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The stochastic vehicle routing problem, a literature review, Part II: solution methods

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EURO Journal on Transportation and Logistics

Abstract

Building on the work of Gendreau et al. (Oper Res 44(3):469–477, 1996), and complementing the first part of this survey, we review the solution methods used for the past 20 years in the scientific literature on stochastic vehicle routing problems (SVRP). We describe the methods and indicate how they are used when dealing with stochastic vehicle routing problems.

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References

  • Adulyasak Y, Jaillet P (2016) Models and algorithms for stochastic and robust vehicle routing with deadlines. Transp Sci 50(2):608–626

    Article  Google Scholar 

  • Ahmadi-Javid A, Seddighi AH (2013) A location-routing problem with disruption risk. Transp Res Part E Log Transp Rev 53:63–82

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ando N, Taniguchi E (2006) Travel time reliability in vehicle routing and scheduling with time windows. Netw Spat Econ 6(3–4):293–311

    Article  Google Scholar 

  • Beraldi P, Ghiani G, Musmanno R, Vocaturo F (2010) Efficient neighborhood search for the probabilistic multi-vehicle pickup and delivery problem. Asia Pac J Oper Res 27(3):301–314

    Article  Google Scholar 

  • Beraldi P, Bruni ME, Lagana D, Musmanno R (2015) The mixed capacitated general routing problem under uncertainty. Eur J Oper Res 240(2):382–392

    Article  Google Scholar 

  • Bertsimas D, Chervi P, Peterson M (1995) Computational approaches to stochastic vehicle routing problems. Transp Sci 29(4):342–352

    Article  Google Scholar 

  • Bianchi L, Birattari M, Chiarandini M, Manfrin M, Mastrolilli M, Paquete L, Rossi-Doria O, Schiavinotto T (2005) Hybrid metaheuristics for the vehicle routing problem with stochastic demands. Technical report, Dalle Molle Institute for Artificial Intelligence, Manno

    Google Scholar 

  • Chang MS (2005) A vehicle routing problem with time windows and stochastic demands. J Chin Inst Eng 28(5):783–794

    Article  Google Scholar 

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

  • Chen L, Ha MH, Langevin A, Gendreau M (2014) Optimizing road network daily maintenance operations with stochastic service and travel times. Transp Res Part E Log Transp Rev 64:88–102

  • Chepuri K, Homem-de Mello T (2005) Solving the vehicle routing problem with stochastic demands using the cross-entropy method. Ann Oper Res 134(1):153–181

    Article  Google Scholar 

  • Christiansen CH, Lysgaard J (2007) A branch-and-price algorithm for the capacitated vehicle routing problem with stochastic demands. Oper Res Lett 35(6):773–781

    Article  Google Scholar 

  • Christiansen CH, Lysgaard J, Wøhlk S (2009) A branch-and-price algorithm for the capacitated arc routing problem with stochastic demands. Oper Res Lett 37(6):392–398

    Article  Google Scholar 

  • Clarke C, Wright J (1964) Scheduling of vehicles from a central depot to a number of delivery points. Oper Res 12:432–441

    Article  Google Scholar 

  • Cordeau J-F, Gendreau M, Laporte G, Potvin J-Y, Semet F (2002) A guide to vehicle routing heuristics. J Oper Res Soc 53(5):512

  • Dantzig GB, Ramser JH (1959) The truck dispatching problem. Manag Sci (pre-1986) 6(1):80

  • Desrochers M (1988) An algorithm for the shortest path problem with resource constraints. In: Technical report, Cahiers du GERAD G-88-27, University of Montreal

  • Dueck G (1993) New optimization heuristics: the Great Deluge algorithm and the record-to-record travel. J Comput Phys 104(1):86–92

    Article  Google Scholar 

  • Ehmke JF, Campbell AM, Urban TL (2015) Ensuring service levels in routing problems with time windows and stochastic travel times. Eur J Oper Res 240(2):539–550

    Article  Google Scholar 

  • Eksioglu B, Vural AV, Reisman A (2009) The vehicle routing problem: a taxonomic review. Comput Ind Eng 57(4):1472–1483

