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On the exact calculation of the mean stock level in the base stock periodic review policy

机译:关于基本库存定期审查策略中平均库存水平的精确计算

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Purpose: One of the most usual indicators to measure the performance of any inventory policy is the mean stock level. In the generalized base stock, periodic review policy, the expected mean stock during the replenishment cycle is usually estimated by practitioners and researchers with the traditional Hadley-Whitin approximation. However it is not accurate enough and exact methods suggested on the related literature focus on specific demand distributions. This paper proposes a generalized method to compute the exact value of the expected mean stock to be used when demand is modelled by any uncorrelated, discrete and stationary demand pattern.Design/methodology/approach: The suggested method is based on computing the probability of every stock level at every point of the replenishment cycle for which it is required to know the probability of any stock level at the beginning of the cycle and the probability transition matrix between two consecutive periods of time. Furthermore, the traditional Hadley-Whitin approximation is compared with the proposed exact method over different discrete demand distributionsFindings: This paper points out the lack of accuracy that the Hadley-Whitin approximation shows over a wide range of service levels and discrete demand distributions. Research limitations/implications: The suggested method requires the availability of appropriate tools as well as a sound mathematical background. For this reason, approximations to it are the logical further research of this work. Practical implications: The use of the Hadley-Whitin approximation instead of an exact method can lead to underestimate systematically the expected mean stock level. This fact may increase total costs of the inventory system.Originality/value: The original derivation of an exact method to compute the expected mean stock level for the base stock, periodic review policy when demand is modelled by any discrete function and backlog is not allowed.
机译:目的:衡量任何库存政策绩效的最常用指标之一是平均库存水平。在广义基础库存的定期检查策略中,补充周期内的预期平均库存通常由从业人员和研究人员使用传统的Hadley-Whitin近似进行估算。但是,它不够准确,相关文献中建议的确切方法集中在特定的需求分布上。本文提出了一种通用方法来计算当需求通过任何不相关,离散和固定的需求模式进行建模时所使用的预期平均库存的精确值。设计/方法/方法:所建议的方法基于计算每一个概率的概率。需要在补货周期的每个点上了解库存水平的情况,为此需要知道周期开始时任何库存水平的概率以及两个连续时间段之间的概率转换矩阵。此外,将传统的Hadley-Whitin近似与在不同离散需求分布上提出的精确方法进行了比较。发现:本文指出了Hadley-Whitin近似在广泛的服务水平和离散需求分布下显示出的准确性不足。研究限制/意义:建议的方法需要适当的工具以及良好的数学背景。因此,对其进行近似是对这项工作的逻辑深入研究。实际意义:使用Hadley-Whitin逼近法而不是精确方法,可能会导致系统地低估预期的平均库存水平。这个事实可能会增加库存系统的总成本。原始数据/价值:一种原始方法的原始推导,用于计算基本库存的预期平均库存水平,当需求由任何离散函数建模且不允许积压时,采用定期审查策略。

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