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Monotone optimal control for a class of Markov decision processes

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  • Zhuang, Weifen
  • Li, Michael Z.F.
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    Abstract

    This paper provides a unified framework to study monotone optimal control for a class of Markov decision processes through D-multimodularity. We demonstrate that each system in this class can be classified as either a substitution-type or a complement-type system according to the possible transition set, which can be used as a classification mechanism that integrates a variety of models in the literature. We develop a generic proof of the structural properties of both types of system. In particular, we show that D-multimodularity is a generally sufficient condition for monotone optimal control of different types of system in this class. With this unified theory, there is no need to pursue each problem ad hoc and the structural properties of this class of MDPs follow with ease.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 217 (2012)
    Issue (Month): 2 ()
    Pages: 342-350

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    Handle: RePEc:eee:ejores:v:217:y:2012:i:2:p:342-350

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    Web page: http://www.elsevier.com/locate/eor

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    Keywords: Markov processes; D-multimodularity; Monotone optimal control; Substitution; Complement;

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    1. Ghoneim, Hussein A. & Stidham, Shaler, 1985. "Control of arrivals to two queues in series," European Journal of Operational Research, Elsevier, vol. 21(3), pages 399-409, September.
    2. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
    3. Alec Morton, 2006. "Structural properties of network revenue management models: an economic perspective," LSE Research Online Documents on Economics 2563, London School of Economics and Political Science, LSE Library.
    4. Albert Y. Ha, 1997. "Inventory Rationing in a Make-to-Stock Production System with Several Demand Classes and Lost Sales," Management Science, INFORMS, vol. 43(8), pages 1093-1103, August.
    5. Gabriel R. Bitran & Susana V. Mondschein, 1997. "Periodic Pricing of Seasonal Products in Retailing," Management Science, INFORMS, vol. 43(1), pages 64-79, January.
    6. Wen Zhao & Yu-Sheng Zheng, 2000. "Optimal Dynamic Pricing for Perishable Assets with Nonhomogeneous Demand," Management Science, INFORMS, vol. 46(3), pages 375-388, March.
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