Analysis of make-to-stock queues with general processing times and start-up and lost sales costs




Production, make-to-stock, production and inventory control, queueing theory, renewal theory


We consider a make-to-stock environment with a single production unit that corresponds to a single machine or a line. Production and hence inventory are controlled by the two-critical-number policy. Production times are independent and identically distributed general random variables and demands are generated according to a stationary Poisson process. We model this production-inventory system as an M/G/1 make-to-stock queue. The main contribution of the study is to extend the control of make-to-stock literature by considering general production times, lost sales and fixed production costs at the same time. We characterize the long-run behaviour of the system and also propose a simple but very effective approximation to calculate the control parameters of the two-critical-number policy. An extensive numerical study exhibits the effects of the production time distribution, start-up cost and traffic intensity on the optimal policy parameters and system cost.


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Author Biographies

Sinem Özkan, Department of Industrial Engineering, Yaşar University, Turkey

Sinem Özkan received her MSc degree from the Industrial Engineering Department of Yaşar University in 2016. She has been continuing her PhD studies in the same department since 2016. Her research interests include production/inventory systems and stochastic modeling.

Önder Bulut, Department of Industrial Engineering, Yaşar University, Turkey

Önder Bulut is Assistant Professor in the Department of Industrial Engineering at Yaşar University. He received his Ph.D. degree from the Industrial Engineering Department of Bilkent University. His research interests include stochastic modeling, production and inventory systems, simulation, dynamic programming and optimal control.


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How to Cite

Özkan, S., & Bulut, Önder. (2021). Analysis of make-to-stock queues with general processing times and start-up and lost sales costs. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 12(1), 8–19.



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