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Inventory Control Under Parametric Uncertainty of Underlying Models

机译：底层模型参数不确定性下的库存控制

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摘要

A large number of problems in inventory control, production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty of underlying models. In the present paper we consider the case, where it is known that the underlying distribution belongs to a parametric family of distributions. The problem of determining an optimal decision rule in the absence of complete information about the underlying distribution, i.e., when we specify only the functional form of the distribution and leave some or all of its parameters unspecified, is seen to be a standard problem of statistical estimation. Unfortunately, the classical theory of statistical estimation has little to offer in general type of situation of loss function. In the paper, for improvement or optimization of statistical decisions under parametric uncertainty, a new technique of invariant embedding of sample statistics in a performance index is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant decision rules, which have smaller risk than any of the well-known decision rules. A numerical example is given.
机译：库存控制，生产计划和调度，位置，运输，财务和工程设计中的许多问题都要求在存在基础模型不确定性的情况下做出决策。在本文中，我们考虑以下情况：已知基础分布属于分布的参数族。在没有有关基础分布的完整信息的情况下确定最佳决策规则的问题，即当我们仅指定分布的功能形式而未指定其某些或所有参数时，这被视为统计的标准问题。估计。不幸的是，经典的统计估计理论在损失函数的一般情况下几乎没有提供。为了改善或优化参数不确定性下的统计决策，提出了一种将样本统计量不变地嵌入性能指标中的新技术。这项技术基于在数学统计中不变性原理的建设性使用，代表了一种简单且具有计算吸引力的统计方法。与贝叶斯方法不同，不变嵌入技术与先验的选择无关。它允许人们从问题中消除未知参数，并找到最佳的不变决策规则，该规则的风险要小于任何知名决策规则。给出了一个数值例子。

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