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A hybrid metaheuristic for the vehicle routing problem with stochastic demand and duration constraints

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Abstract

The vehicle routing problem with stochastic demands (VRPSD) consists in designing optimal routes to serve a set of customers with random demands following known probability distributions. Because of demand uncertainty, a vehicle may arrive at a customer without enough capacity to satisfy its demand and may need to apply a recourse to recover the route’s feasibility. Although travel times are assumed to be deterministic, because of eventual recourses the total duration of a route is a random variable. We present two strategies to deal with route-duration constraints in the VRPSD. In the first, the duration constraints are handled as chance constraints, meaning that for each route, the probability of exceeding the maximum duration must be lower than a given threshold. In the second, violations to the duration constraint are penalized in the objective function. To solve the resulting problem, we propose a greedy randomized adaptive search procedure (GRASP) enhanced with heuristic concentration (HC). The GRASP component uses a set of randomized route-first, cluster-second heuristics to generate starting solutions and a variable-neighborhood descent procedure for the local search phase. The HC component assembles the final solution from the set of all routes found in the local optima reached by the GRASP. For each strategy, we discuss extensive computational experiments that analyze the impact of route-duration constraints on the VRPSD. In addition, we report state-of-the-art solutions for a established set of benchmarks for the classical VRPSD.

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Notes

  1. The mechanism has been given different names, but we believe the term heuristic concentration best encapsulates the spirit of the idea.

  2. SA was tested on Intel Xeon X5660 2.8 GHz processors with 12Gb of RAM (running CentOS 5.3), MSH was tested on a PC with an Intel Xeon 2.4 GHz and 12 Gb of RAM (running Windows Server 2008 64 bit).

  3. In fact, customer 2 violates one of the basic assumptions of the problem since \(Pr(\tilde{\xi }_{2}>Q)=0.1573\). Because of the high failure probability and the travel time to the depot, it is impossible to include customer 2 in a route, even the trivial route \((0,2,0)\), without violating the DC for \(\beta <0.1573\).

References

  • Ak, A., Erera, A.: A paired-vehicle recourse strategy for the vehicle-routing problem with stochastic demands. Transp. Sci. 41(2), 222–237 (2007)

    Article  Google Scholar 

  • Bent, R., Van Hentenryck, P.: Scenario-based planning for partially dynamic vehicle routing with stochastic customers. Oper. Res. 52(6), 977–987 (2004)

    Article  MATH  Google Scholar 

  • Bent, R., Van Hentenryck, P.: Waiting and relocation strategies in online stochastic vehicle routing. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI’07), pp. 1816–1821 (2007)

  • Bianchi, L., Birattari, M., Chiarandini, M., Manfrin, M., Mastrolilli, M., Paquete, L., Rossi-Doria, O., Schiavinotto, T.: Metaheuristics for the vehicle routing problem with stochastic demands. Parallel Problem Solving from Nature—PPSN VIII. Lecture Notes in Computer Science, pp. 450–460. Springer, Berlin (2004)

    Chapter  Google Scholar 

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • Contardo, C., Cordeau, J.F., Gendron, B.: A GRASP + ILP-based metaheuristic for the capacitated location-routing problem. J. Heuristics 20(1), 1–38 (2014)

    Article  MathSciNet  Google Scholar 

  • Cordeau, J.F., Laporte, G., Savelsbergh, M., Vigo, D.: Vehicle routing. In: Barnhart, C., Laporte, G. (eds.) Handbooks in Operations Research and Management Science: Transportation, vol. 14, pp. 367–428. Elsevier, Amsterdam (2006)

    Google Scholar 

  • Erera, A., Morales, J.C., Savelsbergh, M.: The vehicle routing problem with stochastic demands and duration constraints. Transp. Sci. 44(4), 474–492 (2010)

    Article  Google Scholar 

  • Gauvin, C.: Un algorithme de génération de colonnes pour le problème de tournées de véhicules avec demandes stochastiques. Master’s thesis, École Polytechnique de Montréal (2012)

  • 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 (1996b)

    Article  MATH  Google Scholar 

  • Goodson, J.C., Ohlmann, J.W., Thomas, B.W.: Cyclic-order neighborhoods with application to the vehicle routing problem with stochastic demand. Eur. J. Oper. Res. 227(2), 312–323 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Goodson, J.C., Ohlmann, J.W., Thomas, B.W.: Rollout policies for dynamic solutions to the multivehicle routing problem with stochastic demand and duration limits. Oper. Res. 61(1), 138–154 (2013)

  • Goodson, J.C., Thomas, B.W., Ohlmann, J.W.: Restocking-based rollout policies for the vehicle routing problem with stochastic demand and duration limits. To appear in Transportation Science

  • Hansen, P., Mladenović, N., Moreno-Pérez, J.: Variable neighbourhood search: Methods and applications. 4OR: A Quart. J. Oper. Res. 6, 319–360 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • Haugland, D., Ho, S., Laporte, G.: Designing delivery districts for the vehicle routing problem with stochastic demands. Eur. J. Oper. Res. 180(3), 997–1010 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Mendoza, J.E., Castanier, B., Guéret, C., Medaglia, A.L., Velasco, N.: A simulation-based MOEA for the multi-compartment vehicle routing problem with stochastic demands. In: Proceedings of the VIII Metaheuristics International Conference (MIC). Hamburg, Germany (2009)

