本文引入了一种新的休假策略, 研究在该策略下带有损失销售和(s, S)库存策略的排队库存系统。当库存为空时, 服务员开始工作休假, 工作休假期间, 若补货成功, 服务员立刻开始正常服务顾客; 当工作休假结束时, 若库存仍为空, 服务员开始多重休假过程, 否则转为正常工作状态。利用马尔可夫过程方法对此系统进行稳态分析, 得到该策略下排队库存系统的稳态分布, 进而获得系统的一些稳态性能指标以及系统的平均费用函数。通过数值分析研究系统参数对最优策略和最优费用的影响。

In this paper, we introduce a new vacation strategy. We consider an queueing-inventory system with lost sales and (s, S) strategy under the vacation strategy. When inventory level is zero, the server goes to a working vacation in which if the replenishment is successful, the server immediately begins to serve the customer normally. When the working vacation is over, if the inventory level is still zero, the server will take multiple vacations, otherwise he/she will return to the normal working state. We analyze the stationary distributions of the queueing-inventory system under the vacation strategy by using Markov process method. On this basis, some performance indices and average cost function are obtained. Finally, the optimal inventory policy and the optimal expected cost are also discussed by numerical examples.