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本文研究具有复杂装配结构的爱尔朗型按订单装配(ATO)系统的组件生产与库存优化控制问题。系统涉及多种组件,一个最终产品和多类客户需求。在此系统中,各种组件的生产时间服从爱尔朗分布,各类客户的需求为泊松到达过程。针对不同客户需求类型:产品需求与独立组件需求且同为销售损失型,建立基于马尔可夫决策过程(MDP)的平均总成本模型,应用动态规划方法求解最优策略。仿真模拟方法实现最优策略,并通过数值实验分析多生产阶段和系统参数对最优策略的影响。研究结果表明,爱尔朗型生产时间ATO系统的最优策略为状态依赖型策略,即组件的生产与库存分配由动态基础库存水平值和动态库存配给水平值控制。对于任一组件,其基础库存水平值和库存配给水平值均随着生产阶段的增加而降低,且生产阶段对基础库存水平值和平均总成本的影响较显著。
This paper studies the problem of component manufacturing and inventory optimization of Erlang ATO system with complex assembly structure. The system involves a wide range of components, a final product and multiple customer needs. In this system, the production time of various components follows the Erlang distribution, and the demand of various customers is Poisson arrival process. According to different types of customer requirements: the demand of products and the demand of independent components, and the same sales loss model, an average total cost model based on Markov decision process (MDP) is established, and the optimal strategy is solved by using dynamic programming. The simulation method is used to realize the optimal strategy. The influence of multi-stage and system parameters on the optimal strategy is analyzed through numerical experiments. The results show that the optimal strategy of ATL system for Erlang production time is state-dependent strategy, that is, the production and inventory allocation of components are controlled by the dynamic basic inventory level and the dynamic inventory allocation level. For any component, the basic stock level and the stock ration level both decrease with the increase of the production stage, and the production stage has a significant impact on the basic stock level value and the average total cost.