    Article  Google Scholar 

  • Erera AL, Savelsbergh M, Uyar E (2009) Fixed routes with backup vehicles for stochastic vehicle routing problems with time constraints. Networks 54(4):270–283

    Article  Google Scholar 

  • Erera AL, Morales JC, Savelsbergh M (2010) The vehicle routing problem with stochastic demand and duration constraints. Transp Sci 44(4):474–492

    Article  Google Scholar 

  • Errico F, Desaulniers G, Gendreau M, Rei W, Rousseau L-M (2016) 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 

  • Fallahi AE, Prins C, Wolfler Calvo R (2008) A memetic algorithm and a tabu search for the multi-compartment vehicle routing problem. Comput Oper Res 35(5):1725–1741

    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 

  • Fleury G, Lacomme P, Prins C, Randame-Chérif W (2002) Robustness evaluation of solutions for the capacitated arc routing problem. In: Barros FJ, Gambiasi N (eds) Simulation and planning in high autonomy systems. CARP, Lisbon

  • Fleury G, Lacomme P, Prins C (2004) Evolutionary algorithms for stochastic arc routing problems. Lecture notes in computer science, vol 3005. Springer, Berlin, pp 501–512

    Google Scholar 

  • Fleury G, Lacomme P, Prins C, Ramdane-Cérif W (2005) Improving robustness of solutions to arc routing problems. J Oper Res Soc 56(5):526–538

  • Fleury G, Philippe L, Prins C (2005) Stochastic capacitated arc routing problem. In: Technical report LIMOS/RR-05-12, Laboratorie d’informatique (LIMOS), Université Blaise Pascal

  • Gauvin C, Desaulniers G, Gendreau M (2014) A branch-cut-and-price algorithm for the vehicle routing problem with stochastic demands. Comput Oper Res 50:141–153

    Article  Google Scholar 

  • Gendreau M, Laporte G, Seguin R (1996) A tabu search heuristic for the vehicle routing problem with stochastic demands and customers. Oper Res 44(3):469–477

    Article  Google Scholar 

  • Gendreau M, Jabali O, Rei W (2014) Stochastic vehicle routing problems. In: Toth P, Vigo D (eds) Vehicle routing: problems, methods, and applications, 2nd edn, Society for Industrial and Applied Mathematics, pp 213–239

  • Gómez A, No RM, Akhavan-Tabatabaei R, Medaglia AL, Mendoza JE (2016) On modeling stochastic travel and service times in vehicle routing. Transp Sci 50(2):627–641

  • Goodson JC (2015) A priori policy evaluation and cyclic-order-based simulated annealing for the multi-compartment vehicle routing problem with stochastic demands. Eur J Oper Res 241(2):361–369

    Article  Google Scholar 

  • Goodson JC, Ohlmann JW, Thomas BW (2012) Cyclic-order neighborhoods with application to the vehicle routing problem with stochastic demand. Eur J Oper Res 217(2):312–323

    Article  Google Scholar 

  • Gounaris CE, Wiesemann W, Floudas CA (2013) The robust capacitated vehicle routing problem under demand uncertainty. Oper Res 61(3):677–693

    Article  Google Scholar 

  • Groër C, Golden B, Wasil E (2009) The consistent vehicle routing problem. Manuf Serv Oper Manag 11(4):630–643

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Hjorring C, Holt J (1999) New optimality cuts for a single-vehicle stochastic routing problem. Ann Oper Res 86:569–584

    Article  Google Scholar 

  • Hvattum LM, Løkketangen A, Laporte G (2006) Solving a dynamic and stochastic vehicle routing problem with a sample scenario hedging heuristic. Transp Sci 40(4):421–438

    Article  Google Scholar 

  • Jabali O, Rei W, Gendreau M, Laporte G (2014) Partial-route inequalities for the multi-vehicle routing problem with stochastic demands. Discrete Appl Math 177:121–136

