Fill rate of general periodic review two-stage inventory systems

This paper studies how to compute fill rate, the most commonly used customer service level, in a two-stage serial inventory system that uses base-stock-level inventory policy. We consider a general periodic review system instead of the traditional normalised periodic review system. We assume both stages have the same review intervals and provide exact formulas for the fill rate computation under general lead time and demand distribution. An approximation that employs only a single stage fill rate formula is also discussed. Numerical examples with normal random demands are used to illustrate the proposed fill rate formula. Our results show the monotonicity of the fill rate on parameters such as lead time, review cycle and echelon base-stock levels for both stages. Particularly, we find that the lead time and review length in the lower stage are more crucial than those in the upper stage in achieving higher system fill rates.