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

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...

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Bibliographic Details
Published in:An international journal of optimization and control 2022-01, Vol.12 (1), p.8-19
Main Authors: Sinem Özkan, Önder Bulut
Format: Article
Language:English
Subjects:
make-to-stock
Mühendislik
Production
production and inventory control
queueing theory
renewal theory
Online Access:Get full text
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Summary: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.
ISSN:2146-0957
2146-5703
DOI:10.11121/ijocta.2022.1034