  A project schedule contains a network of activities, the activity durations,
the early and late finish dates for each activity, and the associated total
float or slack times, the difference between the late and early dates. Here I
show that the distribution of activity durations and total floats of
construction project schedules exhibit a power law scaling. The power law
scaling of the activity durations is explained by a historical process of
specialization fragmenting old activities into new activities with shorter
duration. In contrast, the power law scaling of the total floats distribution
across activities is determined by the activity network. I demonstrate that the
power law scaling of the activity duration distribution is essential to obtain
a good estimate of the project delay distribution, while the actual total float
distribution is less relevant. Finally, using extreme value theory and scaling
arguments, I provide a mathematical proof for reference class forecasting for
the project delay distribution. The project delay cumulative distribution
function is $G(z) = \exp( - (z_c/z)^{1/s})$, where $s>0$ and $z_c>0$ are shape
and scale parameters. Furthermore, if activity delays follow a lognormal
distribution, as the empirical data suggests, then $s=1$ and $z_c \sim
N^{0.20}d_{\max}^{1+0.20(1-\gamma_d)}$, where $N$ is the number of activities,
$d_{\max}$ the maximum activity duration in units of days and $\gamma_d$ the
power law exponent of the activity duration distribution. These results offer
new insights about project schedules, reference class forecasting and delay
risk analysis.
