服务员休假的库存系统的性能分析与优化

Analysis and Optimization of Inventory System with Server Vacation

研究了一个(r,Q)策略和损失销售的库存系统,其中库存为零时服务员进行多重休假.顾客到达服从泊松过程,休假时间服从指数分布,系统补货时间服从k阶Erlang分布.建立了系统的三维Markov过程,求出了系统的稳态概率分布.利用稳态分布,得到了平均库存水平、单位时间的平均订货率和平均损失率等性能指标,进而得到了系统的平均费用函数.数值分析了系统参数对最优策略和最优费用的影响.

This paper studies an inventory system with(r,Q) strategy and lost sales,in which the server takes multiple vacations when inventory is zero.Customers arrive in the system according to a Poisson process.The vacation time is an exponential distribution,and the lead time is a k-order Erlang distribution.The three dimensions Markov Process of the system is established.The steady-state probability distribution of the system is obtained.Using the steady-state distribution,some performance measures such as the average inventory level,the average order rate per unit time and the average shortage rate are obtained.Also the average cost function of the system is obtained.The effects of system parameters on the optimal policy and the optimal cost are numerically analyzed.