Advertisement

Annals of Operations Research

, Volume 236, Issue 2, pp 359–382 | Cite as

Distribution of waiting time for dynamic pickup and delivery problems

  • Stefan VonolfenEmail author
  • Michael Affenzeller
Article

Abstract

Pickup and delivery problems have numerous applications in practice such as parcel delivery and passenger transportation. In the dynamic variant of the problem, not all information is available in advance but is revealed during the planning process. Thus, it is crucial to anticipate future events in order to generate high-quality solutions. Previous work has shown that the use of waiting strategies has the potential to save costs and maximize service quality. We adapt various waiting heuristics to the pickup and delivery problem with time windows. Previous research has shown, that specialized waiting heuristics utilizing anticipatory knowledge potentially outperform general heuristics. Direct policy search based on evolutionary computation and a simulation model is proposed as a methodology to automatically specialize waiting strategies to different problem characteristics. Based on the strengths of the previously introduced waiting strategies, we propose a novel waiting heuristic that can utilize historical request information based on an intensity measure which does not require an additional data preprocessing step. The performance of the waiting heuristics is evaluated on a single set of benchmark instances containing various instance classes that differ in terms of spatial and temporal properties. The diverse set of benchmark instances is used to analyze the influence of spatial and temporal instance properties as well as the degree of dynamism to the potential savings that can be achieved by anticipatory waiting and the incorporation of knowledge about future requests.

Keywords

Dynamic pickup and delivery problem Waiting strategies Direct policy search Simulation-based optimization 

Notes

Acknowledgments

The authors would like to thank the attendees of the ORP3 workshop held during July 2012 in Linz as well as the reviewers for their helpful comments, discussions and feedback. The work described in this article was done within the Regio 13 program sponsored by the European Regional Development Fund and by Upper Austrian public funds.

