Analysis of fill rate in general periodic review two‐stage inventory systems

For echelon base‐stock policies, Zhang et al. (2010) derive the fill rate expression in which both stages have the same review intervals and use numerical examples to show some properties of the fill rate in regard to model parameters. We extent their model by considering the inventory replenishment at both stages which follows an echelon base‐stock policy with periodic batching: each stage is allowed to order at equidistant times and the order interval of the upstream stage is an integer multiple of the order interval of the downstream stage. For such a system, we develop an exact expression for the system's fill rate. Using stochastic comparison approach, we establish some sensitivity analysis results on fill rate with respect to problem parameters.