Decision Variables and Assumptions

Relationship between Construction Administration Quality and Administration Cost

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.