Effect of modeling fixed cost in a serial inventory system with periodic review

We study a two-echelon serial inventory system with stochastic demand. We assume that fixed ordering costs are charged only when an order initiates a non-zero shipment. The system is centrally controlled and ordering decisions are based on echelon base stock policies. The review period of the upper echelon is an integer multiple of the review period of the lower echelon. We derive an exact analytical expression for the objective function. From this expression, we determine optimal base stock levels and review periods. Through a numerical study we show that there may be several combinations of optimal review periods and that under high fixed ordering costs both stockpoints have the same order frequency. In addition, we identify parameter settings under which the system behaves like a PUSH-system, where the upstream stockpoint never holds any stock. Generally, in literature fixed ordering costs are charged at every review moment, even if no shipment results due to zero upstream stock. We test the impact of this simplifying assumption and illustrate when it is justified.