THE PRIZE-COLLECTING VEHICLE ROUTING PROBLEM WITH NON-LINEAR COST - Integration of Subcontractors into Route Design of Small Package Shippers

Andreas Stenger

2012

Abstract

In this paper, we propose a new routing problem to model a highly relevant planning problem in small package shipping. The problem, called Prize-Collecting Vehicle Routing Problem with Non-Linear cost (PCVRPNL), allows for each customer the choice of being serviced by a vehicle of the private fleet or being outsourced to a subcontractor. A lower bound on the total customer demand serviced by the private fleet ensures a constant capacity utilization. The subcontracting costs follow a non-linear function representing the discount given by a subcontractor if larger amounts of packages are assigned. To solve the NP-hard problem, we propose a Variable Neighborhood Search algorithm. In numerical studies performed on benchmark instances adapted from classical VRP, we demonstrate the strong performance of our algorithm and study the effect of different cost functions on the routing solution.

References

  1. Balas, E. (1989). The prize collecting traveling salesman problem. Networks, 19(6):621-636.
  2. Bolduc, M.-C., Renaud, J., and Boctor, F. (2007). A heuristic for the routing and carrier selection problem. European Journal of Operational Research, 183(2):926- 932.
  3. Bolduc, M.-C., Renaud, J., Boctor, F., and Laporte, G. (2008). A perturbation metaheuristic for the vehicle routing problem with private fleet and common carriers. Journal of the Operational Research Society, 59(6):776-787.
  4. Bräysy, O. (2003). A reactive variable neighborhood search for the vehicle routing problem with time windows. INFORMS Journal on Computing, 15(4):347-368.
  5. Chaves, A. A. and Lorena, L. A. N. (2008). Hybrid metaheuristic for the prize collecting travelling salesman problem. In van Hemert, J. and Cotta, C., editors, EvoCOP 2008. LNCS, vol. 4972. Springer, Heidelberg.
  6. Christofides, N. and Eilon, S. (1969). An algorithm for one vehicle-dispatching problem. Operational Research Quarterly, 20(3):309-318.
  7. Chu, C.-W. (2005). A heuristic algorithm for the truckload and less-than-truckload problem. European Journal of Operational Research, 165(3):657-667.
  8. Clarke, G. and Wright, J. W. (1964). Scheduling of vehicles from a central depot to a number of delivery points. Operations Research, 12(4):568-581.
  9. Cordeau, J.-F., Gendreau, M., and Laporte, G. (1997). A tabu search heuristic for periodic and multi-depot vehicle routing problems. Networks, 30(2):105-119.
  10. Coˆté, J.-F. and Potvin, J.-Y. (2009). A tabu search heuristic for the vehicle routing problem with private fleet and common carrier. European Journal of Operational Research, 198(2):464-469.
  11. Dell'Amico, M., Maffioli, F., and Sciomachen, A. (1998). A lagrangian heuristic for the prize collecting travelling salesman problem. Annals of Operations Research, 81(0):289-305.
  12. Feillet, D., Dejax, P., and Gendreau, M. (2005). Traveling salesman problems with profits. Transportation Science, 39(2):188-205.
  13. Hansen, P. and Mladenovic, N. (2001). Variable neighborhood search: Principles and applications. European Journal of Operational Research, 130(3):449 - 467.
  14. Hemmelmayr, V. C., Doerner, K. F., and Hartl, R. F. (2009). A variable neighborhood search heuristic for periodic routing problems. European Journal of Operational Research, 195(3):791-802.
  15. Kytöjoki, J., Nuortio, T., Bräysy, O., and Gendreau, M. (2007). An efficient variable neighborhood search heuristic for very large scale vehicle routing problems. Computers & Operations Research, 34:2743-2757.
  16. Lin, S. (1965). Computer solutions to the travelingsalesman problem. Bell System Technical Journal, 44(10):2245-2269.
  17. Or, I. (1976). Traveling salesman-type problems and their relation to the logistics of regional blood banking. PhD thesis, Department of Industrial Engineering and Management Sciences, Northwestern University Evanston, IL.
  18. Potvin, J.-Y. and Naud, M.-A. (2011). Tabu search with ejection chains for the vehicle routing problem with private fleet and common carrier. Journal of the Operational Research Society, 62(2):326-336.
  19. Stenger, A., Vigo, D., Enz, S., and Schwind, M. (2011). An adaptive variable neighborhood search algorithm for a vehicle routing problem arising in small package shipping. to appear in: Transportation Science.
  20. Tang, L. and Wang, X. (2006). Iterated local search algorithm based on very large-scale neighborhood for prize-collecting vehicle routing problem. The International Journal of Advanced Manufacturing Technology, 29(11-12):1246-1258.
  21. Thompson, P. M. and Psaraftis, H. N. (1993). Cyclic transfer algorithms for multivehicle routing and scheduling problems. Operations Research, 41(5):935-946.
  22. Vidal, T., Crainic, T. G., Gendreau, M., Lahrichi, N., and Rei, W. (2011). A hybrid genetic algorithm for multidepot and periodic vehicle routing problems. Technical report, CIRRELT-2011-05.
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Paper Citation


in Harvard Style

Stenger A. (2012). THE PRIZE-COLLECTING VEHICLE ROUTING PROBLEM WITH NON-LINEAR COST - Integration of Subcontractors into Route Design of Small Package Shippers . In Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-8425-97-3, pages 265-273. DOI: 10.5220/0003740002650273


in Bibtex Style

@conference{icores12,
author={Andreas Stenger},
title={THE PRIZE-COLLECTING VEHICLE ROUTING PROBLEM WITH NON-LINEAR COST - Integration of Subcontractors into Route Design of Small Package Shippers},
booktitle={Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2012},
pages={265-273},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003740002650273},
isbn={978-989-8425-97-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - THE PRIZE-COLLECTING VEHICLE ROUTING PROBLEM WITH NON-LINEAR COST - Integration of Subcontractors into Route Design of Small Package Shippers
SN - 978-989-8425-97-3
AU - Stenger A.
PY - 2012
SP - 265
EP - 273
DO - 10.5220/0003740002650273