## 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

A construction team consisting of sufficient crew members could improve construction quality and consume a reasonable cost, but the construction team hardly impacts on construction productivities. Therefore it is assumed that administration cost and administration quality are an approximate linear function:

$\mathrm{AC}_{(i)}=\mathrm{AC}_{i}^{\min }+\mathrm{AQK}_{i} \times\left(\mathrm{AQ}_{(i)}-\mathrm{AQ}_{i}^{\min }\right)$        (7)

where $\mathrm{AQ}_{(i)}=$ actual quality level of construction administration $(i)$ in activity $(i)$, $\mathrm{AQ}_{(i)} \in\left(\mathrm{AQ}_{i}^{\min }, \mathrm{AQ}_{i}^{\max }\right) ; \quad \mathrm{AQ}_{i}^{\min }=$ minimum quality level of construction administration $(i)$ in activity $(i) ; \mathrm{AQ}_{i}^{\max }=$ maximum quality level of construction administration $(i)$ in activity $(i) ; \mathrm{AQK}_{i}=\left(\mathrm{AC}_{i}^{\max }-\mathrm{AC}_{i}^{\min }\right) /\left(\mathrm{AQ}_{i}^{\max }-\mathrm{AQ}_{i}^{\min }\right) ;$

$\mathrm{AC}_{i}^{\min }=$ minimum cost of construction administration $(i)$ in activity $(i) ;$

$\mathrm{AC}_{i}^{\max }=$ maximum cost of construction administration $(i)$ in activity $(i) ;$

$\mathrm{AC}_{(i)}=$ actual cost of construction administration $(i)$ in activity,

$\mathrm{AC}_{(i)} \in\left(\mathrm{AC}_{i}^{\min }, \mathrm{AC}_{i}^{\max }\right) .$

Since work overtime might increase administration cost, the construction administration cost will be modified by factor $\beta_{i}$:

\begin{aligned} \mathrm{AC}_{(i)}=& {\left[\mathrm{AC}_{i}^{\min }+\mathrm{AQK}_{i} \times\left(\mathrm{AQ}_{i}-\mathrm{AQ}_{i}^{\min }\right)\right] \times \beta_{i} } \\=& {\left[\mathrm{AC}_{(i)}=\mathrm{AC}_{i}^{\min }+\mathrm{AQK}_{i} \times\left(\mathrm{AQ}_{(i)}-\mathrm{AQ}_{i}^{\min }\right)\right] } \\ & \times\left[\mathrm{ACRK}_{i}+\frac{1-\mathrm{ACRK}_{i}}{\mathrm{DPK}_{(i)}}\right], \end{aligned}   (8)

where $\beta_{i}=$ administration cost modification factor during work overtime because of extra or additional construction equipment, $\beta_{i}=\mathrm{ACRK}_{i}+\left(1-\mathrm{ACRK}_{i}\right) / \mathrm{DPK}_{(i)}$; $\mathrm{ACRK}_{i}=$ administration hourly cost rate factors in activity $(i)$ when overtime working is applicable, usually $2.0$.