We consider the end-of-life inventory problem for the supplier of a product in its final phase of the service life cycle. This phase starts when the production of the items stops and continues until the warranty of the last sold item expires. At the beginning of this phase the supplier places a final order for spare parts to serve customers coming with defective items. At any time during the final phase the supplier may also decide to switch to an alternative and more cost effective service policy. This alternative policy may be in the form of replacing defective items with substitutable products or offering discounts/rebates on the new generation ones. In this setup, the objective is to find a final order quantity and a time to switch to an alternative policy which will minimize the total expected discounted costs of the supplier. The switching time is a stopping time and is based on the realization of the arrival process of defective items. In this paper, we study this problem under a general cost structure in a continuous-time framework where the arrival of customers is given by a non-homogeneous Poisson process. We show in detail how to compute the value function, and illustrate our approach on numerical examples.

中文翻译：

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报废库存问题的最佳停止方法

我们考虑产品供应商在其生命周期的最后阶段的报废库存问题。此阶段从停止生产物料开始，一直持续到最后出售的物料的保修到期为止。在此阶段开始时，供应商会下达最终订购备件的订单，以服务有缺陷物品的客户。在最后阶段的任何时候，供应商还可以决定切换到另一种更具成本效益的服务策略。这种替代政策的形式可以是用可替代产品代替有缺陷的物品，或为新一代产品提供折扣/折扣。在这种设置中，目标是找到最终订单数量和切换到替代策略的时间，该策略将使供应商的总预期折扣成本最小化。切换时间是停止时间，并且基于缺陷物品到达过程的实现。在本文中，我们在连续时间框架下的一般成本结构下研究此问题，其中客户的到来是通过非均匀的Poisson过程给出的。我们详细展示了如何计算值函数，并通过数值示例说明了我们的方法。