Abstract
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 distributions Findings: 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.
Highlights
Introduction and related literatureThe control procedure of the traditional periodic-review, base stock policy consists on examining the status of an item every R fixed time periods and launching a replenishment order which raise the inventory position to the order up to level S
They apply only under specific demand distributions, such as the Hadley and Whitin (1963) method that apply only when demand is Poisson distributed; the Nahmias and Smith (1994) method that calculates the mean stock level based on the two parameters of a negative binomial demand distribution in a multilevel inventory system; or the van der Heijden and de Kok (1992) method that applies for compound Poisson demand process with gamma distributed customers
The estimating errors arising from estimating the mean stock level using the Hadley-Whitin approximation instead or the exact method are analyzed by using the relative error expressed in terms of per 100, by means of the following expression: Re lative Error = Ψ − ΨSilver−Within Ψ
Summary
The control procedure of the traditional periodic-review, base stock policy consists on examining the status of an item every R fixed time periods and launching a replenishment order which raise the inventory position (on-hand stock plus onorder stock minus backorders) to the order up to level S. Apart from the Hadley-Whitin approximation, there is a handful of works that are dedicated to derive exact methods to estimate the mean stock level in the (R, S) policy They apply only under specific demand distributions, such as the Hadley and Whitin (1963) method that apply only when demand is Poisson distributed; the Nahmias and Smith (1994) method that calculates the mean stock level based on the two parameters of a negative binomial demand distribution in a multilevel inventory system; or the van der Heijden and de Kok (1992) method that applies for compound Poisson demand process with gamma distributed customers.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
