具有Erlang分布供应提前期的服务—库存系统最优控制策略  

Optimal control strategy of service-inventory system with Erlang distributed lead time

作　　者：狄俊珂 龚红仿 孙中宇 DI Jun-ke;GONG Hong-fang;SUN Zhong-yu(School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114,China)

机构地区：[1]长沙理工大学数学与统计学院

出　　处：《长沙理工大学学报（自然科学版）》2019年第3期90-98,共9页Journal of Changsha University of Science and Technology:Natural Science

基　　金：湖南省教育厅重点项目(18A145);国家自然科学基金资助项目(61972055)

摘　　要：研究一个具有(r,Q)补货策略的服务-库存系统。考虑将具有Erlang分布的供应提前期的服务-库存系统建模为M/M/1排队系统。根据M/M/1队列的平稳分布,推导出作为系统利润控制的稳态性能指标,并构建系统平均利润函数。以最大化系统利润为目标,构建系统可满足率和服务可靠性水平约束的优化控制模型,导出服务-库存系统最优控制策略。通过证明利润函数的凸性,用遗传算法求解了该约束优化模型,获得了利润函数的唯一最大值以及决策变量r和Q的最优值。数值实验分析了系统性能的灵敏度,表明了具有Erlang分布的供应提前期的最优控制策略能提高系统的利润。This paper studies a service-inventory system with(r, Q) replenishment strategy,considering modeling a service-inventory system with Erlang distribution lead time as an M/M/1 queuing system.According to the stationary distribution of M/M/1 queue, the steady-state performance index for system profit control is derived, and the system average profit function is constructed.Aiming at maximizing system profit,we construct the optimal control model of system with satisfaction rate and service reliability level constraintting, and seek for the optimal control strategy of service-inventory system.By proving the convexity of profit function, the constrained optimization model is solved by genetic algorithm, and the unique maximum value of profit function and the optimal value of decision variables r and Q are obtained.The sensitivity of the system performance is analyzed by numerical experiments, which show that the optimal control strategy with Erlang distribution can improve the profit of the system.

关 键 词：服务-库存系统 ERLANG分布 供应提前期 长期平均利润函数 排队系统 

分 类 号：O29[理学—应用数学]