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 \(\mathrm{EST}_{(1)}=0\).