On spare parts demand and the installed base concept: A theoretical approach

Original Equipment Manufacturers (OEMs) aim to design their service supply chain before the introduction of their products to maximize their aftersales business revenues, reduce waste and achieve sustainability. In this study, we develop a stochastic model that unifies the installed base, i.e., the number of products in use, spare parts demand, and the number of discarded products within a single modeling framework based on three product characteristics: sales rate, usage time, and failure rate. Our model describes the installed base and spare part demand evolution over the entire life cycle of a parent product using stochastic point processes. At the same time we propose under very general assumptions on the cdf of the usage time and the mean arrival functions of the sales and failure processes an easy bisection procedure to compute the time at which the expected installed base and rate of the expected demand for spare parts is maximal. Our numerical experiments show that the volume of aftersales services increases in the expected usage time if the products face an increasing failure rate. The same experiments also reveal a 20 percent shift of the time at which the expected installed base is maximal in case the expected usage time is increased threefold. At the same time, we observe a boosting effect of the intensity of the sales process on this point in time.