Analysis of Two-Echelon Inventory System With Two Demand Classes With Direct Demand

Abstract

This paper deals with a continuous review two-echelon inventory system with two demand classes.. The demand at retailer is of two types. The First type of demand is usual single unit and the second type is of bulk or packet demand. The arrival distribution for single and packet demands are assumed to be independent Poisson with rates $\lambda_{1}\ (>0)$ and $\lambda_{q}\ (>0)$ respectively. The model permits a direct demand of distributor which follows Poisson with rate $\lambda_{d}\ (>0) $. The operating policy at the lower echelon for the (s, S) that is whenever the inventory level drops to `\textbf{s'} on order for $Q = (S-s)$ items is placed, the ordered items are received after a random time which is distributed as exponential with rate $\mu>0$. We assume that the demands occurring during the stock-out period are lost. The retailer replenishes the stock from the distributor which adopts $(0, M)$ policy. The objective is to minimize the anticipated total cost rate by simultaneously optimizing the inventory level at all the equations. The joint probability disruption of the inventory levels at retailer and the distributor 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.