Time-Cost-Quality Tradeoff Modeling based on Resource Allocation

The overall time $T$ of a construction project can be easily calculated by nodes as activities in an acyclic digraph network:

$T=\max _{i=1, n}\left(\mathrm{EST}_{(i)}+\operatorname{Dur}_{(i)}\right),$           (3)

where $T=$ overall time in construction project, $\operatorname{EST}_{(i)}=\max _{h=1, i-1}\left(\operatorname{EST}_{(h)}+\operatorname{Dur}_{(h)}\right)$, as well as the earliest starting time of activity $(i)$ derived by its predecessors, and the first $\mathrm{EST}_{(1)}=0$.