## Time-Cost-Quality Tradeoff Modeling based on Resource Allocation

Read this article. The paper presents an optimization model that enables managers to effectively evaluate trade-offs related to time, cost, and other competing priorities. Pay particular attention to Section 6 as it provides an illustrated example of building a home.

### 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 $2.0.$