A Multistage Stochastic Programming Approach to the Dynamic and Stochastic VRPTW

  • Michael Saint-GuillainEmail author
  • Yves Deville
  • Christine Solnon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9075)


We consider a dynamic vehicle routing problem with time windows and stochastic customers (DS-VRPTW), such that customers may request for services as vehicles have already started their tours. To solve this problem, the goal is to provide a decision rule for choosing, at each time step, the next action to perform in light of known requests and probabilistic knowledge on requests likelihood. We introduce a new decision rule, called Global Stochastic Assessment (GSA) rule for the DS-VRPTW, and we compare it with existing decision rules, such as MSA. In particular, we show that GSA fully integrates nonanticipativity constraints so that it leads to better decisions in our stochastic context. We describe a new heuristic approach for efficiently approximating our GSA rule. We introduce a new waiting strategy. Experiments on dynamic and stochastic benchmarks, which include instances of different degrees of dynamism, show that not only our approach is competitive with state-of-the-art methods, but also enables to compute meaningful offline solutions to fully dynamic problems where absolutely no a priori customer request is provided.


Stochastic Program Dynamic Vehicle Vehicle Route Relocation Strategy Waiting Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ahmed, S., Shapiro, A.: The sample average approximation method for stochastic programs with integer recourse (Submitted for publication, 2002)Google Scholar
  2. 2.
    Asmussen, S., Glynn, P.W.: Stochastic Simulation: Algorithms and Analysis: Algorithms and Analysis, vol. 57. Springer (2007)Google Scholar
  3. 3.
    Bent, R., Van Hentenryck, P.: Regrets only! online stochastic optimization under time constraints. In: AAAI, pp. 501–506 (2004)Google Scholar
  4. 4.
    Bent, R., Van Hentenryck, P.: The value of consensus in online stochastic scheduling. In: ICAPS, (1), pp. 219–226 (2004)Google Scholar
  5. 5.
    Bent, R., Van Hentenryck, P.: Waiting and relocation strategies in online stochastic vehicle routing. In: IJCAI, pp. 1816–1821 (2007)Google Scholar
  6. 6.
    Bent, R., Katriel, I., Van Hentenryck, P.: Sub-optimality approximations. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 122–136. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  7. 7.
    Bent, R.W., Van Hentenryck, P.: Scenario-based planning for partially dynamic vehicle routing with stochastic customers. Operations Research 52(6), 977–987 (2004)CrossRefzbMATHGoogle Scholar
  8. 8.
    Bertsimas, D.J., Van Ryzin, G.: A stochastic and dynamic vehicle routing problem in the Euclidean plane. Operations Research (1991)Google Scholar
  9. 9.
    Bertsimas, D.J., Van Ryzin, G.: Stochastic and Dynamic Vehicle Routing in the Euclidean Plane with Multiple Capacitated Vehicles. Operations Research (1993)Google Scholar
  10. 10.
    Cordeau, J.-F., Laporte, G.: The dial-a-ride problem (DARP): Variants, modeling issues and algorithms. 4OR: A Quarterly Journal of Operations Research 1(2), 89–101 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Mathematical Programming 91(2), 201–213 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Flatberg, T., Hasle, G., Kloster, O., Nilssen, E.J., Riise, A.: Dynamic and stochastic vehicle routing in practice. In: Dynamic Fleet Management, pp. 41–63. Springer (2007)Google Scholar
  13. 13.
    Ghiani, G., Manni, E., Quaranta, A., Triki, C.: Anticipatory algorithms for same-day courier dispatching. Transportation Research Part E: Logistics and Transportation Review 45(1), 96–106 (2009)CrossRefGoogle Scholar
  14. 14.
    Hvattum, L.M., Løkketangen, A., Laporte, G.: Solving a Dynamic and Stochastic Vehicle Routing Problem with a Sample Scenario Hedging Heuristic. Transportation Science 40(4), 421–438 (2006)CrossRefGoogle Scholar
  15. 15.
    Ichoua, S., Gendreau, M., Potvin, J.-Y.: Exploiting Knowledge About Future Demands for Real-Time Vehicle Dispatching. Transportation Science 40(2), 211–225 (2006)CrossRefGoogle Scholar
  16. 16.
    Kindervater, G.A.P., Savelsbergh, M.W.P.: Vehicle routing: handling edge exchanges. In: Local Search in Combinatorial Optimization, pp. 337–360 (1997)Google Scholar
  17. 17.
    Mitrović-Minić, S., Laporte, G.: Waiting strategies for the dynamic pickup and delivery problem with time windows. Transportation Research Part B: Methodological 38(7), 635–655 (2004)CrossRefGoogle Scholar
  18. 18.
    Pillac, V., Gendreau, M., Guéret, C., Medaglia, A.L.: A review of dynamic vehicle routing problems. European Journal of Operational Research 225(1), 1–11 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Pillac, V., Guéret, C., Medaglia, A.L.: An event-driven optimization framework for dynamic vehicle routing. Decision Support Systems 54(1), 414–423 (2012)CrossRefGoogle Scholar
  20. 20.
    Psaraftis, H.N.: A dynamic programming solution to the single vehicle many-to-many immediate request dial-a-ride problem. Transportation Science 14(2), 130–154 (1980)CrossRefGoogle Scholar
  21. 21.
    Psaraftis, H.N.: Dynamic vehicle routing: Status and prospects. Annals of Operations Research 61(1), 143–164 (1995)CrossRefzbMATHGoogle Scholar
  22. 22.
    Schilde, M., Doerner, K.F., Hartl, R.F.: Metaheuristics for the dynamic stochastic dial-a-ride problem with expected return transports. Computers & Operations Research 38(12), 1719–1730 (2011)CrossRefzbMATHGoogle Scholar
  23. 23.
    Shapiro, A., Dentcheva, D., Ruszczyński, A.P.: Lectures on stochastic programming: modeling and theory, vol. 9. SIAM (2009)Google Scholar
  24. 24.
    Shaw, P.: Using constraint programming and local search methods to solve vehicle routing problems. In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 417–431. Springer, Heidelberg (1998) CrossRefGoogle Scholar
  25. 25.
    Solomon, M.M.: Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research 35(2) (1987)Google Scholar
  26. 26.
    Taillard, É., Badeau, P.: A tabu search heuristic for the vehicle routing problem with soft time windows. Transportation..., pp. 1–36 (1997)Google Scholar
  27. 27.
    Van Hentenryck, P., Bent, R., Upfal, E.: Online stochastic optimization under time constraints, vol. 177 (September 2009)Google Scholar
  28. 28.
    Verweij, B., Ahmed, S., Kleywegt, A.J., Nemhauser, G., Shapiro, A.: The sample average approximation method applied to stochastic routing problems: a computational study. Computational Optimization and Applications 24(2–3), 289–333 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  29. 29.
    Wilson, N.H.M., Colvin, N.J.: Computer control of the Rochester dial-a-ride system. Massachusetts Institute of Technology, Center for Transportation Studies (1977)Google Scholar
  30. 30.
    Saint-Guillain, M., Deville, Y., Solnon, C.: A Multistage Stochastic Programming Approach to the Dynamic and Stochastic VRPTW (2015). Extended version. arXiv:1502.01972 [cs.AI]

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Michael Saint-Guillain
    • 1
    Email author
  • Yves Deville
    • 1
  • Christine Solnon
    • 2
  1. 1.ICTEAMUniversité catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Université de Lyon, CNRS, INSA-Lyon, LIRIS, UMR5205LyonFrance

Personalised recommendations