Analysis of make-to-stock queues with general processing times and start-up and lost sales costs
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Published:2021-10-24
Issue:1
Volume:12
Page:8-19
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ISSN:2146-5703
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Container-title:An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
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language:
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Short-container-title:Int. J. Optim. Control, Theor. Appl. (IJOCTA)
Author:
Sinem Özkan ORCID,
Önder Bulut ORCID
Abstract
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 and the system parameters on the policy control levels and average system cost.
Publisher
International Journal of Optimization and Control: Theories and Applications
Subject
Applied Mathematics,Control and Optimization