Newsvendor Equations for Optimal Reorder Levels of Serial Inventory Systems with Fixed Batch Sizes

We consider a multi-echelon serial inventory system with stochastic demand, a given fixed batch size per stage, and linear holding and penalty costs for backorders. Under the average costs criterium, echelon stock $(R,nQ)$ policies are known to be optimal. In this paper, we derive new formulas for relevant cost functions and newsvendor equations for the optimal reorder levels.