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Some indexable families of restless bandit problems

  • K. D. Glazebrook (a1), D. Ruiz-Hernandez (a2) and C. Kirkbride (a1)

Abstract

In 1988 Whittle introduced an important but intractable class of restless bandit problems which generalise the multiarmed bandit problems of Gittins by allowing state evolution for passive projects. Whittle's account deployed a Lagrangian relaxation of the optimisation problem to develop an index heuristic. Despite a developing body of evidence (both theoretical and empirical) which underscores the strong performance of Whittle's index policy, a continuing challenge to implementation is the need to establish that the competing projects all pass an indexability test. In this paper we employ Gittins' index theory to establish the indexability of (inter alia) general families of restless bandits which arise in problems of machine maintenance and stochastic scheduling problems with switching penalties. We also give formulae for the resulting Whittle indices. Numerical investigations testify to the outstandingly strong performance of the index heuristics concerned.

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Copyright

Corresponding author

Postal address: Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK. Email address: k.glazebrook@lancaster.ac.uk
∗∗ Postal address: Department of Economics and Business, Universitat Pompeu Fabra, E-08005 Barcelona, Spain.
∗∗∗ Postal address: Department of Management Science, Lancaster University, Lancaster, LA1 4YX, UK.

References

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Some indexable families of restless bandit problems

  • K. D. Glazebrook (a1), D. Ruiz-Hernandez (a2) and C. Kirkbride (a1)

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