Analysis of M/M/s make-to-stock queues with production start-up costs for both lost sales and backordering cases
研究了具有生产启动成本和并行生产线的生产库存系统，采用扩展双临界数策略控制，通过M/M/s队列模型分析丢单和延期交货两种情况下的系统成本，并提出了近似方法计算控制参数。
This study considers a production-inventory system with production start-up costs and parallel production lines. Production times are independent and identically distributed exponential random variables and demands are generated according to a stationary Poisson process. Production and inventory are controlled by the extended-two-critical-number policy. The system is modelled as an M/M/s make-to-stock queue and analysed for both lost sales and backordering cases. A renewal approach is developed to calculate the expected average system cost. Furthermore, an approximation is proposed to calculate the control parameters of the extended-two-critical-number policy. An extensive numerical study is conducted to illustrate the effects of changes in system parameters and the effectiveness of the proposed approximation. The analysis shows that the proposed approximation performs well across various system conditions.