Skip to main content
SpringerLink
Log in

The vehicle routing problem with hard time windows and stochastic service times

  • Research Paper
  • Published:
EURO Journal on Transportation and Logistics

Abstract

In this paper we consider the vehicle routing problem with hard time windows and stochastic service times (VRPTW-ST); in this variant of the classic VRPTW the service times are random variables. In particular, given a set of vehicle routes, some of the actual service times might not lead to a feasible solution, given the customer time windows. We consider a chance-constrained program to model the VRPTW-ST and provide a new set partitioning formulation that includes a constraint on the minimum success probability of the set of vehicle routes. Under some mild conditions, we develop a method to exactly compute the success probability of the routes. We then solve the VRPTW-ST by a branch-price-and-cut algorithm, where the main challenges are in the solution of the subproblems of the column generation procedure. We adapt the dynamic programming algorithm to account for the probabilistic resource consumption by extending the label dimension and by providing new dominance rules. Extensive computational experiments prove the effectiveness of both the solution method and the stochastic model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Adulyasak Y, Jaillet P (2014) Models and algorithms for stochastic and robust vehicle routing with deadlines. Transp Sci 50(2):608–626

    Article  Google Scholar 

  • Baldacci R, Mingozzi A, Roberti R (2011) New route relaxation and pricing strategies for the vehicle routing problem. Oper Res 59(5):1269–1283

    Article  Google Scholar 

  • Bertsimas DJ (1992) A vehicle routing problem with stochastic demand. Oper Res 40(3):574–585

    Article  Google Scholar 

  • Boland N, Dethridge J, Dumitrescu I (2006) Accelerated label setting algorithms for the elementary resource constrained shortest path problem. Oper Res Lett 34(1):58–68

    Article  Google Scholar 

  • Campbell AM, Thomas BW (2008) Probabilistic traveling salesman problem with deadlines. Transp Sci 42(1):1–21

    Article  Google Scholar 

  • Chang T-S, Wan Y-W, Ooi WT (2009) A stochastic dynamic traveling salesman problem with hard time windows. Eur J Oper Res 198(3):748–759

    Article  Google Scholar 

  • Cortés C, Gendreau M, Rousseau L-M, Souyris S, Weintraub A (2014) Branch-and-price and constraint programming for solving a real-life technician dispatching problem. Eur J Oper Res 238(1):300–312

    Article  Google Scholar 

  • Desaulniers G, Lessard F, Hadjar A (2008) Tabu search, partial elementarity, and generalized k-path inequalities for the vehicle routing problem with time windows. Transp Sci 42(3):387–404

    Article  Google Scholar 

  • Dror M (1994) Note on the complexity of the shortest path models for column generation in VRPTW. Oper Res 42(5):977–978

    Article  Google Scholar 

  • Errico F, Desaulniers G, Gendreau M, Rei W, Rousseau LM (2015) A priori optimization with recourse for the vehicle routing problem with hard time windows and stochastic service times. Eur J Oper Res 249(1):55–66

    Article  Google Scholar 

  • Feillet D, Dejax P, Gendreau M, Gueguen C (2004) An exact algorithm for the elementary shortest path problem with resource constraints: application to some vehicle routing problems. Networks 44(3):216–229

    Article  Google Scholar 

  • Gendreau M, Jabali O, Rei W (2014) Stochastic vehicle routing problems. Vehicle routing: problems, methods, and applications, 2nd edn, Chapter 8. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, pp 213–239

  • Gendreau M, Laporte G, Séguin R (1995) An exact algorithm for the vehicle routing problem with stochastic demands and customers. Transp Sci 29(2):143–155

    Article  Google Scholar 

  • Irnich S, Desaulniers G (2005) Shortest path problems with resource constraints, Chapter 2, GERAD 25th Anniversary Series. Springer, Berlin, pp 33–65

  • Irnich S, Villeneuve D (2006) The shortest-path problem with resource constraints and k-cycle elimination for \(k \ge 3\). INFORMS J Comput 18(3):391–406

    Article  Google Scholar 

  • Jepsen M, Petersen B, Spoorendonk S, Pisinger D (2008) Subset-row inequalities applied to the vehicle-routing problem with time windows. Oper Res 56(2):497–511

    Article  Google Scholar 

  • Jula H, Dessouky M, Ionnou PA (2006) Truck route planning in nonstationary stochastic networks with time windows at customer locations. IEEE Trans Intell Transp Syst 7(1):51–62

