A Modified Lost Sales Inventory System with Two Types of Customers

Abstract

In this work, we consider a continuous review ( 5, S ) inventory system in which the arriving customers belong to any one of two types such that the type-1 customer would be willing to wait for delivery of the demanded item and the type-2 customers would not be willing to do so. When the stock is more than s, the customers are not distinguished as to their type and their demanded items are delivered immediately to them. Once the inventory level drops to s ( > 0), an order for Q (= S - s ) items is placed and thereafter the demand of type-2 customers alone are satisfied. The type-1 customers are asked to wait until the ordered items are received. The maximum number of type-1 customers allowed to wait is fixed as M( < Q - s ). The arrivals of both types of customers are assumed to follow a Markovian arrival process (MAP) and the lead time has exponential distribution. The life time of each item is assumed to have exponential distribution. Further we assume that the demand, the lead time and the life time of each items are mutually independent. The limiting distribution of inventory level is computed and the measures of system performance in the steady state are derived. The results are illustrated numerically.