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Spinning plates and squad systems: policies for bi-directional restless bandits

Part of: Hamilton-Jacobi theories, including dynamic programming Numerical methods in calculus of variations and optimal control

Published online by Cambridge University Press:  01 July 2016

K. D. Glazebrook ,
C. Kirkbride  and
D. Ruiz-Hernandez
K. D. Glazebrook*
Affiliation:
Lancaster University
C. Kirkbride*
Affiliation:
Lancaster University
D. Ruiz-Hernandez*
Affiliation:
Universitat Pompeu Fabra
*
∗ Postal address: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK. Email address: k.glazebrook@lancaster.ac.uk
∗∗ Postal address: Department of Management Science, Lancaster University, Lancaster LA1 4YX, UK.
∗∗∗ Department of Economics and Business, Universitat Pompeu Fabra, Barcelona, E-08005, Spain.
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Abstract

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This paper concerns two families of Markov decision problem that fall within the family of (bi-directional) restless bandits, an intractable class of decision processes introduced by Whittle. The spinning plates problem concerns the optimal management of a portfolio of reward-generating assets whose yields grow with investment but otherwise tend to decline. In the model of asset exploitation called the squad system, the yield from an asset tends to decline when it is used but will recover when the asset is at rest. In all cases, simply stated conditions are given that guarantee indexability of the problem, together with conditions necessary and sufficient for its strict indexability. The index heuristics for asset activation that emerge from the analysis are assessed numerically and found to perform very strongly.

Keywords

Index policyLagrangian methodMarkov decision problemrestless banditstochastic dynamic programming

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes
Secondary: 49L20: Dynamic programming method 90C39: Dynamic programming 49M20: Methods of relaxation type
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 1 , March 2006 , pp. 95 - 115
Copyright
Copyright © Applied Probability Trust 2006 

References

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