Scheduling, Queues and Dynamic Allocation Indices

A theorem is stated giving conditions under which the optimal allocation of a scarce resource between different tasks of uncertain characteristics is expressible by a priority index. When this can be done the problem is much simpler. The paper aims to give an overview of the kind of situations in which such a result does or does not hold, and the mathematical treatment is informal. Applications are described to priority queues, chemical research, search procedures, and the two-armed bandit problem.