A Continuous-Time Examination of End-of-Life Parts Acquisition With Limited Customer Information

Manufacturers often encounter difficulties in supplying an adequate number of spare parts for a product that is in its post-production phase. Current solution methods for optimal spare part order amounts use assumptions that require knowledge of the number of products in operation at any time t. In the business situation presented here, the manufacturer only has knowledge of the part and product failure rates and a probability distribution on the number of products still in operation; unless the manufacturer and customer have a close working relationship, it is likely that this information is all that the manufacturer will have available in a typical business environment. We model time-discounted revenues and costs as a function of the spare parts order amount. We consider two different versions of the problem—incremental replenishment and no replenishment—that operate by determining the rate of change of the total profit with respect to the order amount q.