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The Parameter Iteration Method in Dynamic Programming

Author

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  • Shmuel Gal

    (IBM Israel Scientific Center, Technion City, Haifa 32000, Israel)

Abstract

Many practical problems involve making optimal decisions for systems with state characterized by many components. These problems lead to dynamic programming problems with a very large number of state variables. Thus, an exact derivation of the optimal policy for such problems is not feasible to solve numerically due to the great amount of computer time and storage involved. This paper presents a practical method, denoted as the Parameter Iteration Method, for obtaining an approximate solution for the above described problem. The computational difficulty caused by the tremendously large dimensionality of the state variable is overcome by means of an iterative method which combines simulation and recursive estimation to compute successive approximations of the value function. The implementation of the Parameter Iteration Method is illustrated for the problem of optimal replacement policy for a multi-item Markovian system.

Suggested Citation

  • Shmuel Gal, 1989. "The Parameter Iteration Method in Dynamic Programming," Management Science, INFORMS, vol. 35(6), pages 675-684, June.
    • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:6:p:675-684
    DOI: 10.1287/mnsc.35.6.675
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    Cited by:

    1. Archibald, T. W. & Buchanan, C. S. & Thomas, L. C. & McKinnon, K. I. M., 2001. "Controlling multi-reservoir systems," European Journal of Operational Research, Elsevier, vol. 129(3), pages 619-626, March.
    2. Luckny Zéphyr & Pascal Lang & Bernard Lamond, 2015. "Controlled approximation of the value function in stochastic dynamic programming for multi-reservoir systems," Computational Management Science, Springer, vol. 12(4), pages 539-557, October.
    3. Pourmoayed, Reza & Nielsen, Lars Relund, 2019. "An approximate dynamic programming approach for sequential pig marketing decisions at herd level," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1056-1070.
    4. Drouin, Nicol & Gautier, Antoine & Lamond, Bernard F. & Lang, Pascal, 1996. "Piecewise affine approximations for the control of a one-reservoir hydroelectric system," European Journal of Operational Research, Elsevier, vol. 89(1), pages 53-69, February.

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