New Insights into the Bromilow's Time-Cost Model from Fractal Activity Networks

In a recent paper titled "Deduction of the Bromilow's time-cost model from the fractal nature of activity networks," author Alexei Vazquez presents a mathematical derivation of the Bromilow's time-cost model, which has been observed to relate the time required to execute construction projects to the cost of those projects. This relationship follows a power law scaling, expressed as $T \sim C^B$, where $T$ is the time, $C$ is the cost, and $B$ is the exponent that describes the scaling behavior.

The Bromilow's time-cost model has been validated through extensive empirical testing across various countries and project types. However, until now, there has been no theoretical framework to explain the observed algebraic scaling. Vazquez's work addresses this gap by linking the model to the fractal nature of activity networks. He identifies the Bromilow's exponent as $B = 1 - \alpha$, where $\alpha$ is a scaling exponent that relates the number of activities in the critical path of a project to the total number of activities involved.

Vazquez provides empirical data indicating that projects with lower serial/parallel (SP) percentages exhibit lower $B$ values compared to those with higher SP percentages. He concludes that the Bromilow's time-cost model is not merely an empirical observation but a law of activity networks, suggesting that the Bromilow's exponent is a characteristic property of these networks. Furthermore, he advises that forecasting project duration based on cost should be limited to projects with high SP percentages.

This research has implications for project management and planning, particularly in construction and engineering sectors, where understanding the relationship between time and cost can lead to more accurate project forecasts and better resource allocation.

For further details, the paper can be accessed at arXiv:2409.00110.