Lin-Kernighan algorithm for the traveling salesman problem. The method consists of two phases. In the first phase, a feasible route is constructed; in the second phase, it is iteratively improved. In both phases, we use a variable-depth search built up out of seven basic types of arc-exchange procedures. When tested on real-life problems, the method is shown to produce near-optimal solutions in a reasonable amount of computation time. In spite of this, there is the theoretical possibility that the method may end up with a poor or even infeasible solution. As a safeguard against such an emergency, we have developed an alternative algorithm based on simulated annealing. As a rule, it finds high quality solutions in a relatively large computation time.

Suggested Citation

  • L. J. J. van der Bruggen & J. K. Lenstra & P. C. Schuur, 1993. "Variable-Depth Search for the Single-Vehicle Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 27(3), pages 298-311, August.
    • Handle: RePEc:inm:ortrsc:v:27:y:1993:i:3:p:298-311
    DOI: 10.1287/trsc.27.3.298
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    Cited by:

    1. Schaumann, Sarah K. & Bergmann, Felix M. & Wagner, Stephan M. & Winkenbach, Matthias, 2023. "Route efficiency implications of time windows and vehicle capacities in first- and last-mile logistics," European Journal of Operational Research, Elsevier, vol. 311(1), pages 88-111.
    2. Ghorpade, Tejas & Rangaraj, Narayan, 2022. "Order first split second heuristic for alternative routing strategy for freight railways," Transport Policy, Elsevier, vol. 124(C), pages 139-148.
    3. Yanik, Seda & Bozkaya, Burcin & deKervenoael, Ronan, 2014. "A new VRPPD model and a hybrid heuristic solution approach for e-tailing," European Journal of Operational Research, Elsevier, vol. 236(3), pages 879-890.
    4. Lu, Quan & Dessouky, Maged M., 2006. "A new insertion-based construction heuristic for solving the pickup and delivery problem with time windows," European Journal of Operational Research, Elsevier, vol. 175(2), pages 672-687, December.
    5. Luo, Ying & Schonfeld, Paul, 2007. "A rejected-reinsertion heuristic for the static Dial-A-Ride Problem," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 736-755, August.
    6. Nanry, William P. & Wesley Barnes, J., 2000. "Solving the pickup and delivery problem with time windows using reactive tabu search," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 107-121, February.
    7. Coslovich, Luca & Pesenti, Raffaele & Ukovich, Walter, 2006. "A two-phase insertion technique of unexpected customers for a dynamic dial-a-ride problem," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1605-1615, December.
    8. Francesco Carrabs & Jean-François Cordeau & Gilbert Laporte, 2007. "Variable Neighborhood Search for the Pickup and Delivery Traveling Salesman Problem with LIFO Loading," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 618-632, November.
    9. Diana, Marco & Dessouky, Maged M., 2004. "A new regret insertion heuristic for solving large-scale dial-a-ride problems with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 38(6), pages 539-557, July.
    10. Luca Maria Gambardella & Marco Dorigo, 2000. "An Ant Colony System Hybridized with a New Local Search for the Sequential Ordering Problem," INFORMS Journal on Computing, INFORMS, vol. 12(3), pages 237-255, August.
    11. Mitrovic-Minic, Snezana & Krishnamurti, Ramesh & Laporte, Gilbert, 2004. "Double-horizon based heuristics for the dynamic pickup and delivery problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 38(8), pages 669-685, September.
    12. Fabri, A. & Recht, P., 2006. "On dynamic pickup and delivery vehicle routing with several time windows and waiting times," Transportation Research Part B: Methodological, Elsevier, vol. 40(4), pages 335-350, May.
    13. Mitrovic-Minic, Snezana & Laporte, Gilbert, 2004. "Waiting strategies for the dynamic pickup and delivery problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 38(7), pages 635-655, August.
    14. Grunert, Tore & Sebastian, Hans-Jurgen, 2000. "Planning models for long-haul operations of postal and express shipment companies," European Journal of Operational Research, Elsevier, vol. 122(2), pages 289-309, April.

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