On the end-of-life inventory problem

We consider the so-called End-of-Life inventory problem for a manufacturer of spare parts in the final phase of the service life cycle. The final phase starts when the part production is terminated and continues until the last service contract expires. One of the most popular tactics to cope with this problem is to place a sufficient volume of spare parts at the beginning of the final phase which is called the nal order quantity. Then the repair-replacement policy serves the costumers by repairing or replacing the defective items. On the other hand, nowadays, a considerable price erosion happens for the products while repair and service costs stay steady over time. If so, it is more cost effective to consider an alternative policy to meet the service demands after some time. This policy may offer the costumers a new product of similar type or a discount on a next generation product. In this setup, the purpose is to find an optimal pair of final order quantity and switching time to an alternative policy which minimizes the total expected discounted costs. We study this problem under the static and dynamic approaches which require different mathematical techniques