几何批量需求下库存系统稳态分析  

Steady-State Analysis of Inventory System Under Geometric Batch Demand

作　　者：丁凯 杨建奎[1] 范佳琦 DING Kai;YANG Jian-kui;FAN Jia-qi(School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China)

机构地区：[1]北京邮电大学理学院,北京100876

出　　处：《数学的实践与认识》2023年第2期174-182,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11971074)。

摘　　要：研究了几何批量需求下库存系统模型.假设顾客到达的时间间隔、顾客接受服务的时间、系统补货的时间以及系统中服务员休假的时间均服从指数分布,其中库存为空时服务员开始多重休假.利用拟生灭过程和矩阵几何解理论得到了系统的稳态分布,在此基础上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参数进行了敏感性分析.结果可以为实际库存管理提供理论依据。This paper studies the inventory system model under geometric batch demand.It is assumed that 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 multiple vacation when the on-hand inventory level 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.

关 键 词：批量需求 服务员休假 拟生灭过程 矩阵几何解 遗传算法 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] F274[自动化与计算机技术—控制科学与工程]