Modelling and Analysis of Compliment Inventory System in Supply Chain with Partial Backlogging

This paper presents a continuous review two echelon inventory systems with two different items in stock, one is main product and other one is complement item for the main product. The operating policy at the lower echelon for the main product is (s, S) that is whenever the inventory level drops 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 the stock of main product from the supplier which adopts (0,M) policy. The complement product is replenished instantaneously from local supplier. The joint probability disruption of the inventory levels of main product, complement item at retailer and the main product at 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.