Metaheuristics for the Pick-Up and Delivery Problem with Contracted Orders

  • Philip Mourdjis
  • Peter Cowling
  • Martin Robinson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8600)

Abstract

Contracted orders represent a novel extension to the Pick-up and Delivery Problem (PDP) with soft time windows. This extension to the multiple depot problem has depots managed by separate, competing haulage companies “carriers”. Orders may be assigned to a specific carrier “contracted”, “allocated” to a specific carrier but allowed to swap if this improves the solution or free to use any carrier “spot hired”. Soft time windows lead to a multi-objective problem of minimising distance travelled and delay incurred. In this paper we use real order data supplied by 3 large distributors and 220 carriers. Additional, randomised, orders are generated to match the distributions observed in this data, representing backhaul orders for which no data is available. We compare a manual scheduling technique based on discussions with industry partners to popular metaheuristics for similar problems namely Tabu Search (TS), Variable Neighbourhood Search (VNS) and Hybrid Variable Neighbourhood Tabu Search (HVNTS), using our modified local search operators. Results show that VNS and HVNTS produce results which are 50% shorter than greedy approaches across test instances of 300 orders in a one week period.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Desrosiers, J., Dumas, Y., Solomon, M.M., Soumis, F.: Time Constrained Routing and Scheduling. Handbooks in Operations Research and Management Science 8, 35–139 (1995)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Bräysy, O., Gendreau, M.: Vehicle Routing Problem with Time Windows, Part I: Route Construction and Local Search Algorithms. Transportation Science 39(1), 104–118 (2005)CrossRefGoogle Scholar
  3. 3.
    Bräysy, O., Gendreau, M.: Vehicle Routing Problem with Time Windows, Part II: Metaheuristics. Transportation Science 39(1), 119–139 (2005)CrossRefGoogle Scholar
  4. 4.
    Berbeglia, G., Cordeau, J.F., Gribkovskaia, I., Laporte, G.: Static pickup and delivery problems: a classification scheme and survey. TOP 15(1), 1–31 (2007)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Parragh, S.N., Doerner, K.F., Hartl, R.F.: A survey on pickup and delivery problems. Journal für Betriebswirtschaft 58(2), 81–117 (2008)CrossRefGoogle Scholar
  6. 6.
    Dumas, Y., Desrosiers, J., Soumis, F.: The pickup and delivery problem with time windows. European Journal of Operational Research 54, 7–22 (1991)CrossRefMATHGoogle Scholar
  7. 7.
    Ropke, S., Pisinger, D.: An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows. Transportation Science 40(4), 455–472 (2005)CrossRefGoogle Scholar
  8. 8.
    Malca, F., Semet, F.: A tabu search heuristic for the pickup and delivery problem with time windows and a fixed size fleet, 1–5 (2003) (unpublished manuscript)Google Scholar
  9. 9.
    Gendreau, M., Guertin, F., Potvin, J.Y., Séguin, R.: Neighborhood Search Heuristics for a Dynamic Vehicle Dispatching Problem with Pick-ups and Deliveries. Transportation Research Part C: Emerging Technologies 14(3), 157–174 (2006)CrossRefGoogle Scholar
  10. 10.
    Taillard, E.D., Badeau, P., Gendreau, M., Guertin, F., Potvin, J.Y.: A Tabu Search Heuristic for the Vehicle Routing Problem with Soft Time Windows. Transportation Science 31(2), 170–186 (1997)CrossRefMATHGoogle Scholar
  11. 11.
    Cordeau, J.F., Laporte, G., Mercier, A.: A unified tabu search heuristic for vehicle routing problems with time windows. Journal of the Operational Research Society 52(8), 928–936 (2001)CrossRefMATHGoogle Scholar
  12. 12.
    Cordeau, J.F., Laporte, G., Mercier, A.: Improved tabu search algorithm for the handling of route duration constraints in vehicle routing problems with time windows. Journal of the Operational Research Society 55(5), 542–546 (2004)CrossRefMATHGoogle Scholar
  13. 13.
    Mladenović, N., Hansen, P.: Variable Neighbourhood Search. Computers & Operations Research 24(1), 1097–1100 (1997)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Hansen, P., Mladenović, N., Moreno Pérez, J.A.: Variable Neighbourhood Search: Methods and Applications. Annals of Operations Research 175(1), 367–407 (2009)CrossRefGoogle Scholar
  15. 15.
    Bräysy, O.: A Reactive Variable Neighborhood Search for the Vehicle-Routing Problem with Time Windows. INFORMS Journal On Computing 15(4), 347–368 (2003)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Polacek, M., Hartl, R.F., Doerner, K.F.: A Variable Neighborhood Search for the Multi Depot Vehicle Routing Problem with Time Windows. Journal of Heuristics 10, 613–627 (2004)CrossRefGoogle Scholar
  17. 17.
    Belhaiza, S., Hansen, P., Laporte, G.: A hybrid variable neighborhood tabu search heuristic for the vehicle routing problem with multiple time windows. Computers & Operations Research (August 2013)Google Scholar
  18. 18.
    Gendreau, M., Hertz, A., Laporte, G.: New Insertion and Post Optimization Procedures for the Traveling Salesman Problem. Operations Research 40(6), 1086–1095 (1992)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Glover, F.: Artificial Intelligence, Heuristic Frameworks and Tabu Search. Managerial and Decision Economics 11(5), 365–375 (1990)CrossRefGoogle Scholar
  20. 20.
    Barr, R.S., Golden, B.L., Kelly, J.P., Resende, M.G.C., Stewart, W.R.: Designing and Reporting on Computational Experiments with Heuristic Methods. Journal of Heuristics 1(1), 9–32 (1995)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Philip Mourdjis
    • 1
  • Peter Cowling
    • 1
  • Martin Robinson
    • 2
  1. 1.York Center for Complex Systems Analysis (YCCSA) and Department of Computer ScienceUniversity of YorkYorkUK
  2. 2.Transfaction Ltd.SuffolkUK

Personalised recommendations