Approximate evaluation of the project completion time of stochastic activity networks

Abstract

This work describes a new method, numerically stable and computationally efficient, to evaluate the probability distribution function (PDF) of the project completion time of stochastic activity networks (SAN). It is well known that the exact evaluation of the PDF of a project completion time is an #p-complete problem. To mitigate the high computational effort associated to the PDF evaluation, we propose a method that discards, in each step of the method, those times that has a low probability associated. This allows to consider only those relevant time elements of the project. The discard procedure is made with the restriction that a pre-established maximum accumulated error is achieved. In this way the method arrives to a compromise between accuracy and speed. To the best of our knowledge, this is the first time that an approximation method with a bounded cumulated error to the PDF evaluation of a SAN is proposed.