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

## Decision Variables and Assumptions

### Relationship between Material Quality and Material Cost

The time of a construction activity is mainly determined by its job quantities and productivities rather than its material or machine quality, and the material can hardly interfere with the activity's time, either. Thereafter an approximate linear relationship between material quality and material cost is determined.

The relationship between quality and quality cost for a manufacturing company

$\mathrm{MC}_{(i)}=\mathrm{MC}_{i}^{\mathrm{min}}+\mathrm{MQK}_{i} \times\left(\mathrm{MQ}_{(i)}-\mathrm{MQ}_{i}^{\mathrm{min}}\right)$          (2)

where $\mathrm{MQ}_{(i)}=$ actual quality level of construction material in activity (i), $\mathrm{MQ}_{(i)} \in\left(\mathrm{MQ}_{i}^{\min }, \mathrm{MQ}_{i}^{\max }\right) ; \mathrm{MQ}_{i}^{\min }=$ minimum quality level of construction material in activity $(i) ; \mathrm{MQ}_{i}^{\max }=$ maximum quality level of construction material in activity $(i)$; $\mathrm{MQK}_{i}=\left(\mathrm{MC}_{i}^{\max }-\mathrm{MC}_{i}^{\min }\right) /\left(\mathrm{MQ}_{i}^{\max }-\mathrm{MQ}_{i}^{\min }\right) ; \quad \mathrm{MC}_{i}^{\min }=\operatorname{minimum} \quad$ cost of construction material in activity $(i) ; \mathrm{MC}_{i}^{\max }=$ maximum cost of construction material in activity $(i) ; \mathrm{MC}_{(i)}=a$ $\mathrm{MC}_{(i)} \in\left(\mathrm{MC}_{i}^{\min }, \mathrm{MC}_{i}^{\max }\right)$