Abstract
In this paper, we consider a production inventory system with service time and production vacations. Customers arrive in the system according to a Poisson process requiring service from a single server. The single production facility produces items according to an (s, S) policy, and it takes a vacation of random duration once the inventory level becomes (S. It is assumed that all arriving customers are lost during the stock out period. We first derive the stationary joint distribution of the queue length and the on-hand inventory level in product form. Then, we compute explicitly some performance measures, and develop a cost function based on these performance measures. Finally, some numerical results are presented.
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Acknowledgements
The authors sincerely thank the anonymous reviewers for their helpful comments that improved the quality of the paper. This work was supported in part by the Natural Science Foundation of Hebei Province, China (No. A2017203078).
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Dequan Yue is a professor of Department of Statistics, School of Science at Yanshan University, Qinhuangdao, China. He received his Ph. D in operations research and cybernetics from the Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China. His main research areas include queueing theory, inventory control, production management, and stochastic order and its applications. He has published more than 60 papers in journals including Naval Research Logistics, Operations Research Letters, Computer Communications, Applied Mathematical Modelling, Journal of Industrial and Management Optimization, Optimization and Engineering, and other journals.
Yaling Qin is a Ph.D candidate of School of Economics and Management at Yanshan University, Qinhuangdao, China. She received her BS degree in statistics from Yanshan University in 2003, and her MS degree in computational mathematics from Yanshan University in 2005. Her major research interests include queuing theory, and systems reliability analysis.
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Yue, D., Qin, Y. A Production Inventory System with Service Time and Production Vacations. J. Syst. Sci. Syst. Eng. 28, 168–180 (2019). https://doi.org/10.1007/s11518-018-5402-8
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DOI: https://doi.org/10.1007/s11518-018-5402-8