Project duration in stochastic networks by the PERT-path technique

Market turbulence, higher innovation rates and increasing organisational complexity, are among the reasons that have made project management concepts spread to several industries. This has emphasised complexity of projects and uncertainty in estimating activity duration, resulting in a higher criticality of project scheduling. PERT-state and PERT-path techniques address the project scheduling problem, focusing on network complexity and time uncertainty. Moving from these techniques, we discuss the concept of project evolution, which is defined as the sequence of project states (path) with the dates of transition between states. After a brief analysis of the stochastic project scheduling problem, we derive the equations that put into relation the duration of the project and those of every possible PERT-path. Based on these equations, an algorithm for determining the precise project duration is developed. It requires that path data be determined, which is possible and relatively easy when project activities are characterised by stochastic independence. Should not this be the case, the approach provides an approximate estimate of the project duration.