turkmath.org

We consider an inventory problem of controlling the inventory of spare parts in the final phase of the service life cycle. The final phase starts when the production of a product is terminated and it continues until the last service contract or warranty period expires. Placing final orders for service parts at the end of the production cycle of a product is considered to be a popular tactic to satisfy demand during this period and to mitigate the effect of part obsolescence at the end of the service life cycle. Previous research focuses on repairing defective products by replacing the defective parts with properly functioning spare ones. However, for most of the inventory problems with the product in a no production phase there is typically a price erosion for the new type of product presently in production while repair cost for a defective product of a previous generation stays steady over time. As a consequence, there might be a point in time at which the unit price of a new generation product drops below the repair costs. If so, it is more cost effective to adopt an alternative policy to meet service demands toward the end of the final phase, such as offering customers the new product of a similar type or a discount on a next generation product. As an example we mention the handling of old generation iPhones after the introduction of a new type of iPhone. This study examines the cost trade-offs of implementing alternative policies for the repair policy and develops an exact expression for the expected total cost function under the assumption that the arrival process of demands for repairing defective products of an old type is given by a nonhomogeneous Poisson process with a given arrival rate function. This problem is know as the end of life problem and to derive this expression under very general cost assumptions we use well known results from martingale theory. As such this talk focuses on ongoing research and the use of more sophisticated techniques well known within the theory of stochastic processes contrary to the Markovian techniques used within inventory theory.