Invariant problems in dynamic programming- average reward criterion

A dynamic programming problem is called invariant if its transition mechanism depends only on the action taken and does not depend on the current state of the systm. Replacement and maintenance problems are two typical types of problems which arise in applications and are often invariant. The paper studies properties of invariant problems when the state space is arbitrary and the action space is finite. The main result is a method of obtaining optimal policies for this case when the optimality criterion is that of maximizing the average reward per unit time. Results are illustrated by examples.