## 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

#### Relationship between Labor Productivity and Labor Quality

Assign a construction team to excavate earth, to erect formwork, to mix concrete, or to do other jobs; their working quality will decline if they intend to increase productivity, and an approximate linear relationship between labor productivity and labor quality is observed here. A more complex relationship function between labor productivity and labor quality is also considered in later case study:

$\mathrm{LPRD}_{(i)}=\mathrm{LPRD}_{i}^{\max }-\mathrm{LQK}_{i} \times\left(\mathrm{LQ}_{(i)}-\mathrm{LQ}_{i}^{\min }\right),$           (1)

where $L Q_{(i)}=$ actual quality level of construction labor $(i)$ working in activity $(i)$, $\mathrm{LQ}_{(i)} \in\left(\mathrm{LQ}_{i}^{\min }, \mathrm{LQ}_{i}^{\max }\right) ; \mathrm{LQ}_{i}^{\max }=$ maximum quality level of construction labor $(i)$ working in activity $(i) ; \quad \mathrm{LQK}_{i}=\left(\mathrm{LPRD}_{i}^{\max }-\mathrm{LPRD}_{i}^{\min }\right) /\left(\mathrm{LQ}_{i}^{\max }-\mathrm{LQ}_{i}^{\min }\right)$; LPRD $_{i}^{\min }=$ minimum productivity level of construction labor $(i)$ working in activity (i); LPRD $_{i}^{\max }=$ maximum productivity level of construction labor (i) working in activity $(i)$; LPRD $_{(i)}=$ actual productivity level of construction labor $(i)$ working in activity $(i), \operatorname{LPRD}_{(i)} \in\left(\operatorname{LPRD}_{i}^{\min }, \operatorname{LPRD}_{i}^{\max }\right)$.