Applications of graph theory to pert critical path analysis

TL;DRAbstract

The first part of this dissertation is concerned with the study of the detailed structure of networks sometimes referred to as directed acyclic networks. A number of new properties in theorems concerning such networks have been derived and although they do not necessarily assist in the generalization of the statistical PERT algorithms, they are useful in surveying the multiplicity of networks that might be encountered and in establishing convergence proofs and other properties of the algorithms that have been developed to date. Based upon the study of the properties of PERT networks an attempt is made to develop algorithms which at least provide approximate answers for both the statistical distribution of the project competition times as well as for their expectations. The procedure developed is an adaptation of an approximate statistical PERT technique recently developed as part of this research jointly with H. O. Hartley and R. L. Sielken. In this technique the statistical PERT algor

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