Analysis of make-to-stock queues with general processing times and start-up and lost sales costs
DOI:
https://doi.org/10.11121/ijocta.2022.1034Keywords:
Production, make-to-stock, production and inventory control, queueing theory, renewal theoryAbstract
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.Downloads
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