Optimal Replacement Last With Continuous and Discrete Policies

This paper proposes age and periodic replacement last models with continuous, and discrete policies. That is, an operating unit is replaced preventively at time T of operation as a strategic policy, or at a number N of working cycles to satisfy successive job completion, whichever occurs last. Such policies are named as replacement last, and their expected cost rates and optimal policies are obtained. However, the focus of this paper is to compare replacement last with replacement first policies, which are formulated under the classical assumption of whichever occurs first. From the points of cost and performability, different comparative methods for continuous and discrete optimizations are demonstrated to determine in what cases we should adopt replacement last rather than replacement first. All theoretical discussions in this paper are made analytically, and are computed numerically.