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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.