  • 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)

    Article  MathSciNet  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Mendoza, J.E., Guéret, C., Hoskins, M., Lobit, H., Pillac, V., Vidal, T., Vigo, D.: VRP-REP: the vehicle routing community repository. In: Third Meeting of the EURO Working Group on Vehicle Routing and Logistics Optimization (VeRoLog). Oslo, Norway (2014)

  • Mendoza, J.E., Villegas, J.G.: A multi-space sampling heuristic for the vehicle routing problem with stochastic demands. Optim. Lett. 7(7), 1503–1516 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • Novoa, C., Berger, R., Linderoth, J., Storer, R.: A set-partitioning-based model for the stochastic vehicle routing problem. Texas State University, Tech. rep. (2006)

  • Pillac, V., Gendreau, M., Guéret, C., Medaglia, A.L.: A review of dynamic vehicle routing problems. Eur. J. Oper. Res. 225(1), 1–11 (2013a)

    Article  MathSciNet  MATH  Google Scholar 

  • Pillac, V., Guret, C., Medaglia, A.L.: A parallel matheuristic for the technician routing and scheduling problem. Optim. Lett. 7(7), 1525–1535 (2013b)

    Article  MathSciNet  MATH  Google Scholar 

  • Prins, C.: A simple and effective evolutionary algorithm for the vehicle routing problem. Comput. Oper. Res. 31(12), 1985–2002 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Rosing, K.E., Revelle, C.S.: Heuristic concentration: two stage solution construction. Eur. J. Oper. Res. 17(96), 75–86 (1997)

    Article  MATH  Google Scholar 

  • Savelsbergh, M., Goetschalckx, M.: A comparison of the efficiency of fixed versus variable vehicle routes. J. Bus. Logist. 16, 163–187 (1995)

    Google Scholar 

  • Secomandi, N., Margot, F.: Reoptimization approaches for the vehicle-routing problem with stochastic demands. Oper. Res. 57(1), 214–230 (2009)

    Article  MATH  Google Scholar 

  • Sörensen, K., Sevaux, M.: MA\(|\)PM: memetic algorithms with population management. Comput. Oper. Res. 33(5), 1214–1225 (2006)

    Article  MATH  Google Scholar 

  • Sörensen, K., Sevaux, M.: A practical approach for robust and flexible vehicle routing using metaheuristics and Monte Carlo sampling. J. Math. Model. Algorithms 8(4), 387–407 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Subramanian, A., Uchoa, E., Ochi, L.S.: A hybrid algorithm for a class of vehicle routing problems. Comput. Oper. Res. 40(10), 2519–2531 (2013)

    Article  Google Scholar 

  • Tan, K.C., Cheong, C.Y., Goh, C.K.: Solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation. Eur. J. Oper. Res. 177(2), 813–839 (2007)

    Article  MATH  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Tricoire, B.: Optimisation dans les réseaux logistiques: du terrain à la prospective. PhD thesis, Université d’Angers (France) (2013)

  • Villegas, J.G., Prins, C., Prodhon, C., Medaglia, A.L., Velasco, N.: A matheuristic for the truck and trailer routing problem. Eur. J. Oper. Res. 230(2), 231–244 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • Yang, W.H., Mathur, K., Ballou, R.: Stochastic vehicle routing with restocking. Transp. Sci. 34(1), 99–112 (2000)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This research was partially funded by the Region Pays de la Loire (France) through project LigéRO, Universidad de Antioquia (Colombia) through project CODI MDC11-01-09, and École Polytechnique de Montréal (Canada). The authors would like to thank Charles Gauvin at CIRRELT (Montreal) for providing the optimal solutions for the VRSPD instances used in Sect. 4.1.

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Authors and Affiliations

  1. LUNAM Université, Université Catholique de l’Ouest, LARIS (EA 7315), 3 Place André Leroy, 49008, Angers, France

    Jorge E. Mendoza

  2. Université François-Rabelais de Tours, CNRS, LI EA 6300, OC ERL CNRS 6305, 64 Avenue Jean Portalis, 37300, Tours, France

    Jorge E. Mendoza

  3. CIRRELT, École Polytechnique de Montréal, Succ. Centre-ville, C.P. 6079, Montreal, QC, H3C 3A7, Canada

    Louis-Martin Rousseau

  4. Departamento de Ingeniería Industrial, Facultad de Ingeniería, Universidad de Antioquia, Calle 70 No. 52 - 21, 050010, Medellín, Colombia

    Juan G. Villegas

Authors
  1. Jorge E. Mendoza
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  2. Louis-Martin Rousseau
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  3. Juan G. Villegas
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Corresponding author

Correspondence to Jorge E. Mendoza.

Appendices

Appendix 1: Detailed results for VRPSD instances

See Table 8

Table 8 Results for the Christiansen and Lysgaard (2007) instances
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Appendix 2: Detailed CPU times

See Table 9

Table 9 Average running times (in seconds) over ten runs of GRASP + HC for the different VRPSD-DC formulations
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Mendoza, J.E., Rousseau, LM. & Villegas, J.G. A hybrid metaheuristic for the vehicle routing problem with stochastic demand and duration constraints. J Heuristics 22, 539–566 (2016). https://doi.org/10.1007/s10732-015-9281-6

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  • DOI: https://doi.org/10.1007/s10732-015-9281-6

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