A Net Present Value Analysis of Opportunity-Based Age Replacement Models in Discrete Time

Two important opportunistic age replacement models, under replacement first and last disciplines, are generalized in discrete time. The net present value (NPV) is applied to formulate the expected total costs. The priority of multiple replacement options is considered to classify the cost model with discounting into six cases. Since the NPV method accurately calculates the expected replacement costs over an infinite horizon in an unstable economic environment, we discuss some optimal opportunistic age replacement policies which minimize the expected total discounted costs over an infinite time horizon. Furthermore, we formulate a unified model under each discipline, merging six discrete time replacement models with probabilistic priority. Finally, a case study on optimal replacement first and last policies for pole air switches in a Japanese power company is presented.