References

  1. Affenzeller, M., Winkler, S., Wagner, S., & Beham, A. (2009). Genetic algorithms and genetic programming: Modern concepts and practical applications (Numerical Insights) (1st ed.). UK: Chapman & Hall.CrossRefGoogle Scholar
  2. Attanasio, A., Cordeau, J. F., Ghiani, G., & Laporte, G. (2004). Parallel tabu search heuristics for the dynamic multi-vehicle dial-a-ride problem. Parallel Computing, 30(3), 377–387.CrossRefGoogle Scholar
  3. Beham, A., Kofler, M., Wagner, S., Affenzeller, M. (2009). Coupling simulation with heuristiclab to solve facility layout problems. In: Simulation Conference (WSC), Proceedings of the 2009 Winter, pp. 2205–2217. doi: 10.1109/WSC.2009.5429238.
  4. Bent, R., Van Hentenryck, P. (2007). Waiting and relocation strategies in online stochastic vehicle routing. In: IJCAI, pp. 1816–1821.Google Scholar
  5. Berbeglia, G., Cordeau, J. F., & Laporte, G. (2010). Dynamic pickup and delivery problems. European Journal of Operational Research, 202(1), 8–15. doi: 10.1016/j.ejor.2009.04.024.CrossRefGoogle Scholar
  6. Beyer, H. G., & Schwefel, H. P. (2002). Evolution strategies: A comprehensive introduction. Natural Computing, 1(1), 3–52.CrossRefGoogle Scholar
  7. Branke, J., Middendorf, M., Noeth, G., Dessouky, M. (2005). Waiting strategies for dynamic vehicle routing. Transportation Science 39:298–312. doi: 10.1287/trsc.1040.0095.
  8. Burke, E. K., Gendreau, M., Hyde, M., Kendall, G., Ochoa, G., Özcan, E., et al. (2013). Hyper-heuristics: A survey of the state of the art. Journal of the Operational Research Society, 64(12), 1695–1724.CrossRefGoogle Scholar
  9. Can, B., Beham, A., Heavey, C. (2008). A comparative study of genetic algorithm components in simulation-based optimisation. In: Proceedings of the 40th Conference on Winter Simulation, Winter Simulation Conference, WSC ’08, pp 1829–1837, URL http://dl.acm.org/citation.cfm?id=1516744.1517063
  10. Cordeau, J., & Laporte, G. (2003). A tabu search heuristic for the static multi-vehicle dial-a-ride problem. Transportation Research Part B: Methodological, 37(6), 579–594.CrossRefGoogle Scholar
  11. Cordeau, J., Laporte, G., & Mercier, A. (2001). A unified tabu search heuristic for vehicle routing problems with time windows. Journal of the Operational research society, 52(8), 928–936.CrossRefGoogle Scholar
  12. Cordeau, J., Gendreau, M., Laporte, G., Potvin, J., & Semet, F. (2002). A guide to vehicle routing heuristics. Journal of the Operational Research Society, 53(5), 512–522.Google Scholar
  13. Cordeau, J. F., & Laporte, G. (2007). The dial-a-ride problem: Models and algorithms. Annals of Operations Research, 153(1), 29–46.CrossRefGoogle Scholar
  14. Coslovich, L., Pesenti, R., & Ukovich, W. (2006). A two-phase insertion technique of unexpected customers for a dynamic dial-a-ride problem. European Journal of Operational Research, 175(3), 1605–1615.CrossRefGoogle Scholar
  15. Dantzig, G. B., & Ramser, J. H. (1959). The truck dispatching problem. Management Science, 6(1), 80–91. doi: 10.2307/2627477.CrossRefGoogle Scholar
  16. Eksioglu, B., Vural, A. V., & Reisman, A. (2009). The vehicle routing problem: A taxonomic review. Computers and Industrial Engineering, 57(4), 1472–1483. doi: 10.1016/j.cie.2009.05.009.CrossRefGoogle Scholar
  17. Ferrucci, F., Bock, S., & Gendreau, M. (2012). A pro-active real-time control approach for dynamic vehicle routing problems dealing with the delivery of urgent goods. European Journal of Operational Research, 225(1), 130–141.Google Scholar
  18. Fu, M. C. (2002). Feature article: Optimization for simulation: Theory vs. practice. INFORMS Journal on Computing, 14(3), 192–215. doi: 10.1287/ijoc.14.3.192.113.CrossRefGoogle Scholar
  19. Gendreau, M., & Potvin, J. (2004). Issues in real-time fleet management. Transportation Science, 38(4), 397–398.CrossRefGoogle Scholar
  20. Ghiani, G., Guerriero, F., Laporte, G., & Musmanno, R. (2003). Real-time vehicle routing: Solution concepts, algorithms and parallel computing strategies. European Journal of Operational Research, 151(1), 1–11. doi: 10.1016/S0377-2217(02)00915-3.CrossRefGoogle Scholar
  21. Golden, B., Raghavan, S., & Wasil, E. (2008). The vehicle routing problem: Latest advances and new challenges. Operations Research/Computer Science Interfaces. Dordrecht: Springer.CrossRefGoogle Scholar
  22. Gutenschwager, K., Niklaus, C., & Voß, S. (2004). Dispatching of an electric monorail system: Applying metaheuristics to an online pickup and delivery problem. Transportation science, 38(4), 434–446.CrossRefGoogle Scholar
  23. Hentenryck, P. V., & Bent, R. (2009). Online stochastic combinatorial optimization. Cambridge: The MIT Press.Google Scholar
  24. Ichoua, S., Gendreau, M., & Potvin, J. Y. (2006). Exploiting knowledge about future demands for real-time vehicle dispatching. Transportation Science, 40, 211–225. doi: 10.1287/trsc.1050.0114.CrossRefGoogle Scholar
  25. Ichoua, S., Gendreau, M., Potvin, JY. (2007). Planned route optimization for real-time vehicle routing. In: Dynamic fleet management, Springer, pp 1–18.Google Scholar
  26. Li, H., Lim, A. (2001). A metaheuristic for the pickup and delivery problem with time windows. In: Tools with artificial intelligence, Proceedings of the 13th International Conference on, pp 160–167, Doi: 10.1109/ICTAI.2001.974461.
  27. Longo, F. (2011). Advances of modeling and simulation in supply chain and industry. Simulation, 87(8), 651–656.CrossRefGoogle Scholar
  28. Mes, M., van der Heijden, M., & van Harten, A. (2007). Comparison of agent-based scheduling to look-ahead heuristics for real-time transportation problems. European Journal of Operational Research, 181(1), 59–75.CrossRefGoogle Scholar
  29. Mitrovic-Minic, S., & Laporte, G. (2004). Waiting strategies for the dynamic pickup and delivery problem with time windows. Transportation Research Part B: Methodological, 38(7), 635–655. doi: 10.1016/j.trb.2003.09.002.CrossRefGoogle Scholar
