cost function and optimal boundaries for a two-level inventory system with information sharing and two identical retailers

In this paper, we consider a two-echelon inventory system with a centralwarehouse and two identical retailers employing information sharing. transportation times to each retailer and the warehouse are constant. retailers face independent poisson demand and apply continuous review policy, i.e., (r, q)-policy. the warehouse initiates with m batches (of given size q) and places an order with an outside supplier when a retailer's inventory position reaches r + s; r + s is the inventory position considered by the central warehouse and s is a non-negative constant. so far, an approximate cost function as well as exact analysis of system for only one retailer has been proposed. however, the derivation of the exact value of the expected total cost of the system for more than one retailer is still an open question. this paper attempts to meet this challenge and derive the exact cost function for two retailers. to achieve this purpose, we resort to conditional probability to split the problem into two simpler problems; then, we obtain the exact expected total costof the system.