几何批量需求下服务台休假的库存系统稳态分析
首发时间:2023-02-03
摘要:本文研究了服务台休假下顾客需求服从几何分布的库存系统模型。在该系统中,假设顾客到达的时间间隔、顾客接受服务所用的时间、系统补货所用的时间以及系统中服务员休假的时间均服从指数分布,其中系统中库存数量为0时服务台开始单重休假。首先给出系统的状态过程,并利用拟生灭过程和矩阵几何解理论得到了系统的稳态概率分布,进一步分析了性能指标以及成本函数。最后,利用遗传算法对系统中给定的参数进行敏感性分析,从而得出不同参数下系统的最优库存策略以及对应的最优成本。本文的结论可以为实际生产管理中的库存系统提供理论依据。
关键词: 运筹学 批量需求 服务台休假 拟生灭过程 矩阵几何解 遗传算法
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Steady-state analysis of inventory system under geometric batch demand with sever vacation
Abstract: This paper studies the inventory system model with server vacation under geometric batch demand. In this system, the interval time, the service time, the replenishment time and the vacation time of the system is subject to exponential distribution. where the server takes single vacation when the number of customers in the system is zero. By using quasi-birth-and-death process and matrix geometric solution theory, the steady-state distribution of the system is obtained, and some performance indexes and cost functions of the system are measured as well. Finally, the sensitivity analysis of the system parameters is carried out by using genetic algorithm. The results of this paper apply directly in inventory management.
Keywords: Operations research;Batch demand Server vacation Quasi-birth-and-death process Matrix-geometric solution Genetic algorithm
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