Analysis of the Queueing-Inventory System with Impatient Customers and Mixed Sales

Abstract

A queueing-inventory system with server’s vacations and impatient customers is investigated. Continuous review $\left(s,S\right)$ policy is considered for the queueing-inventory system. The server leaves for a vacation once the inventory is zero. The customer arrived waits for service with a probability $p$ or is lost forever with a probability $1-p$ when the server is off due to a vacation. Customers are impatient during period when the customer is waiting for service in the queue or when the server is off due to a vacation. The matrix geometric solution of the steady-state probability is obtained using the method of truncated approximation. Furthermore, some performance measures are obtained using the steady-state probability. Finally, the effect of system parameters on the performance measures, the optimal policy and the optimal cost are presented by numerical examples.