A new computational approach for project management networks

Every project, whether large or small, requires a plan, a schedule, a system of control. One method of accomplishing the required function is with an activity network — most notably PERT networks. Recent research has shown numerical approximation methods to be superior to either deterministic analysis (such as critical paths) or simulation sampling techniques in terms of accuracy and run time on comparable problems. In this paper, a new family of Polygonal Approximation and Reduction Techniques (PART) for the linear polynomial approximation of activity time probability distributions in stochastic project management networks is presented. PART is based on the development of the first new method for network approximation and reduction to be advanced since discretization, which was the basis of all previously developed numerical approximation methods. Polygonal approximation overcomes several shortcomings of the previous methods. It provides the user with a menu of available probability distributions (in addition to the beta distribution which is traditionally used) to represent individual tasks. A much smaller amount of computer storage is required to represent a project network. The central limit theorem is not used as an approximation, since the direct convolution of activity task times is calculated. In this paper, we present a description of the PART concept and the construction of PART-based network approximation and reduction algorithms. We have also constructed, though not reported here, a wide range of project management network models using a random network generator to challenge both the new and existing methods. Analysis of algorithm performance over these models has shown that PART executes an order of magnitude faster while requiring less computer memory than its competitors. This means that for the same investment of time and computer resources, larger networks may be analyzed than were previously possible.