  We consider a manufacturer who manages the end-of-life phase and takes one of
the three actions at each period: (1) place an order, (2) use existing
inventory, (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. 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.
Moreover, we show analytical results to understand the additional difficulties
of the problem solved, as well as structural results on optimal stopping times.
Furthermore, we devise an expandable taxonomy and categorize the models in the
literature. Analytical insights from the models as well as an extensive
numerical analysis show the value of our approach. The results indicate that
the loss can be high in case the manufacturer does not exploit flexibility in
placing orders or use an outside source. Several managerial insights are
obtained through numerical analysis as well as structural results to facilitate
decision-making during the end-of-life horizon.
