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

Abstract

We consider a make-to-stock environment with a single production unit that\rcorresponds to a single machine or a line. Production and hence inventory are\rcontrolled by the two-critical-number policy. Production times are independent\rand identically distributed general random variables and demands are generated\raccording to a stationary Poisson process. We model this production-inventory\rsystem as an M/G/1 make-to-stock queue. The main contribution of the study is to\rextend the control of make-to-stock literature by considering general production\rtimes lost sales and fixed production costs at the same time. We characterize the\rlong-run behaviour of the system and also propose a simple but very effective\rapproximation to calculate the control parameters of the two-critical-number\rpolicy. An extensive numerical study exhibits the effects of the production time\rdistribution and the system parameters on the policy control levels and average\rsystem cost.