  30. Mitrovic-Minic, S., Adviser-Krishnamurti, R., & Adviser-Laporte, G. (2001). The dynamic pickup and delivery problem with time windows. Burnaby: Simon Fraser University.Google Scholar
  31. Mitrovic-Minic, S., Krishnamurti, R., & Laporte, G. (2004). Double-horizon based heuristics for the dynamic pickup and delivery problem with time windows. Transportation Research Part B: Methodological, 38(8), 669–685. doi: 10.1016/j.trb.2003.09.001.CrossRefGoogle Scholar
  32. Moriarty, D. E., Schultz, A. C., & Grefenstette, J. J. (1999). Evolutionary algorithms for reinforcement learning. Journal of Artificial Intelligence Research, 11, 241–276.Google Scholar
  33. Pankratz, G. (2005). Dynamic vehicle routing by means of a genetic algorithm. International Journal of Physical Distribution and Logistics Management, 35(5), 362–383. doi: 10.1108/09600030510607346.CrossRefGoogle Scholar
  34. Pappa, GL., Ochoa, G., Hyde, MR., Freitas, AA., Woodward, J., Swan, J. (2013). Contrasting meta-learning and hyper-heuristic research: The role of evolutionary algorithms. Genetic Programming and Evolvable Machines, 1–33.Google Scholar
  35. Parragh, S. N., Doerner, K. F., & Hartl, R. F. (2008). A survey on pickup and delivery problems. Journal für Betriebswirtschaft, 58(1), 21–51.CrossRefGoogle Scholar
  36. Pillac, V., Gendreau, M., Guéret, C., & Medaglia, A. L. (2013). A review of dynamic vehicle routing problems. European Journal of Operational Research, 225(1), 1–11.CrossRefGoogle Scholar
  37. Pitzer, E., Beham, A., Affenzeller, M., Heiss, H., Vorderwinkler, M. (2011). Production fine planning using a solution archive of priority rules. In: Logistics and industrial informatics (LINDI), 2011 3rd IEEE International Symposium on, pp 111–116, Doi: 10.1109/LINDI.2011.6031130.
  38. Psaraftis, H. (1988). Dynamic vehicle routing problems. In: Vehicle routing: Methods and studies, Elsevier Science Publishers, pp 223–249.Google Scholar
  39. R Core Team. (2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, URL http://www.R-project.org
  40. Ropke, S., & Pisinger, D. (2006). An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transportation science, 40(4), 455–472.CrossRefGoogle Scholar
  41. Sáez, D., Cortés, C. E., & Núñez, A. (2008). Hybrid adaptive predictive control for the multi-vehicle dynamic pick-up and delivery problem based on genetic algorithms and fuzzy clustering. Computers and Operations Research, 35(11), 3412–3438.CrossRefGoogle Scholar
  42. Savelsbergh, M. (1995). The general pickup and delivery problem. Transportation Science, 29(1), 17–29.CrossRefGoogle Scholar
  43. Scheibenpflug, A., Wagner, S., Kronberger, G., Affenzeller, M. (2012). Heuristiclab hive-an open source environment for parallel and distributed execution of heuristic optimization algorithms. In: 1st Australian Conference on the Applications of Systems Engineering ACASE’12, p 63.Google Scholar
  44. Silverthorn, BC. (2012). A probabilistic architecture for algorithm portfolios. PhD thesis, The University of Texas at Austin, may.Google Scholar
  45. Solomon, M. M. (1987). Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research, 35, 254–265. doi: 10.1287/opre.35.2.254.CrossRefGoogle Scholar
  46. Tekin, E., & Sabuncuoglu, I. (2004). Simulation optimization: A comprehensive review on theory and applications. IIE Transactions, 36(11), 1067–1081.CrossRefGoogle Scholar
  47. Tjokroamidjojo, D., Kutanoglu, E., & Taylor, G. D. (2006). Quantifying the value of advance load information in truckload trucking. Transportation Research Part E: Logistics and Transportation Review, 42(4), 340–357.CrossRefGoogle Scholar
  48. Van Hemert, JI., La Poutré, JA. (2004). Dynamic routing problems with fruitful regions: Models and evolutionary computation. In: Parallel problem solving from nature-PPSN VIII, Springer, pp 692–701.Google Scholar
  49. Vonolfen, S., Affenzeller, M., Beham, A., Lengauer, E., & Wagner, S. (2013a). Simulation-based evolution of resupply and routing policies in rich vendor-managed inventory scenarios. Central European Journal of Operations Research, 21(2), 379–400.CrossRefGoogle Scholar
  50. Vonolfen, S., Beham, A., Kommenda, M., Affenzeller, M. (2013b). Structural synthesis of dispatching rules for dynamic dial-a-ride problems. In: Proceedings of the 14th international conference on Computer Aided Systems Theory, Springer.Google Scholar
  51. Wagner, S. (2009). Heuristic optimization software systems - Modeling of heuristic optimization algorithms in the HeuristicLab software environment. PhD thesis, Johannes Kepler University, Linz, Austria.Google Scholar
  52. Waisanen, H. A., Shah, D., & Dahlehm, M. A. (2008). A dynamic pickup and delivery problem in mobile networks under information constraints. Automatic Control, IEEE Transactions on, 53(6), 1419–1433.CrossRefGoogle Scholar
  53. Whiteson, S. (2012). Evolutionary computation for reinforcement learning. In: Reinforcement learning, Springer, pp 325–355.Google Scholar
  54. Wolpert, D. H., & Macready, W. G. (1997). No free lunch theorems for optimization. Evolutionary Computation, IEEE Transactions on, 1(1), 67–82.CrossRefGoogle Scholar
  55. Xiang, Z., Chu, C., & Chen, H. (2008). The study of a dynamic dial-a-ride problem under time-dependent and stochastic environments. European Journal of Operational Research, 185(2), 534–551.CrossRefGoogle Scholar
  56. Zeimpekis, V., Tarantilis, C., Giaglis, G., & Minis, I. (2007). Dynamic fleet management. Operations research/computer science interfaces. New York: Springer.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Informatics, Communication and Media, Heuristic and Evolutionary Algorithms LaboratoryUniversity of Applied Sciences Upper AustriaHagenbergAustria

Personalised recommendations