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Optimization Letters

, Volume 7, Issue 7, pp 1503–1516 | Cite as

A multi-space sampling heuristic for the vehicle routing problem with stochastic demands

  • Jorge E. Mendoza
  • Juan G. Villegas
Original Paper

Abstract

The vehicle routing problem with stochastic demands consists in designing transportation routes of minimal expected cost to satisfy a set of customers with random demands of known probability distributions. This paper proposes a simple yet effective heuristic approach that uses randomized heuristics for the traveling salesman problem, a tour partitioning procedure, and a set partitioning formulation to sample the solution space and find high-quality solutions for the problem. Computational experiments on benchmark instances from the literature show that the proposed approach is competitive with the state-of-the-art algorithm for the problem in terms of both accuracy and efficiency. In experiments conducted on a set of 40 instances, the proposed approach unveiled four new best-known solutions (BKSs) and matched another 24. For the remaining 12 instances, the heuristic reported average gaps with respect to the BKS ranging from 0.69 to 0.15 % depending on its configuration.

Keywords

Vehicle routing Stochastic demands Heuristics  Sampling Logistics 

Notes

Acknowledgments

The authors would like to thank two anonymous referees for insightful comments and valuable advice that helped to improve the paper. This research was partially funded by Region Pays de la Loire (France) through project LigéRO and by the Universidad de Antioquia (Colombia) through project: Desarrollo de metaheurísticos híbridos y métodos cooperativos para problemas de rutas de vehículos con flota heterogénea y restricciones adicionales.

Supplementary material

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References

  1. 1.
    Ak, A., Erera, A.: A paired-vehicle recourse strategy for the vehicle-routing problem with stochastic demands. Transp. Sci. 41(2), 222–237 (2007)CrossRefGoogle Scholar
  2. 2.
    Beasley, J.E.: Route-first cluster-second methods for vehicle routing. Omega 11, 403–408 (1983)CrossRefGoogle Scholar
  3. 3.
    Bentley, J.B.: Fast algorithms for geometric traveling salesman problems. INFORMS J. Comput. 4, 387–411 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bertsimas, D.: A vehicle routing problem with stochastic demand. Oper. Res. 40(3), 574–585 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Boctor, F.F., Renaud, J.: The column-circular, subsets-selection problem: Complexity and solutions. Comput. Oper. Res. 27(4), 383–398 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Christiansen, C., Lysgaard, J.: A branch-and-price algorithm for the capacitated vehicle routing problem with stochastic demands. Oper. Res. Lett. 35(6), 773–781 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Cordeau, J.F., Gendreau, M., Laporte, G., Potvin, J.Y., Semet, F.: A guide to vehicle routing heuristics. J. Oper. Res. Soc. 53(5), 512–522 (2002)CrossRefzbMATHGoogle Scholar
  8. 8.
    Duhamel, C., Lacomme, P., Prodhon, C.: Efficient frameworks for greedy split and new depth first search split procedures for routing problems. Comput. Oper. Res. 38(4), 723–739 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Erera, A., Savelsbergh, M., Uyar, E.: Fixed routes with backup vehicles for stochastic vehicle routing problems with time constraints. Networks 54(4), 270–283 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Foster, B.A., Ryan, D.M.: An integer programming approach to the vehicle scheduling problem. Oper. Res. Q. 27(2), 367–384 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Gendreau, M., Laporte, G., Séguin, R.: A tabu search heuristic for the vehicle routing problem with stochastic demands and customers. Oper. Res. 44(3), 469–477 (1996)CrossRefzbMATHGoogle Scholar
  12. 12.
    Gillett, B.E., Miller, L.R.: A heuristic algorithm for the vehicle dispatch problem. Oper. Res. 22(2), 340–349 (1974)CrossRefzbMATHGoogle Scholar
  13. 13.
    Goodson, J.C., Ohlmann, J.W., Thomas, B.W.: Cyclic-order neighborhoods with application to the vehicle routing problem with stochastic demand. Euro. J. Oper. Res. 217(2), 312–323 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Kelly, J.P., Xu, J.: A set-partitioning-based heuristic for the vehicle routing problem. INFORMS J. Comput. 11(2), 161–172 (1999)Google Scholar
  15. 15.
    Laporte, G., Louveaux, F., Van Hamme, L.: An integer L-shaped algorithm for the capacitated vehicle routing problem with stochastic demands. Oper. Res. 50(3), 415–423 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Mendoza, J.E., Castanier, B., Guéret, C., Medaglia, A.L., Velasco, N.: A memetic algorithm for the multi-compartment vehicle routing problem with stochastic demands. Comput. Oper. Res. 37(11), 1886–1898 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Mendoza, J.E., Castanier, B., Guéret, C., Medaglia, A.L., Velasco, N.: Constructive heuristics for the multicompartment vehicle routing problem with stochastic demands. Transp. Sci. 45(3), 335–345 (2011)CrossRefGoogle Scholar
  18. 18.
    Prins, C.: A simple and effective evolutionary algorithm for the vehicle routing problem. Comput. Oper. Res. 31(12), 1985–2002 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Reinelt, G.: Construction heuristics. In: The traveling salesman, lecture notes in computer science, vol. 840, pp. 73–99. Springer, Berlin (1994)Google Scholar
  20. 20.
    Rochat, Y., Taillard, E.D.: Probabilistic diversification and intensification in local search for vehicle routing. J. Heuristics 1, 147–167 (1995)CrossRefzbMATHGoogle Scholar
  21. 21.
    Ryan, D.M., Hjorring, C., Glover, F.: Extensions of the petal method for vehicle routeing. J. Oper. Res. Soc. 44(3), 289–296 (1993)zbMATHGoogle Scholar
  22. 22.
    Secomandi, N.: A rollout policy for the vehicle routing problem with stochastic demands. Oper. Res. 49(5), 796–804 (2001)CrossRefzbMATHGoogle Scholar
  23. 23.
    Secomandi, N.: Analysis of a rollout approach to sequencing problems with stochastic routing applications. J. Heuristics 9(4), 321–352 (2003)CrossRefzbMATHGoogle Scholar
  24. 24.
    Secomandi, N., Margot, F.: Reoptimization approaches for the vehicle-routing problem with stochastic demands. Oper. Res. 57(1), 214–230 (2009)CrossRefzbMATHGoogle Scholar
  25. 25.
    Teodorović, D., Pavković, G.: A simulated annealing technique approach to the vehicle routing problem in the case of stochastic demands. Transp. Plan. Technol. 16(4), 261–273 (1992)CrossRefGoogle Scholar
  26. 26.
    Villegas, J.G., Prins, C., Prodhon, C., Medaglia, A.L., Velasco, N.: A matheuristic for the truck and trailer routing problem. Department of Industrial Engineering, Universidad de Antioquia, Technical report (2011)Google Scholar
  27. 27.
    Yang, W.H., Mathur, K., Ballou, R.: Stochastic vehicle routing with restocking. Transp. Sci. 34(1), 99–112 (2000)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.LUNAM Université, Université Catholique de l’OuestLISA (EA CNRS 4094)AngersFrance
  2. 2.Departamento de Ingeniería Industrial, Facultad de IngenieríaUniversidad de AntioquiaMedellinColombia

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