Indexable Restless Bandits

This book concerns two broad classes of Markov decision problems that fall within the family of "restless bandits", an intractable class of decision processes introduced by P. Whittle. For the first class of problems, we employ Gittins index theory to establish the indexability of (inter- alia) general families of restless bandits that arise in problems of machine maintenance and stochastic scheduling with switching penalties. We also give formulae for the resulting indices. The second class of problems involves two families of Markov decision problems that can be identified as "bi-directional" restless bandits. 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 both cases simply stated conditions are given which guarantee indexability of the problem. In all cases, numerical investigations testify the outstandingly good performance of the index heuristics concerned.