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

Published online by Cambridge University Press:  01 July 2016

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: [email protected]
∗∗ 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.

Type
General Applied Probability
Copyright
Copyright © Applied Probability Trust 2006 

References

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