Abstract: 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.

Key words: project management, multi-tasking, grey GERT network, optimization of the costs, maximum satisfaction