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Dynamic Programming and Systems of Uncertain Duration

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  • D. J. White

    (University of Strathclyde, Glasgow)

Abstract

This paper deals with the application of dynamic programming to systems whose duration is uncertain, and which duration may or may not be a function of the decisionmaker's policy. It extends some of Bellman's work in that the transformed states at successive stages may not have the properties demanded by Bellman; e.g., the state norm need not diminish at all, and can, in fact, increase. The paper deals primarily with computational considerations since, in general, analytic solutions to functional equations are not forthcoming. Both discrete and continuous formulations are considered, the appropriate one to choose depending on the number of states one wishes to cater for, the continuous formulation having certain advantages which the discrete case does not have when a very large number of states are to be differentiated.

Suggested Citation

  • D. J. White, 1965. "Dynamic Programming and Systems of Uncertain Duration," Management Science, INFORMS, vol. 12(1), pages 37-67, September.
    • Handle: RePEc:inm:ormnsc:v:12:y:1965:i:1:p:37-67
    DOI: 10.1287/mnsc.12.1.37
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    Cited by:

    1. Grosfeld-Nir, Abraham & Anily, Shoshana & Ben-Zvi, Tal, 2006. "Lot-sizing two-echelon assembly systems with random yields and rigid demand," European Journal of Operational Research, Elsevier, vol. 173(2), pages 600-616, September.
    2. Gerchak, Yigal & Grosfeld-Nir, Abraham, 1998. "Multiple lot-sizing, and value of probabilistic information, in production to order of an uncertain size," International Journal of Production Economics, Elsevier, vol. 56(1), pages 191-197, September.
    3. Grosfeld-Nir, Abraham, 1995. "Single bottleneck systems with proportional expected yields and rigid demand," European Journal of Operational Research, Elsevier, vol. 80(2), pages 297-307, January.
    4. Grosfeld-Nir, Abraham & Robinson, Lawrence W., 1995. "Production to order on a two machine line with random yields and rigid demand," European Journal of Operational Research, Elsevier, vol. 80(2), pages 264-276, January.
    5. Shoshana Anily & Avraham Beja & Amit Mendel, 2002. "Optimal Lot Sizes with Geometric Production Yield and Rigid Demand," Operations Research, INFORMS, vol. 50(3), pages 424-432, June.
    6. Wang, Yunzeng & Gerchak, Yigal, 2000. "Input control in a batch production system with lead times, due dates and random yields," European Journal of Operational Research, Elsevier, vol. 126(2), pages 371-385, October.

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