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

**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.

**Author**: Eugenia Babiloni, Manuel CardÃ³s, Ester Guijarro

Journal Code:

**jptindustrigg110022**