https://doi.org/10.1140/epjb/s10051-024-00676-6
Regular Article - Statistical and Nonlinear Physics
Emerge of scaling in project schedules
Nodes & Links Ltd, Salisbury House, Station Road, Cambridge, CB1 2LA, UK
Received:
4
January
2024
Accepted:
15
March
2024
Published online:
9
April
2024
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 , where
and
are shape and scale parameters. Furthermore, if activity delays follow a lognormal distribution, as the empirical data suggests, then
and
, where N is the number of activities,
, the maximum activity duration in units of days and
, the power law exponent of the activity duration distribution. These results offer new insights about project schedules, reference class forecasting and delay risk analysis.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.