Determining the ordering quantity for exponentially deteriorating components under cumulative free-replacement warranty

This article investigates the optimal ordering quantity for exponentially deteriorating components under cumulative free-replacement warranty. When the warranty period of a single component is w, the total warranty period of a batch of k components is cumulated up to kw under cumulative free-replacement warranty. In some cases, system breakdowns are quite costly and therefore a larger batch would translate into a longer warranty period and an increased number of spare parts to avoid system breakdowns. However, a larger batch also incurs more inventory holding cost, especially for expensive components. Thus, there is a tradeoff between the cost of a breakdown and the cost of holding inventory.