## 2 Background
When activities are in series, their durations are added (convoluted) to calculate the path durations. When activities are in parallel, the maximum of several path durations (distributions) has to be calculated instead. If the activity duration distributions of a schedule were sum-stable and max-stable, a distribution of the same family would result after calculating the project duration irrespective of whether the schedule mixed activities in series and parallel. Also, the parameters from such a distribution could be anticipated from the original activity duration distributions. However, as noted above, there are no sum-stable and max-stable distributions. The normal distribution is sum-stable, but not max-stable. The lognormal is product-stable, but neither sum- nor max-stable. Hence, in the absence of a distribution that can be used across a whole schedule involving activities in series and in parallel, approximate approaches must be used. Precisely with the intention of allowing project managers to make probabilistic inferences about the likely project duration, the project evaluation and review technique (PERT) was proposed over 60 years ago ([PERSON], 1997). By means of three-point activity duration estimates (the well-known optimistic, most likely, and pessimistic durations of an activity), the average project duration is assimilated to the average duration of the (longest) critical path. Then, the project duration standard deviation is also assimilated to the duration standard deviation of that same longest critical path. The problem, however, is that PERT underestimates the average project duration and overestimates the project duration standard deviation ([PERSON] and [PERSON], 1993; [PERSON], 1994). Indeed, the PERT average project duration coincides with the one from a deterministic schedule. The project duration standard deviation, on the other hand, assumes that only a single critical path exists. However, despite the limitations of PERT, it is a hugely popular technique in the field of project management. From the research standpoint, practically all its assumptions and calculation procedures were broken down and analyzed in pursuit of improvements from every possible perspective, for example, the activity duration distributions, the resulting project duration distribution, the accuracy of the three-point estimates, the inclusion of activity time-cost trade-offs, the inclusion of extra scheduling operations like minima of multiple paths, and activity self-loops, to cite just a few (see [PERSON] (1993) for an extensive review). Of particular interest, however, may be the work of [PERSON] [28]. He developed the graphical evaluation and review technique (GERT) in 1966. GERT attempted to overcome many of PERT's fundamental problems, including the merge event bias. However, due to its mathematical complexity, its implementation was not possible without resorting to Monte Carlo simulation. More recently, some of GERT's principles plus other convenient features were incorporated into M-PERT [13]. This technique was proposed by [PERSON] et al. and also allows manual calculation of the project duration average and standard deviation. Specifically, M-PERT recursively merges all project activities until there is one activity left which represents the project duration variability. For medium and big project networks, however, this technique can be come time consuming. Hence, there is one common trait among almost all these PERT extensions. Those which (partially) overcome the merge event bias problem do so at the expense of (substantially) increasing the technique complexity and/or the time it takes to calculate the project duration average and standard deviation. That is why our aim here is to resort to a number of operations very similar to the original PERT technique, but which significantly improve its accuracy by allowing multiple critical and subcritical paths.