研究灰色GERT网络在多任务情况下的费用优化问题。当任务网络中流动的费用变量为时间变量的函数时，针对多个存在依赖关系的任务，运用网络中的z标记探寻各任务之间的时间依赖关系，通过对弹性活动的时间安排进行调整，在保证工期不被延误的前提行下使得整个项目的费用达到优化。以某大型客机客舱环境控制系统为例，对项目中各弹性活动的完成时间和费用进行了研究。
During a project, the period and the cost are often what the customer pays closo attertion to. For a multitask one, the ultimate completion time depends the slowest task. As a result, there is certain flexibility for those tasks that could be finished before the last one. We can make good use of the flexible time to reduce the overtime pay and equipment upgrade fee etc. so that the overall expense can be reduced. Based on the previous research, there is a certain relationship between time and expense. For multiple dependent projects, better time schedule could not only slow down the whole project but also reduce the overall expense. In this paper, this problem is addressed by GERT network. To be more specific, in the GERT network, the relationship between the progresses of each task is traced via Z-tags. The fixed time and flexible time are also defined, and the experiments of the expense are conduced involved in flexible time and fixed time respectively. When the flowing money in task network becomes a function of time, we can optimize the overall project fee can be optimized while avoiding delaying the whole project by adjusting the time schedule. Moreover, the customer content maximization (CCM) method is used to optimize the project fee. The CCM is defined as the weighted sum of expense content and risk content. At last, the project of one large passenger cabin environmental control system and work on the flexible time and expense of each task are investigated. It is found that our method is able to make full use of the flexible time of each task so as to reduce the overall project fee, which is full of practical values.
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