One-for-one period policy in a two-echelon inventory system with poisson demand and constraint on total lost sales

In this paper we consider a two- echelon inventory system consisting of one supplier and a number of retailers with independent Poisson demand. Unsatisfied demands in retailers are lost and it is assumed that there is a constraint on total lost sales for the system. Each retailer applies a new ordering policy called one-for-one-period ordering policy for its inventory control. In this ordering policy the order size is equal to one and the time interval between any two consecutive orders is fixed. Thus, the supplier faces a uniform and deterministic demand originated from each retailer and applies one for one ordering policy in response to orders received from all retailers. For this system we derive the total cost function per unit time and show that it is convex. Then, we obtain the optimal time intervals between any two consecutive orders for all retailers which minimizes this total cost function.