Newsboy characterizations for the optimal reorder levels of multi-echelon inventory systems with fixed batch sizes

This note considers an N-stage serial production/inventory system where materials flow from one stage to another in fixed batches. Linear holding and penalty costs (for backorders) are assumed. By Chen [2000], echelon stock (R, nQ) policies are optimal for such systems. Based on the results of Chen [1998], we show that the optimal reorder levels satisfy newsboy inequalities (equalities) when the demand has a discrete (continuous) distribution. The newsboy inequalities/equalities show a direct relation between the probability of no-stockout at the most downstream point and the cost parameters. Thus, they contribute to the understanding of optimal control. Also, they are easy to explain to managers and non-mathematical oriented students