Manufacturers often encounter difficulties in supplying an adequate number of spare parts for a product in its postproduction phase. As a result, manufacturers will sometimes make one final order of a model of spare part that is used to satisfy any demand for the spare part going forward. The problem is compounded when a customer may request an extension to the maintenance or supply contract for which the part is supplied. We present two possible approaches for dealing with the problem: one involves the use of a continuous-time dynamic program that allows for the possibility of salvage, and the other makes use of a two-stage stochastic algorithm that does not consider salvage.
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.
The last buy problem is a stochastic inventory management problem that occurs at the end of a product's life cycle. When production of a given product ceases, it may become necessary to shut down manufacture of all parts of the product. However, there will likely still be demand for spare parts of the product, due to part failure from the product still in use. To meet this demand, a one-time order of spare parts-a last buy-is made to satisfy the demand for all spare parts going forward. vi
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