A periodic‐review inventory control policy for a two‐level supply chain with multiple retailers and stochastic demand

We consider a time‐based inventory control policy for a two‐level supply chain with one warehouse and multiple retailers in this paper. Let the warehouse order in a fixed base replenishment interval. The retailers are required to order in intervals that are integer‐ratio multiples of the base replenishment interval at the warehouse. The warehouse and the retailers each adopt an order‐up‐to policy, i.e. order the needed stock at a review point to raise the inventory position to a fixed order‐up‐to level. It is assumed that the retailers face independent Poisson demand processes and no transshipments between them are allowed. The contribution of the study is threefold. First, we assume that when facing a shortage the warehouse allocates the remaining stock to the retailers optimally to minimize system cost in the last minute before delivery and provide an approach to evaluate the exact system cost. Second, we characterize the structural properties and develop an exact optimal solution for the inventory control system. Finally, we demonstrate that the last minute optimal warehouse stock allocation rule we adopt dominates the virtual allocation rule in which warehouse stock is allocated to meet retailer demand on a first‐come first‐served basis with significant cost benefits. Moreover, the proposed time‐based inventory control policy can perform equally well or better than the commonly used stock‐based batch‐ordering policy for distribution systems with multiple retailers.