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An exact algorithm to solve the vehicle routing problem with stochastic demands under an optimal restocking policy

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  • Salavati-Khoshghalb, Majid
  • Gendreau, Michel
  • Jabali, Ola
  • Rei, Walter

Abstract

This paper examines the Vehicle Routing Problem with Stochastic Demands (VRPSD), in which the actual demand of customers can only be realized upon arriving at the customer location. Under demand uncertainty, a planned route may fail at a specific customer when the observed demand exceeds the residual capacity. There are two ways to face such failure events, a vehicle can either execute a return trip to the depot at the failure location and refill the capacity and complete the split service, or in anticipation of potential failures perform a preventive return to the depot whenever the residual capacity falls below a threshold; overall, these return trips are called recourse actions. In the context of VRPSD, a recourse policy which schedules various recourse actions based on the visits planned beforehand on the route must be designed. An optimal recourse policy prescribes the cost-effective returns based on a set of optimal customer-specific thresholds. We propose an exact solution method to solve the multi-VRPSD under an optimal restocking policy. The Integer L-shaped algorithm is adapted to solve the VRPSD in a branch-and-cut framework. To enhance the efficiency of the presented algorithm, several lower bounding schemes are developed to approximate the expected recourse cost.

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  • Salavati-Khoshghalb, Majid & Gendreau, Michel & Jabali, Ola & Rei, Walter, 2019. "An exact algorithm to solve the vehicle routing problem with stochastic demands under an optimal restocking policy," European Journal of Operational Research, Elsevier, vol. 273(1), pages 175-189.
  • Handle: RePEc:eee:ejores:v:273:y:2019:i:1:p:175-189
    DOI: 10.1016/j.ejor.2018.07.039
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    1. G. B. Dantzig & J. H. Ramser, 1959. "The Truck Dispatching Problem," Management Science, INFORMS, vol. 6(1), pages 80-91, October.
    2. Nicola Secomandi, 2001. "A Rollout Policy for the Vehicle Routing Problem with Stochastic Demands," Operations Research, INFORMS, vol. 49(5), pages 796-802, October.
    3. Walter Rei & Michel Gendreau & Patrick Soriano, 2010. "A Hybrid Monte Carlo Local Branching Algorithm for the Single Vehicle Routing Problem with Stochastic Demands," Transportation Science, INFORMS, vol. 44(1), pages 136-146, February.
    4. Wen-Huei Yang & Kamlesh Mathur & Ronald H. Ballou, 2000. "Stochastic Vehicle Routing Problem with Restocking," Transportation Science, INFORMS, vol. 34(1), pages 99-112, February.
    5. Nicola Secomandi & François Margot, 2009. "Reoptimization Approaches for the Vehicle-Routing Problem with Stochastic Demands," Operations Research, INFORMS, vol. 57(1), pages 214-230, February.
    6. Moshe Dror & Gilbert Laporte & Pierre Trudeau, 1989. "Vehicle Routing with Stochastic Demands: Properties and Solution Frameworks," Transportation Science, INFORMS, vol. 23(3), pages 166-176, August.
    7. Dror, Moshe & Trudeau, Pierre, 1986. "Stochastic vehicle routing with modified savings algorithm," European Journal of Operational Research, Elsevier, vol. 23(2), pages 228-235, February.
    8. C. Hjorring & J. Holt, 1999. "New optimality cuts for a single‐vehicle stochastic routing problem," Annals of Operations Research, Springer, vol. 86(0), pages 569-584, January.
    9. Jorge Oyola & Halvard Arntzen & David L. Woodruff, 2017. "The stochastic vehicle routing problem, a literature review, Part II: solution methods," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 349-388, December.
    10. James R. Yee & Bruce L. Golden, 1980. "A note on determining operating strategies for probabilistic vehicle routing," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 27(1), pages 159-163, March.
    11. Gilbert Laporte, 2009. "Fifty Years of Vehicle Routing," Transportation Science, INFORMS, vol. 43(4), pages 408-416, November.
    12. Dimitris J. Bertsimas & Patrick Jaillet & Amedeo R. Odoni, 1990. "A Priori Optimization," Operations Research, INFORMS, vol. 38(6), pages 1019-1033, December.
    13. Michel Gendreau & Gilbert Laporte & René Séguin, 1995. "An Exact Algorithm for the Vehicle Routing Problem with Stochastic Demands and Customers," Transportation Science, INFORMS, vol. 29(2), pages 143-155, May.
    14. Gilbert Laporte & FranÇois V. Louveaux & Luc van Hamme, 2002. "An Integer L -Shaped Algorithm for the Capacitated Vehicle Routing Problem with Stochastic Demands," Operations Research, INFORMS, vol. 50(3), pages 415-423, June.
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    4. Glomb, Lukas & Liers, Frauke & Rösel, Florian, 2023. "Optimizing integrated aircraft assignment and turnaround handling," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1051-1071.
    5. Bashiri, Mahdi & Nikzad, Erfaneh & Eberhard, Andrew & Hearne, John & Oliveira, Fabricio, 2021. "A two stage stochastic programming for asset protection routing and a solution algorithm based on the Progressive Hedging algorithm," Omega, Elsevier, vol. 104(C).
    6. Vidal, Thibaut & Laporte, Gilbert & Matl, Piotr, 2020. "A concise guide to existing and emerging vehicle routing problem variants," European Journal of Operational Research, Elsevier, vol. 286(2), pages 401-416.
    7. Byungjun Ju & Minsu Kim & Ilkyeong Moon, 2021. "Vehicle Routing Problem Considering Reconnaissance and Transportation," Sustainability, MDPI, vol. 13(6), pages 1-19, March.
    8. Florio, Alexandre M. & Gendreau, Michel & Hartl, Richard F. & Minner, Stefan & Vidal, Thibaut, 2023. "Recent advances in vehicle routing with stochastic demands: Bayesian learning for correlated demands and elementary branch-price-and-cut," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1081-1093.
    9. De La Vega, Jonathan & Gendreau, Michel & Morabito, Reinaldo & Munari, Pedro & Ordóñez, Fernando, 2023. "An integer L-shaped algorithm for the vehicle routing problem with time windows and stochastic demands," European Journal of Operational Research, Elsevier, vol. 308(2), pages 676-695.
    10. Karels, Vincent C.G. & Rei, Walter & Veelenturf, Lucas P. & Van Woensel, Tom, 2024. "A vehicle routing problem with multiple service agreements," European Journal of Operational Research, Elsevier, vol. 313(1), pages 129-145.
    11. Majid Salavati-Khoshghalb & Michel Gendreau & Ola Jabali & Walter Rei, 2019. "A Rule-Based Recourse for the Vehicle Routing Problem with Stochastic Demands," Transportation Science, INFORMS, vol. 53(5), pages 1334-1353, September.
    12. Alexandre M. Florio & Richard F. Hartl & Stefan Minner & Juan-José Salazar-González, 2021. "A Branch-and-Price Algorithm for the Vehicle Routing Problem with Stochastic Demands and Probabilistic Duration Constraints," Transportation Science, INFORMS, vol. 55(1), pages 122-138, 1-2.

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