急件冲击下关键设备生产缓冲的 GERT 模型

摘要

为了降低非预期生产急件对关键设备正常生产活动的冲击，保证生产计划的稳定性，研究了关键设备的应急生产缓冲设计问题，为生产管理者合理地确定预留产能提供了理论依据。结合排队理论，分析了生产急件到达和处理活动，证明其属于一类负指数随机过程，揭示了生产状态的动态转移规律和实现条件；将关键设备组的急件加工过程描述为一类GERT（ graphic evaluation and review technology ）模型，测算状态转移过程的状态转移参数和矩母函数；结合梅森公式，设计系统状态稳态概率的求解方法，分析关键设备生产缓冲与稳态概率之间的关系，探寻其定量化表征。通过某研究院加工中心设备组的案例研究，发现关键设备组因急件冲突导致月生产计划变更的情况平均降低14.6％，较好地控制生产计划与调度工作的不良波动，从而验证了模型和方法的可行性和适用性。%In order to reduce the negative fluctuation of unexpected urgent jobs on the normal production of critical equipment and assure the consistency of production schedule , a novel method for determining the production buffering of critical equipment in a manufacturing system containing unexpected urgent jobs is developed .The production manager can confirm the proper reserved capabilities according to the research result .Specifically , the procedures of urgent job arrival and manufacturing are discussed based on the queuing theory with a negative exponential distribution , and the transferring rules and realistic conditions are revealed.Additionally, a kind of graphic evaluation and review technology (GERT) model is utilized to describe the operation of urgent jobs in critical equipment and the transfer between adjacent nodes is studied.In doing so, the node transferring parameters and the moment generating functions are calculated . Furthermore , by the Mason rule , the probabilities of the stable states are determined to provide support for obtaining the buffering capacity of critical equipment .Finally, a group of machining centers in a research institution is used as a case study .It is shown that the average reduction of adjusted situations of monthly production plan of critical equipment group reaches to 14.6%.Thus, the fluctuation of production sched-ule can be effectively controlled and the feasibility and practicality of the proposed method are verified .