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Solving the Vehicle Routing Problem with Stochastic Demands using the Cross-Entropy Method

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  • Krishna Chepuri
  • Tito Homem-de-Mello

Abstract

An alternate formulation of the classical vehicle routing problem with stochastic demands ( VRPSD) is considered. We propose a new heuristic method to solve the problem, based on the Cross-Entropy method. In order to better estimate the objective function at each point in the domain, we incorporate Monte Carlo sampling. This creates many practical issues, especially the decision as to when to draw new samples and how many samples to use. We also develop a framework for obtaining exact solutions and tight lower bounds for the problem under various conditions, which include specific families of demand distributions. This is used to assess the performance of the algorithm. Finally, numerical results are presented for various problem instances to illustrate the ideas. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Krishna Chepuri & Tito Homem-de-Mello, 2005. "Solving the Vehicle Routing Problem with Stochastic Demands using the Cross-Entropy Method," Annals of Operations Research, Springer, vol. 134(1), pages 153-181, February.
    • Handle: RePEc:spr:annopr:v:134:y:2005:i:1:p:153-181:10.1007/s10479-005-5729-7
    DOI: 10.1007/s10479-005-5729-7
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    1. Pierre Trudeau & Moshe Dror, 1992. "Stochastic Inventory Routing: Route Design with Stockouts and Route Failures," Transportation Science, INFORMS, vol. 26(3), pages 171-184, August.
    2. Michel Gendreau & Gilbert Laporte & René Séguin, 1996. "A Tabu Search Heuristic for the Vehicle Routing Problem with Stochastic Demands and Customers," Operations Research, INFORMS, vol. 44(3), pages 469-477, June.
    3. Gilbert Laporte & François Louveaux & Hélène Mercure, 1992. "The Vehicle Routing Problem with Stochastic Travel Times," Transportation Science, INFORMS, vol. 26(3), pages 161-170, August.
    4. Gutjahr, W. J. & Hellmayr, A. & Pflug, G. Ch., 1999. "Optimal stochastic single-machine-tardiness scheduling by stochastic branch-and-bound," European Journal of Operational Research, Elsevier, vol. 117(2), pages 396-413, September.
    5. Bastian, Cock & Rinnooy Kan, Alexander H. G., 1992. "The stochastic vehicle routing problem revisited," European Journal of Operational Research, Elsevier, vol. 56(3), pages 407-412, February.
    6. Alrefaei, Mahmoud H. & Andradottir, Sigrun, 2001. "A modification of the stochastic ruler method for discrete stochastic optimization," European Journal of Operational Research, Elsevier, vol. 133(1), pages 160-182, August.
    7. G. Alon & D. Kroese & T. Raviv & R. Rubinstein, 2005. "Application of the Cross-Entropy Method to the Buffer Allocation Problem in a Simulation-Based Environment," Annals of Operations Research, Springer, vol. 134(1), pages 137-151, February.
    8. Dimitris Bertsimas & Philippe Chervi & Michael Peterson, 1995. "Computational Approaches to Stochastic Vehicle Routing Problems," Transportation Science, INFORMS, vol. 29(4), pages 342-352, November.
    9. 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.
    10. Laporte, Gilbert & Louveaux, Francois & Mercure, Helene, 1989. "Models and exact solutions for a class of stochastic location-routing problems," European Journal of Operational Research, Elsevier, vol. 39(1), pages 71-78, March.
    11. Stewart, William R. & Golden, Bruce L., 1983. "Stochastic vehicle routing: A comprehensive approach," European Journal of Operational Research, Elsevier, vol. 14(4), pages 371-385, December.
    12. Dimitris J. Bertsimas, 1992. "A Vehicle Routing Problem with Stochastic Demand," Operations Research, INFORMS, vol. 40(3), pages 574-585, June.
    13. 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.
    14. 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.
    15. G. Clarke & J. W. Wright, 1964. "Scheduling of Vehicles from a Central Depot to a Number of Delivery Points," Operations Research, INFORMS, vol. 12(4), pages 568-581, August.
    16. Nicola Secomandi, 2001. "A Rollout Policy for the Vehicle Routing Problem with Stochastic Demands," Operations Research, INFORMS, vol. 49(5), pages 796-802, October.