    Article  Google Scholar 

  • Kenyon AS, Morton DP (2003) Stochastic vehicle routing with random travel times. Transp Sci 37(1):69–82

    Article  Google Scholar 

  • Lambert V, Laporte G, Louveaux FV (1993) Designing collection routes through bank branches. Comput Oper Res 20(7):783–791

    Article  Google Scholar 

  • Laporte G, Louveaux FV, Hamme L (2002) An integer L-shaped algorithm for the capacitated vehicle routing problem with stochastic demands. Oper Res 50(3):415–423

    Article  Google Scholar 

  • Laporte G, Louveaux FV, Mercure H (1992) The vehicle routing problem with stochastic travel times. Transp Sci 26(3):161–170

    Article  Google Scholar 

  • Lee C, Lee K, Park S (2012) Robust vehicle routing problem with deadlines and travel time/demand uncertainty. J Oper Res Soc 60:1294–1306

    Article  Google Scholar 

  • Lei H, Laporte G, Guo B (2012) A generalized variable neighborhood search heuristic for the capacitated vehicle routing problem with stochastic service times. Top 20:99–118

    Article  Google Scholar 

  • Li X, Tian P, Leung SCH (2010) Vehicle routing problems with time windows and stochastic travel and service times: models and algorithm. Int J Prod Econ 125(1):137–145

    Article  Google Scholar 

  • Lübbecke ME, Desrosiers J (2005) Selected topics in column generation. Oper Res 53(6):1007–1023

    Article  Google Scholar 

  • Righini G, Salani M (2008) New dynamic programming algorithms for the resource constrained elementary shortest path problem. Networks 51(3):155–170

    Article  Google Scholar 

  • Solomon MM (1987) Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper Res 35:254–265

    Article  Google Scholar 

  • Souyris S, Cortés CE, Ordóñez F, Weintraub A (2013) A robust optimization approach to dispatching technicians under stochastic service times. Optim Lett 7(7):1549–1568

  • Sungur I, Ren Y, Ordóñez F, Dessouky M, Zhong H (2010) A model and algorithm for the courier delivery problem with uncertainty. Transp Sci 44(2):193–205

    Article  Google Scholar 

  • Taş D, Dellaert N, van Woensel T, de Kok T (2012) Vehicle routing problem with stochastic travel times including soft time windows and service costs. Technical report, Beta Research School for Operations Management and Logistics. WP 364

  • Taş D, Gendreau M, Dellaert N, van Woensel T, de Kok A (2014) Vehicle routing with soft time windows and stochastic travel times: a column generation and branch-and-price solution approach. Eur J Oper Res 236(3):789–799

    Article  Google Scholar 

  • Wang X, Regan CA (2001) Assignment models for local truckload trucking problems with stochastic service times and time window constraints. Transp Res Rec 1771:61–68

    Article  Google Scholar 

  • Wellman M, Ford M, Larson K (1995) Path planning under time-dependent uncertainty. In: Proceedings of the eleventh conference on uncertainty in artificial intelligence, August 18–20, 1995. Montréal, pp 532–539

Download references

Author information

Authors and Affiliations

  1. CIRRELT Interuniversity Research Center on Enterprise Networks, Logistics and Transportation, GERAD Group for Research in Decision Analysis, Montreal, Canada

    F. Errico

  2. Département de génie de la construction, École de Technologie Supérieure de Montréal, Montreal, Canada

    F. Errico

  3. GERAD Group for Research in Decision Analysis, Montreal, Canada

    G. Desaulniers

  4. Département de mathématiques et génie industriel, École Polytechnique de Montréal, Montreal, Canada

    G. Desaulniers, M. Gendreau & L.-M. Rousseau

  5. CIRRELT Interuniversity Research Center on Enterprise Networks, Logistics and Transportation, Montreal, Canada

    M. Gendreau, W. Rei & L.-M. Rousseau

  6. Département de management et de technologie, Université du Québec à Montréal, Montreal, Canada

    W. Rei

Authors
  1. F. Errico
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Desaulniers
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Gendreau
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. W. Rei
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. L.-M. Rousseau
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Errico.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Errico, F., Desaulniers, G., Gendreau, M. et al. The vehicle routing problem with hard time windows and stochastic service times. EURO J Transp Logist 7, 223–251 (2018). https://doi.org/10.1007/s13676-016-0101-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13676-016-0101-4

Keywords

Search

Navigation