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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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    References listed on IDEAS

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    1. Warren B. Powell & Pierre Humblet, 1986. "The Bulk Service Queue with a General Control Strategy: Theoretical Analysis and a New Computational Procedure," Operations Research, INFORMS, vol. 34(2), pages 267-275, April.
    2. Luca Bertazzi & Maria Grazia Speranza, 1999. "Minimizing logistic costs in multistage supply chains," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(4), pages 399-417, June.
    3. M. G. Speranza & W. Ukovich, 1996. "An algorithm for optimal shipments with given frequencies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(5), pages 655-671, August.
    4. Bertazzi, Luca & Grazia Speranza, Maria, 1999. "Inventory control on sequences of links with given transportation frequencies," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 261-270, March.
    5. Ravi Anupindi & Sridhar Tayur, 1998. "Managing Stochastic Multiproduct Systems: Model, Measures, and Analysis," Operations Research, INFORMS, vol. 46(3-supplem), pages 98-111, June.
    6. Gregory A. Godfrey & Warren B. Powell, 2001. "An Adaptive, Distribution-Free Algorithm for the Newsvendor Problem with Censored Demands, with Applications to Inventory and Distribution," Management Science, INFORMS, vol. 47(8), pages 1101-1112, August.
    7. Howard J. Weiss, 1981. "Technical Note—Further Results on an Infinite Capacity Shuttle with Control at a Single Terminal," Operations Research, INFORMS, vol. 29(6), pages 1212-1217, December.
    8. Maria Grazia Speranza & Walter Ukovich, 1994. "Minimizing Transportation and Inventory Costs for Several Products on a Single Link," Operations Research, INFORMS, vol. 42(5), pages 879-894, October.
    9. Yehuda Bassok & Ravi Anupindi & Ram Akella, 1999. "Single-Period Multiproduct Inventory Models with Substitution," Operations Research, INFORMS, vol. 47(4), pages 632-642, August.
    10. Howard J. Weiss & Stanley R. Pliska, 1976. "Optimal Control of Some Markov Processes with Applications to Batch Queueing and Continuous Review Inventory Systems," Discussion Papers 214, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Edward Ignall & Peter Kolesar, 1972. "Operating Characteristics of a Simple Shuttle under Local Dispatching Rules," Operations Research, INFORMS, vol. 20(6), pages 1077-1088, December.
    12. Warren B. Powell, 1985. "Analysis of Vehicle Holding and Cancellation Strategies in Bulk Arrival, Bulk Service Queues," Transportation Science, INFORMS, vol. 19(4), pages 352-377, November.
    13. Rajat K. Deb, 1978. "Optimal Dispatching of a Finite Capacity Shuttle," Management Science, INFORMS, vol. 24(13), pages 1362-1372, September.
    14. Rajat K. Deb & Charles P. Schmidt, 1987. "Optimal Average Cost Policies for the Two-Terminal Shuttle," Management Science, INFORMS, vol. 33(5), pages 662-669, May.
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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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