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An Adaptive Dynamic Programming Algorithm for Dynamic Fleet Management, II: Multiperiod Travel Times

Author

Listed:
  • Gregory A. Godfrey

    (Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544)

  • Warren B. Powell

    (Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544)

Abstract

In a companion paper (Godfrey and Powell 2002) we introduced an adaptive dynamic programming algorithm for stochastic dynamic resource allocation problems, which arise in the context of logistics and distribution, fleet management, and other allocation problems. The method depends on estimating separable nonlinear approximations of value functions, using a dynamic programming framework. That paper considered only the case in which the time to complete an action was always a single time period. Experiments with this technique quickly showed that when the basic algorithm was applied to problems with multiperiod travel times, the results were very poor. In this paper, we illustrate why this behavior arose, and propose a modified algorithm that addresses the issue. Experimental work demonstrates that the modified algorithm works on problems with multiperiod travel times, with results that are almost as good as the original algorithm applied to single period travel times.

Suggested Citation

  • Gregory A. Godfrey & Warren B. Powell, 2002. "An Adaptive Dynamic Programming Algorithm for Dynamic Fleet Management, II: Multiperiod Travel Times," Transportation Science, INFORMS, vol. 36(1), pages 40-54, February.
    • Handle: RePEc:inm:ortrsc:v:36:y:2002:i:1:p:40-54
    DOI: 10.1287/trsc.36.1.40.572
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    References listed on IDEAS

    as
    1. Brian Rexing & Cynthia Barnhart & Tim Kniker & Ahmad Jarrah & Nirup Krishnamurthy, 2000. "Airline Fleet Assignment with Time Windows," Transportation Science, INFORMS, vol. 34(1), pages 1-20, February.
    2. Warren B. Powell & Tassio A. Carvalho, 1998. "Dynamic Control of Logistics Queueing Networks for Large-Scale Fleet Management," Transportation Science, INFORMS, vol. 32(2), pages 90-109, May.
    3. Gregory A. Godfrey & Warren B. Powell, 2002. "An Adaptive Dynamic Programming Algorithm for Dynamic Fleet Management, I: Single Period Travel Times," Transportation Science, INFORMS, vol. 36(1), pages 21-39, February.
    4. 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.
    5. Warren B. Powell, 1989. "A Review of Sensitivity Results for Linear Networks and a New Approximation to Reduce the Effects of Degeneracy," Transportation Science, INFORMS, vol. 23(4), pages 231-243, November.
    6. Tassio A. Carvalho & Warren B. Powell, 2000. "A Multiplier Adjustment Method for Dynamic Resource Allocation Problems," Transportation Science, INFORMS, vol. 34(2), pages 150-164, May.
    7. Russell A. Rushmeier & Spyridon A. Kontogiorgis, 1997. "Advances in the Optimization of Airline Fleet Assignment," Transportation Science, INFORMS, vol. 31(2), pages 159-169, May.
    8. Warren B. Powell & Wayne Snow & Raymond K. Cheung, 2000. "Adaptive Labeling Algorithms for the Dynamic Assignment Problem," Transportation Science, INFORMS, vol. 34(1), pages 50-66, February.
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