An optimal stopping approach for the end-of-life inventory problem

We consider the end-of-life inventory problem for the supplier of a product in its final phase of the service life cycle. This phase starts when the production of the items stops and continues until the warranty of the last sold item expires. At the beginning of this phase the supplier places a final order for spare parts to serve customers coming with defective items. At any time during the final phase the supplier may also decide to switch to an alternative and more cost effective service policy. This alternative policy may be in the form of replacing defective items with substitutable products or offering discounts/rebates on the new generation ones. In this setup, the objective is to find a final order quantity and a time to switch to an alternative policy which will minimize the total expected discounted costs of the supplier. The switching time is a stopping time and is based on the realization of the arrival process of defective items. In this paper, we study this problem under a general cost structure in a continuous-time framework where the arrival of customers is given by a non-homogeneous Poisson process. We show in detail how to compute the value function, and illustrate our approach on numerical examples.