【摘要】 研究了一个由生产中心和分销中心组成的两阶段生产–库存排队系统，针对生产中心提出了一个新的生产策略—(rQ+m, KQ)生产策略，分销中心采取(s, Q)库存补货策略。顾客到达过程为泊松过程，补货时间、服务时间和生产时间均服从指数分布。首先，建立连续时间Markov模型，利用拟生灭过程理论，求出了系统稳态平衡条件。其次，通过求解修正系统模型的稳态概率分布，获得了系统的稳态概率分布的乘积解，进而给出了系统的稳态性能指标的计算公式。最后，以系统平均费用最小为目标，利用遗传算法计算系统的最优库存策略和平均费用。通过数值算例对系统采取的4种生产库存策略进行了比较分析，结果显示：在一定的条件下，生产中心采取(m, KQ)策略时，系统的平均费用更小。更多还原

【Abstract】 This paper studies a two-stage production-service inventory system which is composed of a production center and a distribution center. A new production strategy,(rQ+m, KQ)production strategy, is proposed for the production center. The distribution center adopts(s, Q)inventory replenishment strategy. Customers arrive according to a Poisson process, and the lead time, the service time and the production time are assumed to be exponentially distributed.Firstly, the continuous-time Markov model is established, and the steady-state condition of the system is obtained by using the theory of quasi-birth-and-death process. Secondly, by solving the steady-state probability distribution of the modified system model, some steady-state probability distribution of the system is obtained. Then formula of computing of the steady-state performance indexes of the system are given. Finally, by using genetic algorithm, the optimal inventory strategies and average cost of the system that aim to minimize the average cost of the system are calculated. The four production inventory strategies of the system are compared by numerical examples. The results show that under certain conditions, the average cost of the system is the lowest when the production center adopts the(m, KQ) strategy.更多还原