    17. Frank A. Tillman, 1969. "The Multiple Terminal Delivery Problem with Probabilistic Demands," Transportation Science, INFORMS, vol. 3(3), pages 192-204, August.
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    4. Goodson, Justin C. & Ohlmann, Jeffrey W. & Thomas, Barrett W., 2012. "Cyclic-order neighborhoods with application to the vehicle routing problem with stochastic demand," European Journal of Operational Research, Elsevier, vol. 217(2), pages 312-323.
    5. Florent Hernandez & Michel Gendreau & Ola Jabali & Walter Rei, 2019. "A local branching matheuristic for the multi-vehicle routing problem with stochastic demands," Journal of Heuristics, Springer, vol. 25(2), pages 215-245, April.
    6. Dimitrakos, T.D. & Kyriakidis, E.G., 2015. "A single vehicle routing problem with pickups and deliveries, continuous random demands and predefined customer order," European Journal of Operational Research, Elsevier, vol. 244(3), pages 990-993.
    7. Prasanna Balaprakash & Mauro Birattari & Thomas Stützle & Marco Dorigo, 2015. "Estimation-based metaheuristics for the single vehicle routing problem with stochastic demands and customers," Computational Optimization and Applications, Springer, vol. 61(2), pages 463-487, June.
    8. Florio, Alexandre M. & Hartl, Richard F. & Minner, Stefan, 2020. "Optimal a priori tour and restocking policy for the single-vehicle routing problem with stochastic demands," European Journal of Operational Research, Elsevier, vol. 285(1), pages 172-182.
    9. Chiang, Wen-Chyuan & Russell, Robert & Xu, Xiaojing & Zepeda, David, 2009. "A simulation/metaheuristic approach to newspaper production and distribution supply chain problems," International Journal of Production Economics, Elsevier, vol. 121(2), pages 752-767, October.
    10. Majid Salavati-Khoshghalb & Michel Gendreau & Ola Jabali & Walter Rei, 2019. "A hybrid recourse policy for the vehicle routing problem with stochastic demands," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(3), pages 269-298, September.
    11. Novoa, Clara & Storer, Robert, 2009. "An approximate dynamic programming approach for the vehicle routing problem with stochastic demands," European Journal of Operational Research, Elsevier, vol. 196(2), pages 509-515, July.
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    13. 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.
    14. Jorge Oyola & Halvard Arntzen & David L. Woodruff, 2018. "The stochastic vehicle routing problem, a literature review, part I: models," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 193-221, September.
    15. Zamar, David S. & Gopaluni, Bhushan & Sokhansanj, Shahab, 2017. "Optimization of sawmill residues collection for bioenergy production," Applied Energy, Elsevier, vol. 202(C), pages 487-495.
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    17. Pieter-Tjerk de Boer & Dirk Kroese & Shie Mannor & Reuven Rubinstein, 2005. "A Tutorial on the Cross-Entropy Method," Annals of Operations Research, Springer, vol. 134(1), pages 19-67, February.
    18. Emelogu, Adindu & Chowdhury, Sudipta & Marufuzzaman, Mohammad & Bian, Linkan & Eksioglu, Burak, 2016. "An enhanced sample average approximation method for stochastic optimization," International Journal of Production Economics, Elsevier, vol. 182(C), pages 230-252.
    19. 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.
    20. 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.
    21. Edward Ianovsky & Joseph Kreimer, 2011. "An optimal routing policy for unmanned aerial vehicles (analytical and cross-entropy simulation approach)," Annals of Operations Research, Springer, vol. 189(1), pages 215-253, September.
    22. M. Bayat & F. Hooshmand & S. A. MirHassani, 2024. "Scenario-based stochastic model and efficient cross-entropy algorithm for the risk-budgeting problem," Annals of Operations Research, Springer, vol. 341(2), pages 731-755, October.
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    24. Thi-Phuong Nguyen, 2022. "Evaluation of network reliability for stochastic-flow air transportation network considering discounted fares from airlines," Annals of Operations Research, Springer, vol. 311(1), pages 335-355, April.

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