| A method for the linear polynomial (polygonal) approximation of continuous activity resource consumption (duration) distributions of stochastic project management networks is developed, derived from the spline approximations used in numerical differentiation and integration. It is the first new method for network approximation and reduction to be advanced since discretization, which was the basis for all previously developed algorithms. The method is successfully mated with three network reduction approaches--arc duplication, sequential approximation, and a heuristic for identifying the K most critical paths--to form the members of a new family of Polygonal Approximation and Reduction Techniques (PART). The development of a PART algorithm using "independent multiple arcs" (dual arcs) is the first successful implementation of an arc-duplication reduction method. Collectively, PART algorithms constitute an analytic reduction capability which is operative across the entire range of project management networks.;Algorithm validation is conducted within a design-of-experiments framework, which has not previously been employed in this context. Compared to other existing discretization-based methods, PART algorithms are demonstrated to be as accurate or more accurate in the characterization of the throughput distribution function. Accuracy is observed to be a function of network size, as driven by the number of activities much more strongly than the number of nodes, how great a challenge the activity distribution functions present to series-parallel reduction operations based on the polygonal approximation, and the number of partition classes. PART algorithms are shown to execute an order of magnitude faster than their competitors. Polygonal approximation and associated PART algorithms represent a new and innovative concept in the analytic arsenal aimed at stochastic project management networks. They have the potential to put the power of network management into the hands of anyone in possession of a desktop computing capability. In this research, they demonstrate their worthiness for continued development. |
