A queueing-inventory system with random order size policy and server vacations
- PDF / 720,441 Bytes
- 26 Pages / 439.37 x 666.142 pts Page_size
- 66 Downloads / 173 Views
A queueing-inventory system with random order size policy and server vacations Yuying Zhang1 · Dequan Yue2
· Wuyi Yue3
Accepted: 3 November 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we consider a queueing-inventory system under continuous review with a random order size policy and lost sales. If the inventory is depleted after the service of a customer, a replenishment order is instantaneously triggered. The replenishment order size may be randomized according to a discrete probability distribution. Customers arrive in the system according to a Poisson process and require service from a server. The server takes multiple vacations once the inventory is depleted. The service time, the lead time, and the vacation time are all assumed to be distributed exponentially. We derive the stationary joint distribution of the queue length, the on-hand inventory level, and the status of the server in explicit product form. Furthermore, the conditional distributions of the on-hand inventory level when the server is off due to a vacation or depleted inventory, and when the server is on and working, are derived. Then, we calculate some of the system performance measures. The effect of the server’s vacation on the performance measures is investigated analytically. Finally, some numerical results are presented. The simulation study of the model in the context of more general arrival processes and service time distributions is presented. Keywords Queueing-inventory system · Multiple vacation · Lost sales · Randomized order size · Performance analysis
1 Introduction A queueing-inventory system (QIS) is a queueing system with attached inventory in which customers arrive one by one and need not only an on-hand item but also some form of time-
B
Dequan Yue [email protected] Yuying Zhang [email protected] Wuyi Yue [email protected]
1
School of Economics and Management, Yanshan University, Qinhuangdao 066004, China
2
School of Science, Yanshan University, Qinhuangdao 066004, China
3
Faculty of Intelligence and Informatics, Konan University, Kobe 658-8501, Japan
123
Annals of Operations Research
consuming service. For example, items in inventory require time for retrieval, preparation, packing, and loading (see Saffari et al. 2011). Compared to the traditional inventory system, a QIS is more general and realistic. Over the past decades, research on QIS has attracted significant research attention due to its wide-ranging applications in such fields as integrated supply chain management, vehicle maintenance and medical services (see Schwarz et al. 2006; Krishnamoorthy et al. 2016a; Arun 2010). It seems that the first contribution to QIS research was the work done by Sigman and Simchi-Levi (1992) and Melikov and Molchanov (1992) where the analyses were carried out under the assumptions of an arbitrarily distributed service time in Sigman and SimchiLevi (1992) and an exponentially distributed service time in Melikov and Molchanov (1992). Sigman and Simchi-Levi (1992) investigate
Data Loading...
