The ‘final order’ problem

When the service department of a company selling machines stops producing and supplying spare parts for certain machines, customers are offered an opportunity to place a so-called final order for these spare parts. We focus on one customer with one machine. The customer plans to use this machine up to a fixed horizon. Based on this horizon, and on the failure rates of the components, the prices of spare components and the consequences of the machine failing before the critical lifetime is reached, the size of the final order is determined.