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Embedding a state space model into a Markov decision process

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  • Lars Relund Nielsen
  • Erik Jørgensen
  • Søren Højsgaard

Abstract

In agriculture Markov decision processes (MDPs) with finite state and action space are often used to model sequential decision making over time. For instance, states in the process represent possible levels of traits of the animal and transition probabilities are based on biological models estimated from data collected from the animal or herd. State space models (SSMs) are a general tool for modeling repeated measurements over time where the model parameters can evolve dynamically. In this paper we consider methods for embedding an SSM into an MDP with finite state and action space. Different ways of discretizing an SSM are discussed and methods for reducing the state space of the MDP are presented. An example from dairy production is given. Copyright Springer Science+Business Media, LLC 2011

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  • Lars Relund Nielsen & Erik Jørgensen & Søren Højsgaard, 2011. "Embedding a state space model into a Markov decision process," Annals of Operations Research, Springer, vol. 190(1), pages 289-309, October.
    • Handle: RePEc:spr:annopr:v:190:y:2011:i:1:p:289-309:10.1007/s10479-010-0688-z
    DOI: 10.1007/s10479-010-0688-z
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    References listed on IDEAS

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    1. Lars Relund Nielsen & Daniele Pretolani & Kim Allan Andersen, 2009. "Bicriterion Shortest Paths in Stochastic Time-Dependent Networks," Lecture Notes in Economics and Mathematical Systems, in: Vincent Barichard & Matthias Ehrgott & Xavier Gandibleux & Vincent T'Kindt (ed.), Multiobjective Programming and Goal Programming, pages 57-67, Springer.
    2. Pla, L. M. & Pomar, C. & Pomar, J., 2003. "A Markov decision sow model representing the productive lifespan of herd sows," Agricultural Systems, Elsevier, vol. 76(1), pages 253-272, April.
    3. Nielsen, Lars Relund & Kristensen, Anders Ringgaard, 2006. "Finding the K best policies in a finite-horizon Markov decision process," European Journal of Operational Research, Elsevier, vol. 175(2), pages 1164-1179, December.
    4. P. Diggle & M. G. Kenward, 1994. "Informative Drop‐Out in Longitudinal Data Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 49-73, March.
    5. Kristensen, Anders R., 1988. "Hierarchic Markov processes and their applications in replacement models," European Journal of Operational Research, Elsevier, vol. 35(2), pages 207-215, May.
    6. Kristensen, Anders Ringgaard, 1993. "Bayesian Updating in Hierarchic Markov Processes Applied to the Animal Replacement Problem," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 20(2), pages 223-239.
    7. Anders Kristensen & Erik Jørgensen, 2000. "Multi‐level hierarchic Markov processes as a framework for herd management support," Annals of Operations Research, Springer, vol. 94(1), pages 69-89, January.
    8. Kennedy, John O. S. & Stott, Alistair W., 1993. "An adaptive decision-making aid for dairy cow replacement," Agricultural Systems, Elsevier, vol. 42(1-2), pages 25-39.
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    Cited by:

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    2. Borodin, Valeria & Bourtembourg, Jean & Hnaien, Faicel & Labadie, Nacima, 2016. "Handling uncertainty in agricultural supply chain management: A state of the art," European Journal of Operational Research, Elsevier, vol. 254(2), pages 348-359.

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