Deduction of the Bromilow's time-cost model from the fractal nature of activity networks
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914931620708352 |
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| author | Vazquez, Alexei |
| author_facet | Vazquez, Alexei |
| contents | In 1969 Bromilow observed that the time $T$ to execute a construction project follows a power law scaling with the project cost $C$, $T\sim C^B$ [Bromilow 1969]. While the Bromilow's time-cost model has been extensively tested using data for different countries and project types, there is no theoretical explanation for the algebraic scaling. Here I mathematically deduce the Bromilow's time-cost model from the fractal nature of activity networks. The Bromislow's exponent is $B=1-α$, where $1-α$ is the scaling exponent between the number of activities in the critical path $L$ and the number of activities $N$, $L\sim N^{1-α}$ with $0\leqα<1$ [Vazquez et al 2023]. I provide empirical data showing that projects with low serial/parallel (SP)% have lower $B$ values than those with higher SP%. I conclude that the Bromilow's time-cost model is a law of activity networks, the Bromilow's exponent is a network property and forecasting project duration from cost should be limited to projects with high SP%. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_00110 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deduction of the Bromilow's time-cost model from the fractal nature of activity networks Vazquez, Alexei Physics and Society Social and Information Networks In 1969 Bromilow observed that the time $T$ to execute a construction project follows a power law scaling with the project cost $C$, $T\sim C^B$ [Bromilow 1969]. While the Bromilow's time-cost model has been extensively tested using data for different countries and project types, there is no theoretical explanation for the algebraic scaling. Here I mathematically deduce the Bromilow's time-cost model from the fractal nature of activity networks. The Bromislow's exponent is $B=1-α$, where $1-α$ is the scaling exponent between the number of activities in the critical path $L$ and the number of activities $N$, $L\sim N^{1-α}$ with $0\leqα<1$ [Vazquez et al 2023]. I provide empirical data showing that projects with low serial/parallel (SP)% have lower $B$ values than those with higher SP%. I conclude that the Bromilow's time-cost model is a law of activity networks, the Bromilow's exponent is a network property and forecasting project duration from cost should be limited to projects with high SP%. |
| title | Deduction of the Bromilow's time-cost model from the fractal nature of activity networks |
| topic | Physics and Society Social and Information Networks |
| url | https://arxiv.org/abs/2409.00110 |