Optimal Unit Allocation Policies of Standby Systems

Abstract

In this paper, we consider optimal allocation policies for standby systems in which each unit stochastically fails. When all the units in the system fail, a system failure occurs. Each time the system fails, we determine the optimal number of units in the system to be next used so as to minimize the total expected replacement cost over a finite time horizon. The problems are formulated by dynamic programming, and are solved by a successive approximation method. Moreover, some properties of optimal policies are derived. That is, the optimal number of units of the system decreases in the remaining time, and there exists a critical point in time after which we leave the failed system.