Hidden effects of variable order review intervals in inventory control

Whereas inventory theory traditionally assumes the periodic review inventory model (R, T), with an order‐up‐to level R, has a random demand and lead time coupled with a deterministic review interval T, firms often deviate from a strict adherence to a fixed review interval when they attempt to capture transportation scale efficiencies. Employing this policy introduces additional supply chain variability. This paper aims to provide an expression for the standard deviation of demand during the protection period, important in setting safety stock, as well as an expression for the amount of order variance amplification induced by a stochastic review interval.

Analytical modeling is used to develop the expression for the standard deviation of demand during the protection period as well as the calculation for the amount of order variance amplification induced by a stochastic review interval.

In terms of the variance of demand over the protection period, a stochastic review interval has a similar effect to that of a stochastic lead time, but its impact on demand variance amplification within the supply chain differs fundamentally. Specifically, a stochastic review interval creates an order batching bullwhip effect not identified in existing literature.

This study offers an expression for the standard deviation of demand during the protection period when stochastic review intervals are employed. The expression can be used to more effectively set safety stock. The paper also offers an expression for the order variance amplification induced by a stochastic review interval.

The study offers suggestions for retailers and suppliers regarding when the use of a stochastic review interval is effective in terms of cost efficiencies.

While the existence and effect of lead time variability is well‐established in the literature, traditional approaches the periodic review inventory model ignore the stochastic nature of review interval. This paper highlights the use of stochastic review intervals as a contributing factor to the bullwhip effect.