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A note on evaluating the risk in continuous review inventory systems

机译：关于评估持续审查清单系统中的风险的说明

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This paper is an attempt to evaluate the long term risk of stock-out and obsolescence in continuous review inventory systems, typically of slow-moving but very critical items. Inventory decisions depend very much on the goodness of the estimates of the input parameters like the holding, ordering and stock-out costs. It is a well-known fact that stock-out cost is a very difficult parameter to estimate. The lower it is the lower the quality of service will be while the higher it is the higher the inventory cost would be and possibly higher obsolescence rate too. In this paper, we develop a framework to evaluate the risks, in the long term, of stock-out and obsolescence, especially for inventory of critical spares whose demand rate is not high. For this purpose, we propose the use of quasi-stationary distributions for continuous review (r, Q) inventory systems with the condition that the Laplace transforms of functions of interest are rational algebraic functions. We relate the quasi-stationary distribution to the conditional tail expectation which is a coherent risk measure used in finance and actuarial studies. Numerical illustration is also provided.
机译：本文试图评估连续审查库存系统（通常是速度缓慢但非常关键的物料）中缺货和过时的长期风险。库存决策在很大程度上取决于对输入参数（如持有，订购和缺货成本）的估计的优劣。众所周知，缺货成本是很难估计的参数。数值越低，服务质量将越低，而库存成本越高，则服务成本就越高，过时率也可能更高。在本文中，我们开发了一个框架来长期评估缺货和过时的风险，尤其是对于需求率不高的关键备件的库存而言。为此，我们建议将准平稳分布用于连续审查（r，Q）库存系统，条件是感兴趣函数的拉普拉斯变换是有理代数函数。我们将准平稳分布与条件尾部期望相关联，条件尾部期望是金融和精算研究中使用的相干风险度量。还提供了数字说明。

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