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An adaptive dynamic programming algorithm for a stochastic multiproduct batch dispatch problem

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  • Katerina P. Papadaki
  • Warren B. Powell

Abstract

We address the problem of dispatching a vehicle with different product classes. There is a common dispatch cost, but holding costs that vary by product class. The problem exhibits multidimensional state, outcome and action spaces, and as a result is computationally intractable using either discrete dynamic programming methods, or even as a deterministic integer program. We prove a key structural property for the decision function, and exploit this property in the development of continuous value function approximations that form the basis of an approximate dispatch rule. Comparisons on single product‐class problems, where optimal solutions are available, demonstrate solutions that are within a few percent of optimal. The algorithm is then applied to a problem with 100 product classes, and comparisons against a carefully tuned myopic heuristic demonstrate significant improvements. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 742–769, 2003.

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  • Katerina P. Papadaki & Warren B. Powell, 2003. "An adaptive dynamic programming algorithm for a stochastic multiproduct batch dispatch problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 742-769, October.
    • Handle: RePEc:wly:navres:v:50:y:2003:i:7:p:742-769
    DOI: 10.1002/nav.10087
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    Cited by:

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    2. Daniel R. Jiang & Warren B. Powell, 2015. "Optimal Hour-Ahead Bidding in the Real-Time Electricity Market with Battery Storage Using Approximate Dynamic Programming," INFORMS Journal on Computing, INFORMS, vol. 27(3), pages 525-543, August.
    3. Joel A. Shapiro & Warren B. Powell, 2006. "A Metastrategy for Large-Scale Resource Management Based on Informational Decomposition," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 43-60, February.
    4. Huseyin Topaloglu & Sumit Kunnumkal, 2006. "Approximate dynamic programming methods for an inventory allocation problem under uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(8), pages 822-841, December.
    5. Yongpei Guan & Andrew J. Miller, 2008. "Polynomial-Time Algorithms for Stochastic Uncapacitated Lot-Sizing Problems," Operations Research, INFORMS, vol. 56(5), pages 1172-1183, October.
    6. Tianke Feng & Joseph C. Hartman, 2015. "The dynamic and stochastic knapsack Problem with homogeneous‐sized items and postponement options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(4), pages 267-292, June.
    7. Sumit Kunnumkal & Huseyin Topaloglu, 2008. "Exploiting the Structural Properties of the Underlying Markov Decision Problem in the Q-Learning Algorithm," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 288-301, May.
    8. Wang, Yi & Zhang, Sheng Hao, 2021. "Optimal production and inventory rationing policies with selective-information sharing and two demand classes," European Journal of Operational Research, Elsevier, vol. 288(2), pages 394-407.
    9. Daniel Adelman & Adam J. Mersereau, 2008. "Relaxations of Weakly Coupled Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 56(3), pages 712-727, June.

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