Exact evaluation of batch-ordering inventory policies in two-echelon supply chains with periodic review

This paper studies a two-echelon supply chain with stochastic and discrete consumer demand, batch order quantities, periodic inventory review, and deterministic transportation times. Reorder point policies manage inventories at every location. Average inventory, backorders and fill rates are evaluated exactly for each location. Safety stock is evaluated exactly at the lower echelon and a good approximation is detailed for the upper echelon. Numerical data are presented to demonstrate the model's utility. It is found that system costs generally increase substantially if the upper echelon is restricted to carry no inventory, or if the upper echelon is required to provide a high fill rate. In many cases it is optimal to set the upper echelon's reorder point to yield near zero safety stock, yet in some cases this simple heuristic can significantly increase supply chain operating costs. Finally, policies selected under the assumption of continuous inventory review can perform poorly if implemented in an environment with periodic review.