A study of approximating the moments of the job completion time in PERT networks
提出一种考虑路径依赖性的PERT网络工作完成时间近似方法，利用顺序统计量和关键路径概念，通过混合分布更准确地估计完成时间，对项目规划和投标有实用价值。
Abstract The importance of proper management of projects has not gone unrecognized in industry and academia. Consequently, tools like the Critical Path Method (CPM) and the Program Evaluation Review Technique (PERT) for project planning have been the focus of attention of both practitioners and researchers. Determination of the Time to Complete the Job (TCJ) in PERT networks is important for planning and bidding purposes. The complexity involved in accurately determining the TCJ has led to the development of many approximating procedures. Most of them ignore the dependence between paths in the network. We propose an approximation to determine the TCJ which explicitly recognizes this dependency. Dependency in networks arises due to commonality of activities among various paths in the network. We develop an approximation which is simple to use and makes use of readily available tables. Also, the approximation employs the traditional concept of the critical path which is easy to understand and to operationalize. The activities on the critical paths are divided into an independent portion and a dependent portion. The dependent portion comprises activities common to various critical paths. Order statistics are used in computing the time for the dependent portion of the critical path. We present the theoretical underpinnings of our approach and illustrate its application via an example. In the absence of other measures, we use simulation results as a proxy for the TCJ and as a benchmark to measure the accuracy of our approximation. Empirical results are obtained for a variety of networks in the literature. We show that the distribution of the TCJ is better approximated by a mixture of distributions. Comparison with other approaches from the literature indicates that our approximation yields estimates for the TCJ which are closer to the simulation results.