Spare parts inventory control considering stochastic growth of an installed base

Installed base is a measure describing the number of units of a particular system actually in use. To maintain the performance of the installed units, spare parts inventory control is extremely important and becomes very challenging when the installed base changes over time. This problem is often encountered when a manufacturer starts to deliver a new product to customers and agrees to provide spare parts to replace failed units in the future. To cope with the resulting non-stationary stochastic maintenance demand, a spare parts control strategy needs to be carefully developed. The goal is to ensure that timely replacements can be provided to customers while minimizing the overall cost for spare parts inventory control. This paper provides a model for the aggregate maintenance demand generated by a product whose installed base grows according to a homogeneous Poisson process. Under a special case where the product's failure time follows the exponential distribution, the closed form solutions for the mean and variance of the aggregate maintenance demand are obtained. Based on the model, a dynamic (Q, r) restocking policy is formulated and solved using a multi-resolution approach. Two numerical examples are provided to demonstrate the application of the proposed method in controlling spare parts inventory under a service level constraint. Simulation is utilized to explore the effectiveness of the multi-resolution approach.