Time-Cost-Quality Tradeoff Modeling based on Resource Allocation

Decision Variables and Assumptions

Calculating Labor Cost and Activity Time

When labors are working together as a construction crew in a construction activity \((i)\), their working duration is the time of the construction activity, which could be estimated by the construction quantities (QNT) and the actual productivity, overtime factors:

\( \operatorname{DUR}_{(i)}=\frac{\mathrm{QNT}_{(i)}}{\operatorname{PRD}_{(i)} \times \mathrm{DPK}_{(i)}}, \)           (9)

where \(\mathrm{DUR}_{(i)}=\) duration (time) of construction activity \((i) ; \mathrm{QNT}_{(i)}=\) quantities of construction activity \((i) ; \quad \mathrm{PRD}_{(i)}=\) actual \(\quad\) productivity in activity \(\quad(i)\); \(\mathrm{DPK}_{(i)}=\) overtime factors if accelerated construction speed is desired, \(\mathrm{DPK}_{(i)} \in[1.0,1.5]\) when overtime varies from 0 to 4 hours per day since standard working time is eight hours per day. DPK \(_{(i)}=1.0\) means no overtime work assigned.

Labor cost in construction activity \((i)\) would be determined by standard daily cost and overtime work cost [18]. It is assumed that work overtime is paid in an hourly cost rate comparing with standard labor cost:

\(\begin{aligned} \mathrm{LC}_{(i)}=& \mathrm{LCD}_{i}^{S} \times \mathrm{DUR}_{(i)}+\left(\mathrm{DPK}_{(i)}-1\right) \\ & \times\left(\mathrm{LCRK}_{(i)} \times \mathrm{LCD}_{i}^{S}\right) \times \mathrm{DUR}_{(i)} \\=& \mathrm{LCD}_{i}^{S} \times \mathrm{DUR}_{(i)} \times\left[1+\left(\mathrm{DPK}_{(i)}-1\right) \times \mathrm{LCRK}_{(i)}\right] \\=&\left(\mathrm{LCD}_{i}^{S} \times \mathrm{QNT}_{(i)}\right) \\ & \times\left(\left[\mathrm{LPRD}_{i}^{\max }-\mathrm{LQK}_{i} \times\left(\mathrm{LQ}_{(i)}-\mathrm{LQ}_{i}^{\min }\right)\right]\right.\\ &\left.\times\left[\mathrm{DEK}_{i}^{\min }+\mathrm{DQK}_{i} \times\left(\mathrm{EQ}_{(i)}-\mathrm{EQ}_{i}^{\min }\right)\right]\right)^{-1} \\ & \times\left(\mathrm{LCRK}_{i}+\frac{1-\mathrm{LCRK}_{i}}{\mathrm{DPK}_{(i)}}\right) \end{aligned}\)         (10)

where \(\mathrm{LC}_{(i)}=\) labor cost in construction activity \((i) ; \mathrm{LCD}_{i}^{s}=\) standard labor cost per unit time (e.g., day) in construction activity \((i) ; \mathrm{LCRK}_{i}=\) labor cost rate factors in activity \((i)\) when overtime work is applicable, usually \(2.0.\)