End-of-life inventory management problem: new results and insights

We consider a manufacturer who controls the inventory of spare parts in the end-of-life phase and takes one of three actions at each period: (1) place an order, (2) use existing inventory, or (3) stop holding inventory and use an outside/alternative source. Two examples of this source are discounts for a new generation product and delegating operations. The novelty of our study is allowing multiple orders while using strategies pertinent to the end-of-life phase. Demand is described by a non-homogeneous Poisson process, and the decision to stop holding inventory is described by a stopping time. After formulating this problem as an optimal stopping problem with additional decisions and presenting its dynamic programming algorithm, we use martingale theory to facilitate the calculation of the value function. Comparison with benchmark models and sensitivity analysis show the value of our approach and generate several managerial insights. Next, in a more special environment with a single order and a deterministic time to stop holding inventory, we present structural properties and analytical insights. The results include the optimality of (s, S) policy, and the relation between S and the time to stop holding inventory. Finally, we tackle the issue of selecting the intensity function by allowing it to be a stochastic process. The demand process can be constructed by using a Poisson random measure and an intensity process being measurable with respect to the Skorokhod topology. We show the necessary properties of this process including Laplace functional, strong Markov property and its compensated random measure. In case the intensity process is unobservable, we construct a non-linear filter process and reduce the problem to one with complete observation.