Continuous Review Two-Echelon (s, S) Inventory System with Partial Backlogging

Inventories exist throughout the supply chain in various forms for various reasons. This paper presents a continuous review two echelon inventory system. The operating policy at the lower echelon is (s, S) that is whenever the inventory level traps to s on order for Q = (S-s) items is placed, the ordered items are received after a random time which is distributed as exponential. We assume that the demands accruing during the stock-out period are partially backlogged. The retailer replenishes their stock from the regular supplier which adopts (0, M) policy, M = n1Q. When the regular supplier stock is empty the replacement of retailer stock made by the outside supplier who adopts (0, N) policy N = n2Q. The joint probability disruption of the inventory levels of retailer, regular supplier and the outside supplier are obtained in the steady state case. Various system performance measures are derived and the long run total expected inventory cost rate is calculated. Several instances of numerical examples, which provide insight into the behavior of the system are presented.