O(N³) ALGORITHM FOR OPTIMAL REPLACEMENT PROBLEMS.

This paper considers the general replacement problem of an item which can be in any one of N operating states. At the beginning of each period, one can either keep the item for (at least) one more period or sell it and get a new item. The change of state during each period is assumed to be Markovian. It is assumed that the state of the item is determined by several measurable parameters and not only by its age. In this case the optimal replacement rule is much more complicated than the usual simple rule of replacing the item at a fixed critical age. This problem can be formulated in terms of dynamic programming. In general, however, the usual methods for obtaining the optimal policy can require many iterations. An algorithm which requires a number of iterations not exceeding the number of states in which a replacement decision has to be taken is presented.