Abstract
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.
Graphic abstract
A process of activities duration fragmentation explains the emergence of scaling in the activities duration distribution.
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Data Availability
The projects in the Nodes & Links contain sensitive information about the associated sources. While we can release statistics and analyses about that data, we are not authorized to release the raw schedule data. The code for the duplication-split model is available at github.com/av2atgh/red.
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Acknowledgements
I thank the data science team at Nodes & Links, in particular Hidayet Zaimaga and Georgios Kalogridis, for the generation of the construction project schedules database.
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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Nodes & Links Ltd provided support in the form of salary for A.V., but did not have any additional role in the conceptualization of the study, analysis, decision to publish, or preparation of the manuscript.
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Vazquez, A. Emerge of scaling in project schedules. Eur. Phys. J. B 97, 44 (2024). https://doi.org/10.1140/epjb/s10051-024-00676-6
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DOI: https://doi.org/10.1140/epjb/s10051-024-00676-6