  We develop appropriately generalized notions of indexability for problems of
dynamic resource allocation where the resource concerned may be assigned more
flexibility than is allowed, for example, in classical multi-armed bandits.
Most especially we have in mind the allocation of a divisible resource
(manpower, money, equipment) to a collection of objects (projects) requiring it
in cases where its over-concentration would usually be far from optimal. The
resulting project indices are functions of both a resource level and a state.
They have a simple interpretation as a fair charge for increasing the resource
available to the project from the specified resource level when in the
specified state. We illustrate ideas by reference to two model classes which
are of independent interest. In the first, a pool of servers is assigned
dynamically to a collection of service teams, each of which mans a service
station. We demonstrate indexability under a natural assumption that the
service rate delivered is increasing and concave in the team size. The second
model class is a generalization of the spinning plates model for the optimal
deployment of a divisible investment resource to a collection of reward
generating assets. Asset indexability is established under appropriately drawn
laws of diminishing returns for resource deployment. For both model classes
numerical studies provide evidence that the proposed greedy index heuristic
performs strongly.
