We consider a supplier selling a product with a relatively short life cycle and following a non-increasing price curve. Because of the short cycle, there is a single procurement opportunity at the beginning of the cycle. The objective of the supplier is to determine the initial order quantity and the time to remove the product from the market in order to maximize her profits. We study this problem in a continuous-time framework where the demand is modeled with a non-homogeneous Poisson process having a general intensity function and the pricing strategy is given by an arbitrary non-increasing function. We give a rigorous mathematical analysis for the problem and show how it can be solved in two stages. We also consider the special case with piecewise constant intensity and price functions. For this case, we show that the optimal exit time is included in the set of break points of these functions. This brings a fast method to obtain the optimal solution for this special case.

中文翻译：

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寿命周期短的产品在不增加价格曲线下的订购和退出决策

我们认为供应商销售的产品的生命周期相对较短，并且价格曲线不增加。由于周期短，周期开始时只有一个采购机会。供应商的目标是确定初始订单数量和从市场撤出产品的时间，以最大程度地提高其利润。我们在连续时间框架中研究此问题，在该框架中，需求是使用具有一般强度函数的非均匀泊松过程建模的，而定价策略是通过任意非增量函数给出的。我们对该问题进行了严格的数学分析，并展示了如何分两个阶段解决该问题。我们还考虑具有分段恒定强度和价格函数的特殊情况。对于这种情况，我们表明，最佳退出时间包含在这些函数的断点集中。这带来了一种快速的方法来获得针对这种特殊情况的最佳解决方案。