Calculating Project Completion in Polynomial Processing Time

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Technology-based organizations and knowledge organizations rely on large activity networks to manage Research & Development (R&D) projects. Avoiding optimistic completion times due to the characteristic Program Evaluation and Review Technique (PERT) assumptions is a problem that can grow exponentially in complexity with the number of activities. A recursive technique that solves the problem in a polynomial number of steps has been developed, assuming that all duration times follow beta distributions. It is important to notice that the only two 100% valid approaches to calculate the project completion time are simulation and the stochastic sum for each and every path in the network. Nevertheless, both require finding the shape parameters, and that is precisely the main contribution of this paper: a system of equations to calculate the shape parameters of each activity and the overall project.
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