Study on the Dependence of Duration in Project Scheduling Networks
|Keywords||Project Management Schedule Plan update Working hours Dependencies Bayesian network Copula function|
Working hours between variables of different processes in the practice of project management, there are very common dependencies, various objective factors and human control are possible sources of working hours variable dependent. Currently, the increasingly high demand for project management, more and more demanding requirements for control of the progress of the project. Consider the dependencies between the working hours variables in the actual progress of the project management, reasonable, and fully estimate the uncertainty of the duration plan more accurately predict and assess duration risk, dynamically updated on the schedule, in order to more effectively control the progress of the project. This paper aims at the investigation and analysis of the dependencies between the working hours variable constructed to describe the dependency structure between working hours variable graphical model, establish a reasonable measurement indicator system dependencies, and study the duration of the problem and the progress of the plan in the case of working hours dependent dynamic updates. The main contents include the following aspects: First, a review of the basic structure of the classic CPM / PERT network planning model and working hours randomness, the assumption of independence of their working hours variables. Then investigation through multiple actual projects, dependency indicators of project man-hours data for statistical analysis, the results show that the presence of a strong working hours dependencies between the parallel process of investigation, serial process. Survey content and expert questionnaire and the analysis of the main reason lies in working hours dependencies generated by common factors and the organization and control of the project, and working hours dependencies system classification. Second, by two directed acyclic graph model - AON network planning and Bayesian network analysis, as the background layer to the AON network plan, consider working hours variable sequence between dependency and parallel dependency establish reasonable The model structure of the Bayesian network dependencies between the description of working hours variable Programme (BNP), discussed the the BNP model Figure separated conditions independent nature. Further, the method for determining the probability distribution of the BNP in the model work hours variable, to study the conditions for the determination of the probability variables, the model parameters and lack of value data reduction parameter learning method. Copula function fine nature, based on analysis of the strengths and weaknesses of the linear correlation coefficient in working hours dependency measure, establish metrics based on the the Copula function of working hours dependencies and dependency indicators in estimates for specific projects. In addition, the analysis used Copula function describes the nature and mode of working hours dependencies, mixed Copula function to describe the dependencies between the the various dependencies mode working hours variable. Fourth, the Monte Carlo simulation is applied to the duration of working hours dependent simulation of the basic steps. Combined with the previous theoretical models and metrics dependencies, working hours variable dependent random number generation, and the probability distribution determined, the the BNP network construction period, the probability of completion and process criticality analog simulation of a simple example demonstrates process, and a comparative analysis with other model calculations. Fifth, the combination of Bayes' theorem and Bayesian network inference principle, a the BNP model in working hours variable dynamically updated. Variable for the discrete case, given the variable elimination algorithm the group tree propagation algorithm and Markov chain Monte Carlo algorithm; variables as continuous or mixed case studied continuous BNP model mixed BNP model in working hours variable dynamic update method, and gives the example of calculation. Finally, the application of research results in the actual progress of the project management framework, introduced to consider the working hours the dependency progress of the project planning and dynamic update methods and processes, and analysis to a project, for example. The results show that the method of this study can be a more reasonable estimate of the uncertainty of the schedule, and can be dynamically updated on the progress of the plan according to the dependencies between the working hours, in practice there is a wide range of application prospects and better value.