A Multiperiod Newsvendor Problem with Partially Observed Demand

A. Bensoussan, M. Çakanyıldırım, S. Sethi
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引用次数: 90

Abstract

We consider a newsvendor problem with partially observed Markovian demand. Demand is observed if it is less than the inventory. Otherwise, only the event that it is larger than or equal to the inventory is observed. These observations are used to update the demand distribution from one period to the next. The state of the resulting dynamic programming equation is the current demand distribution, which is generally infinite dimensional. We use unnormalized probabilities to convert the nonlinear state transition equation to a linear one. This helps in proving the existence of an optimal feedback ordering policy. So as to learn more about the demand, the optimal order is set to exceed the myopic optimal order. The optimal cost decreases as the demand distribution decreases in the hazard rate order. In a special case with finitely many demand values, we characterize a near-optimal solution by establishing that the value function is piecewise linear.
具有部分可观察需求的多时段报贩问题
我们考虑一个具有部分观察到的马尔可夫需求的报贩问题。如果需求小于库存,则观察需求。否则,只观察大于或等于库存的事件。这些观察结果用于更新从一个时期到下一个时期的需求分布。得到的动态规划方程的状态为当前需求分布,一般为无限维。我们使用非归一化概率将非线性状态转移方程转化为线性状态转移方程。这有助于证明存在最优反馈排序策略。为了更好地了解需求,将最优订单设置为超过近视最优订单。最优成本按风险率顺序随需求分布的减小而减小。在具有有限多个需求值的特殊情况下,我们通过建立值函数是分段线性的来表征一个近最优解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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