研究了具有顾客批量需求、损失销售和服务员多重工作休假的 $M/M$/1 排队库存系统，其中库存为零时服务员进行多重工作休假。顾客到达服从 Poisson 过程，服务员服务时间、补货时间和工作休假时间均服从指数分布，顾客需求批量服从一般分布。利用拟生灭过程和矩阵几何解法，求出了系统稳态条件和稳态概率分布，进而得到了系统的稳态性能指标的计算公式。基于性能指标建立了系统的长期平均费用函数，通过数值算例分析了系统的最优库存策略和最优费用。

In this paper, we study a continuous review $M/M/1$ queueing-inventory system with customer batch demand, lost sales and multiple working vacations, where the server takes multiple working vacations when the inventory is zero. Customers arrive according to a Poisson process. The service time, the lead time and the working vacation time are assumed to follow exponential distributions, and the batch size of demands is assumed to follow a general distribution. The steady-state condition and the steady-state probability distribution of the system are derived by using quasi-birth-and-death process and matrix geometry solution method, and then the computational formulae for the steady-state performance indicators of the system are obtained. The long-term average cost function of the system is established based on the performance measures, and the optimal inventory strategy and the optimal cost of the system are analyzed by numerical examples.