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A Markov Decision Model and Decomposition Heuristic for Dynamic Vehicle Dispatching

Author

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  • Alan S. Minkoff

    (IBM Corporation, New York, New York)

Abstract

We describe a dynamic and stochastic vehicle dispatching problem called the delivery dispatching problem. This problem is modeled as a Markov decision process. Because exact solution of this model is impractical, we adopt a heuristic approach for handling the problem. The heuristic is based in part on a decomposition of the problem by customer, where customer subproblems generate penalty functions that are applied in a master dispatching problem. We describe how to compute bounds on the algorithm's performance, and apply it to several examples with good results.

Suggested Citation

  • Alan S. Minkoff, 1993. "A Markov Decision Model and Decomposition Heuristic for Dynamic Vehicle Dispatching," Operations Research, INFORMS, vol. 41(1), pages 77-90, February.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:1:p:77-90
    DOI: 10.1287/opre.41.1.77
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    Cited by:

    1. Sila Çetinkaya & Chung-Yee Lee, 2000. "Stock Replenishment and Shipment Scheduling for Vendor-Managed Inventory Systems," Management Science, INFORMS, vol. 46(2), pages 217-232, February.
    2. Frank Chen & Tong Wang & Tommy Xu, 2005. "Integrated Inventory Replenishment and Temporal Shipment Consolidation: A Comparison of Quantity-Based and Time-Based Models," Annals of Operations Research, Springer, vol. 135(1), pages 197-210, March.
    3. Sayarshad, Hamid R. & Gao, H. Oliver, 2018. "A non-myopic dynamic inventory routing and pricing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 83-98.
    4. Anton J. Kleywegt & Vijay S. Nori & Martin W. P. Savelsbergh, 2004. "Dynamic Programming Approximations for a Stochastic Inventory Routing Problem," Transportation Science, INFORMS, vol. 38(1), pages 42-70, February.
    5. Anton J. Kleywegt & Vijay S. Nori & Martin W. P. Savelsbergh, 2002. "The Stochastic Inventory Routing Problem with Direct Deliveries," Transportation Science, INFORMS, vol. 36(1), pages 94-118, February.
    6. Ilya O. Ryzhov & Martijn R. K. Mes & Warren B. Powell & Gerald van den Berg, 2019. "Bayesian Exploration for Approximate Dynamic Programming," Operations Research, INFORMS, vol. 67(1), pages 198-214, January.
    7. Côté, Jean-François & Alves de Queiroz, Thiago & Gallesi, Francesco & Iori, Manuel, 2023. "A branch-and-regret algorithm for the same-day delivery problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
    8. Daniel Adelman, 2004. "A Price-Directed Approach to Stochastic Inventory/Routing," Operations Research, INFORMS, vol. 52(4), pages 499-514, August.
    9. Yves Crama & Mahmood Rezaei & Martin Savelsbergh & Tom Van Woensel, 2018. "Stochastic Inventory Routing for Perishable Products," Transportation Science, INFORMS, vol. 52(3), pages 526-546, June.
    10. Ouyang, Zhiyuan & Leung, Eric Ka Ho & Huang, George Q., 2022. "Community logistics for dynamic vehicle dispatching: The effects of community departure “time” and “space”," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 165(C).
    11. Andreatta, G. & Lulli, G., 2008. "A multi-period TSP with stochastic regular and urgent demands," European Journal of Operational Research, Elsevier, vol. 185(1), pages 122-132, February.
    12. Bertazzi, Luca & Bosco, Adamo & Laganà, Demetrio, 2015. "Managing stochastic demand in an Inventory Routing Problem with transportation procurement," Omega, Elsevier, vol. 56(C), pages 112-121.
    13. Lucas Agussurja & Shih-Fen Cheng & Hoong Chuin Lau, 2019. "A State Aggregation Approach for Stochastic Multiperiod Last-Mile Ride-Sharing Problems," Service Science, INFORMS, vol. 53(1), pages 148-166, February.
    14. Noah Gans & Garrett van Ryzin, 1999. "Dynamic Vehicle Dispatching: Optimal Heavy Traffic Performance and Practical Insights," Operations Research, INFORMS, vol. 47(5), pages 675-692, October.
    15. Alejandro Toriello & George Nemhauser & Martin Savelsbergh, 2010. "Decomposing inventory routing problems with approximate value functions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(8), pages 718-727, December.
    16. Martin I. Reiman & Rodrigo Rubio & Lawrence M. Wein, 1999. "Heavy Traffic Analysis of the Dynamic Stochastic Inventory-Routing Problem," Transportation Science, INFORMS, vol. 33(4), pages 361-380, November.
    17. Çetinkaya, SIla & Bookbinder, James H., 2003. "Stochastic models for the dispatch of consolidated shipments," Transportation Research Part B: Methodological, Elsevier, vol. 37(8), pages 747-768, September.
    18. Anton J. Kleywegt & Jason D. Papastavrou, 1998. "Acceptance and Dispatching Policies for a Distribution Problem," Transportation Science, INFORMS, vol. 32(2), pages 127-141, May.
    19. Zheng Wang & Jiuh‐Biing Sheu & Chung‐Piaw Teo & Guiqin Xue, 2022. "Robot Scheduling for Mobile‐Rack Warehouses: Human–Robot Coordinated Order Picking Systems," Production and Operations Management, Production and Operations Management Society, vol. 31(1), pages 98-116, January.
    20. Ketzenberg, Michael E. & Metters, Richard D., 2020. "Adapting operations to new information technology: A failed “internet of things” application," Omega, Elsevier, vol. 92(C).
    21. Vukadinovic, Katarina & Teodorovic, Dusan & Pavkovic, Goran, 1997. "A neural network approach to the vessel dispatching problem," European Journal of Operational Research, Elsevier, vol. 102(3), pages 473-487, November.
    22. Soumia Ichoua & Michel Gendreau & Jean-Yves Potvin, 2000. "Diversion Issues in Real-Time Vehicle Dispatching," Transportation Science, INFORMS, vol. 34(4), pages 426-438, November.
    23. Leandro C. Coelho & Jean-François Cordeau & Gilbert Laporte, 2014. "Thirty Years of Inventory Routing," Transportation Science, INFORMS, vol. 48(1), pages 1-19, February.

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