Analysis of substitutable inventory system in supply chain with direct demand and partial backlogging

Abstract

This paper presents continuous review two-echelon inventory systems with two different substitutable items in stock. The demand for the products follows independent Poisson with rates and respectively for product and A and B. There is a direct demand at DC follows poison with rate . The operating policy at the lower echelon for the products are (si, Si) that is whenever the inventory level drops to ‘si’ on order for Qi = (Si-si) 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 products from the supplier which adopts (0,M) policy. The joint probability disruption of the inventory levels of the products, at retailer and the products 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.