A generalized discrete-time order replacement model

In this article, we consider a discrete-time order replacement problem. More precisely, we treat a generalized model with more complex cost structure than Kaio & Osaki and with two decision variables: allowable inventory time and ordering time. Based on the discrete probabilistic argument, we derive the optimal ordering policy to deliver a spare unit preventively by a regular order, so as to minimize the expected cost per unit time in the steady state. Numerical examples are devoted to carrying out the sensitivity analysis of model parameters on the optimal ordering policy and its associated expected cost value.