    Article  Google Scholar 

  • Juan A, Faulin J, Grasman S, Riera D, Marull J, Mendez C (2011) Using safety stocks and simulation to solve the vehicle routing problem with stochastic demands. Transp Res Part C Emerg Technol 19(5):751–765 (Freight Transportation and Logistics (selected papers from ODYSSEUS 2009—the 4th international workshop on Freight Transportation and Logistics)

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

    Article  Google Scholar 

  • Lacomme P, Prins C, Ramdane-Chérif W (2001) A genetic algorithm for the capacitated arc routing problem and its extensions. In: Boers E (ed) Lecture notes in computer science, vol 2037. Springer, Berlin, pp 473–483

    Google Scholar 

  • Laporte G, Louveaux FV, Hamme LV (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, Musmanno R, Vocaturo F (2010) An adaptive large neighbourhood search heuristic for the capacitated arc-routing problem with stochastic demands. Transp Sci 44(1):125–135

    Article  Google Scholar 

  • Lecluyse C, Van Woensel T, Peremans H (2009) Vehicle routing with stochastic time-dependent travel times. 4OR 7(4):363–377

  • Lee C, Lee K, Park S (2012) Robust vehicle routing problem with deadlines and travel time/demand uncertainty. J Oper Res Soc 63(9):1294–1306

    Article  Google Scholar 

  • Lei H, Laporte G, Guo B (2011) The capacitated vehicle routing problem with stochastic demands and time windows. Comput Oper Res 38(12):1775–1783

    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(3):99–118

    Article  Google Scholar 

  • Li X, Tian P, Leung SC (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 

  • Maden W, Eglese R, Black D (2010) Vehicle routing and scheduling with time-varying data: a case study. J Oper Res Soc 61(3):515–522

    Article  Google Scholar 

  • Marinakis Y, Iordanidou G-R, Marinaki M (2013) Particle swarm optimization for the vehicle routing problem with stochastic demands. Appl Soft Comput 13(4):1693–1704

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Mendoza JE, Castanier B, Guéret C, Medaglia AL, Velasco N (2010) A memetic algorithm for the multi-compartment vehicle routing problem with stochastic demands. Comput Oper Res 37(11):1886–1898

    Article  Google Scholar 

  • Mendoza JE, Castanier B, Guéret C, Medaglia AL, Velasco N (2011) Constructive heuristics for the multicompartment vehicle routing problem with stochastic demands. Transp Sci 45(3):346–363

    Article  Google Scholar 

  • Mendoza J, Rousseau L-M, Villegas J (2015) A hybrid metaheuristic for the vehicle routing problem with stochastic demand and duration constraints. J Heuristics 1–28

  • Miranda DM, Conceição SV (2016) The vehicle routing problem with hard time windows and stochastic travel and service time. Expert Syst Appl 64:104–116

    Article  Google Scholar 

  • Novoa C, Storer R (2009) An approximate dynamic programming approach for the vehicle routing problem with stochastic demands. Eur J Oper Res 196(2):509–515

    Article  Google Scholar 

  • Oyola J, Arntzen H, Woodruff DL (2016) The stochastic vehicle routing problem, a literature review, part I: models. EURO J Transp Logist. doi:10.1007/s13676-016-0100-5

    Google Scholar 

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

    Article  Google Scholar 

  • Rei W, Gendreau M, Soriano P (2007) Local branching cuts for the 0–1 integer L-shaped algorithm. In: Technical report, CIRRELT-2007-23, Centre interuniversitaire de recherche sur les réseaux d’enterprise, la logistique et le transport, vol 44(1), pp 136–146

  • Rei W, Gendreau M, Soriano P (2010) A hybrid Monte Carlo local branching algorithm for the single vehicle routing problem with stochastic demands. Transp Sci 44(1):136–146

    Article  Google Scholar 

  • Resende MGC, Celso CR (2010) Greedy randomized adaptive search procedures: advances, hybridizations, and applications. In:  Gendreau M, Potvin J-Y (eds) Handbook of metaheuristics. Springer, New York, pp 283–319

  • Ritzinger U, Puchinger J, Hartl RF (2016) A survey on dynamic and stochastic vehicle routing problems. Int J Prod Res 54:215–231

