A Stochastic Inventory System with Two Types of Services and a Finite Populations

Abstract

In this article, we consider a continuous review $(s,S)$ inventory system with a service facility, wherein the demand of a customer is satisfied only after performing some service on the item which is assumed to be of random duration. We also assume that the demands are generated by a finite homogeneous population. We consider that the server provides two types of service, type 1 with probability $p_{1}$ and type 2 with probability $p_{2}$. Each arriving customer may choose either type of service. The joint probability distribution of the number of customers in the system and the inventory level is obtained in the steady state case. The measures of system performance in the steady state are derived and the total expected cost rate is also derived.