Modeling And Analysis Of Multi Parameter Limited State In The Gray GERT Network

With the development of modern social productivity, project management has been paid more and more attention, and a group of representativ project management tools, such as Gantt chart, CPM, PERT, GERT etc. has emerged as the times require.As an effective project management tool, the scope of application of the classical GERT network has covered many fields modeling, including product development management, the management of product quality, reliability evaluation, production capacity evaluation, resource allocation, policy design system analysis and so on.However, in real life, except for probabilistic uncertainty, there still exist many problems of non probabilistic uncertainty. For these kinds of random networks, the classical GERT network is no longer applicable. In order to characterize the project more practical, we need to introduce the uncertainty information of the parameter and limited information to the network, and also fully consider the situation that the multi parameters restraint mutually of the network. We constructing a new model of GERT network, which further expand the theory value and application value of the GERT network.This paper systematically studied the related theory and the properties of the limited state in the gray GERT network, and discussed the situation of the single parameter, the independent multi parameters, the related multi parameters and related multi parameters of multi tasks of the grey GERT. The main research contents of this paper are as follows:(1)This paper firstly introduces the grey single parameter into GERT network, which solves the problem of incomplete information parameter characterization.It characterizes the limited information through customer’s satisfaction, and establishes an optimization model on the maximization of customer’s satisfaction.Through the optimization model, we get the exact value of the solution.(2)This part discussed the algorithm of independent multi parameters of the gray GERT network. According to the multiple constrained conditions, we constructed the weighted customer satisfaction, and established an optimization model on the maximization of customer’s satisfaction.(3)Considering the correlation of each parameter in project implementation, we discussed the algorithm of related multi parameters of the gray GERT network. Based on the function relation between the parameters, we derived the distribution of independent variables by means of a strain distribution. At last, we established an optimization model on the maximization of customer’s satisfaction.(4) When the parameter of network flow task is time parameter’s variable, we considered a situation that there is a plurality of grey GERT tasks. By the application of Z tags, we explored the time dependence of various tasks, so that we can combie the Grey GERT network with the Gantt chart. By adjustments of task activities, we can achieve the optimization of the whole project.