Time-Cost-Quality Tradeoff Modeling based on Resource Allocation

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 \(2.0\).