  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, (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 compute several
metrics of interest including the expected number of orders placed throughout
the end-of-life phase. Furthermore, we devise an expandable taxonomy and relate
the benchmark models to 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. Also, an
outside source can be a significant alternative for the end-of-life inventory
management problem. Finally, we show that some counter-intuitive strategies can
be valuable for future analysis.
