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Sensitivity Analysis in Markov Decision Processes with Uncertain Reward Parameters

Published online by Cambridge University Press:  14 July 2016

Chin Hon Tan  and
Joseph C. Hartman
Chin Hon Tan*
Affiliation:
University of Florida
Joseph C. Hartman*
Affiliation:
University of Florida
*
∗ Postal address: Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, PO Box 116595, Gainesville, FL 32611-6595, USA.
∗ Postal address: Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, PO Box 116595, Gainesville, FL 32611-6595, USA.
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Abstract

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Sequential decision problems can often be modeled as Markov decision processes. Classical solution approaches assume that the parameters of the model are known. However, model parameters are usually estimated and uncertain in practice. As a result, managers are often interested in how estimation errors affect the optimal solution. In this paper we illustrate how sensitivity analysis can be performed directly for a Markov decision process with uncertain reward parameters using the Bellman equations. In particular, we consider problems involving (i) a single stationary parameter, (ii) multiple stationary parameters, and (iii) multiple nonstationary parameters. We illustrate the applicability of this work through a capacitated stochastic lot-sizing problem.

Keywords

Markov decision processdynamic programmingsensitivity analysis

MSC classification

Secondary: 90C40: Markov and semi-Markov decision processes 90C39: Dynamic programming 90C31: Sensitivity, stability, parametric optimization

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 4 , December 2011 , pp. 954 - 967
Copyright
Copyright © Applied Probability Trust 2011 

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