Optimal allocation policies in a two-echelon inventory problem with fixed shipment costs

This study investigates the stock allocation problems in a two-echelon distribution system which consists of a central warehouse and two identical retailers. We restrict our attention to two-period order cycles where the period lengths are allowed to be different. Shipments from the supplier to the warehouse arrive at the beginning of the order cycle (i.e. at the beginning of the first period). In each order cycle, there are two shipment opportunities from the warehouse to the retailers: at the beginning of the first and the second periods. In each shipment realization a fixed shipment cost is incurred. In each period a random demand is observed at each retailer (which is assumed to follow a normal distribution). The overall two-stage problem is to determine the optimal allocation policies at the beginning of each period, so that the expected two-period inventory holding, shortage and the shipment costs will be minimum. In this work, we characterize the optimal policy for the second period allocation problem as a function of the stock levels of the retailers at the beginning of the second period, and the reserve stock held at the warehouse. Furthermore, we provide sufficient conditions for which realizing an allocation yields inferior expected costs over keeping the reserve stock at the warehouse. A simulation model is employed to find the optimal first period decision parameters.