    Article  Google Scholar 

  • Rockafellar R, Wets R-B (1991) Scenarios and policy aggregation in optimization under uncertainty. Math Oper Res 16(1):119–147

    Article  Google Scholar 

  • Rubinstein R (1999) The cross-entropy method for combinatorial and continuous optimization. Methodol Comput Appl Probab 1(2):127–190

    Article  Google Scholar 

  • Russell RA, Urban TL (2008) Vehicle routing with soft time windows and erlang travel times. J Oper Res Soc 59(9):1220–1228

    Article  Google Scholar 

  • Secomandi N (2000) Comparing neuro-dynamic programming algorithms for the vehicle routing problem with stochastic demands. Comput Oper Res 27(1112):1201–1225

  • Secomandi N (2001) A rollout policy for the vehicle routing problem with stochastic demands. Oper Res 49(5):796–802

    Article  Google Scholar 

  • Secomandi N (2003) Analysis of a rollout approach to sequencing problems with stochastic routing applications. J Heuristics 9(4):321–352

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Solano-Charris E, Prins C, Santos AC (2015) Local search based metaheuristics for the robust vehicle routing problem with discrete scenarios. Appl Soft Comput 32:518–531

    Article  Google Scholar 

  • Solomon MM (1987) Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper Res 35(2):254

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

    Article  Google Scholar 

  • Sungur I, Ordóñez F, Dessouky M (2008) A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty. IIE Trans 40:509–523

    Article  Google Scholar 

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

  • Taş D, Dellaert N, van Woensel T, de Kok T (2013) Vehicle routing problem with stochastic travel times including soft time windows and service costs. Comput Oper Res 40(1):214–224

    Article  Google Scholar 

  • Taş D, Dellaert N, van Woensel T, de Kok T (2014a) The time-dependent vehicle routing problem with soft time windows and stochastic travel times. Transp Res Part C Emerg Technol 48:66–83

    Article  Google Scholar 

  • Taş D, Gendreau M, Dellaert N, van Woensel T, de Kok A (2014b) 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 

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

    Article  Google Scholar 

  • Toth P, Vigo D (1998) Exact algorithms for vehicle routing. In: Crainic T, Laporte G (eds) Fleet management and logistics. Kluwer Academic Publishers, New York, pp 1–31

  • Toth P, Vigo D (2002) Models, relaxations and exact approaches for the capacitated vehicle routing problem. Discrete Appl Math 123(1–3):487–512

    Article  Google Scholar 

  • Voß S, Fink A, Duin C (2005) Looking ahead with the pilot method. Ann Oper Res 136(1):285–302

    Article  Google Scholar 

  • Woensel TV, Kerbache L, Peremans H, Vandaele N (2007) A queueing framework for routing problems with time-dependent travel times. J Math Model Algorithms 6(1):151–173

    Article  Google Scholar 

  • Yan S, Wang S-S, Chang Y-H (2014) Cash transportation vehicle routing and scheduling under stochastic travel times. Eng Optim 46(3):289–307

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Zhang T, Chaovalitwongse W, Zhang Y (2012) Scatter search for the stochastic travel-time vehicle routing problem with simultaneous pick-ups and deliveries. Comput Oper Res 39(10):2277–2290

    Article  Google Scholar 

  • Zhang J, Lam WHK, Chen BY (2013) A stochastic vehicle routing problem with travel time uncertainty: trade-off between cost and customer service. Netw Spat Econ 13(4):471–496

    Article  Google Scholar 

  • Zhong H, Hall RW, Dessouky M (2007) Territory planning and vehicle dispatching with driver learning. Transp Sci 41(1):74–89

    Article  Google Scholar 

  • Zhu L, Rousseau L-M, Rei W, Li B (2014) Paired cooperative reoptimization strategy for the vehicle routing problem with stochastic demands. Comput Oper Res 50:1–13

    Article  Google Scholar 

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Oyola, J., Arntzen, H. & Woodruff, D.L. The stochastic vehicle routing problem, a literature review, Part II: solution methods. EURO J Transp Logist 6, 349–388 (2017). https://doi.org/10.1007/s13676-016-0099-7

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