Decision Variables and Assumptions

Relationship among Equipment Productivity, Quality, and Cost

Construction equipment is a crucial factor of construction techniques to increase construction quality, to reduce cost, and to shorten time. In order to calculate construction time variation impacted by equipment, a modified factor to labor productivity caused by equipment \((i)\) is introduced:

\(\operatorname{PRD}_{(i)}=\operatorname{LPRD}_{(i)} \times \operatorname{DEK}_{(i)} \text {, }\)       (3)

where \(\operatorname{PRD}_{(i)}\) is the actual productivity in activity \((i) ; \operatorname{DEK}_{(i)}\) is a modified factor to labor \((i)\) productivity by changes of construction equipment parameters; \(\operatorname{LPRD}_{(i)}\) is labor productivity in activity \((i)\).

A better equipment quality performance will improve construction productivity, so the modified factor \(\mathrm{DEK}_{(i)}\) could be derived from the equipment quality \(\mathrm{EQ}_{(i)}\) :

\(\mathrm{DEK}_{(i)}=\mathrm{DEK}_{i}^{\min }+\mathrm{DQK}_{i} \times\left(\mathrm{EQ}_{(i)}-\mathrm{EQ}_{i}^{\min }\right)\)      (4)

where \(\mathrm{DQK}_{i}=\left(\mathrm{DEK}_{i}^{\max }-\mathrm{DEK}_{i}^{\min }\right) /\left(\mathrm{EQ}_{i}^{\max }-\mathrm{EQ}_{i}^{\min }\right) .\)

Construction equipment quality and equipment cost is also assumed as an approximate linear function just like construction material:

\(\mathrm{EC}_{(i)}=\left[\mathrm{EC}_{i}^{\min }+\mathrm{EQK}_{i} \times\left(\mathrm{EQ}_{(i)}-\mathrm{EQ}_{i}^{\min }\right)\right]\)       (5)

where \(\mathrm{EQ}_{(i)}=\) actual quality level of construction equipment \((i)\) in activity \((i)\), \(\mathrm{EQ}_{(i)} \in\left(\mathrm{EQ}_{i}^{\min }, \mathrm{EQ}_{i}^{\max }\right) ; \mathrm{EQ}_{i}^{\min }=\) minimum quality level of construction equipment (i) in activity \((i) ; \mathrm{EQ}_{i}^{\max }=\) maximum quality level of construction equipment \((i)\) in activity \((i) ; \mathrm{EQK}_{i}=\left(\mathrm{EC}_{i}^{\max }-\mathrm{EC}_{i}^{\min }\right) /\left(\mathrm{EQ}_{i}^{\max }-\mathrm{EQ}_{i}^{\min }\right) ; \mathrm{EC}_{i}^{\min }=\) minimum cost of construction equipment \((i)\) in activity \((i) ; \mathrm{EC}_{i}^{\max }=\) maximum cost of construction equipment \((i)\) in activity \((i) ; \mathrm{EC}_{(i)}=\) actual cost of construction equipment in activity (i), \(\mathrm{EC}_{(i)} \in\left(\mathrm{EC}_{i}^{\min }, \mathrm{EC}_{i}^{\max }\right)\).

Work overtime usually decreases construction productivity and increases hourly cost rate. Then construction equipment cost \(\mathrm{EC}_{(i)}\) will be modified by factor \(\alpha_{i}\) :

\(\begin{aligned} \mathrm{EC}_{(i)}=& {\left[\mathrm{EC}_{i}^{\min }+\mathrm{EQK}_{i} \times\left(\mathrm{EQ}_{(i)}-\mathrm{EQ}_{i}^{\min }\right)\right] \times \alpha_{i} } \\ =& {\left[\mathrm{EC}_{i}^{\min }+\mathrm{EQK}_{i} \times\left(\mathrm{EQ}_{(i)}-\mathrm{EQ}_{i}^{\min }\right)\right] } \\ & \times\left[1+\left(\mathrm{DPK}_{(i)}-1\right) \times \mathrm{EOK}_{i}\right], \end{aligned}\)        (6)  

where \(\alpha_{i}=\) construction equipment cost modification factor during overtime because of extra or additional construction equipment, \(\alpha_{i}=1+\left(\mathrm{DPK}_{(i)}-1\right) \times \mathrm{EOK}_{i}\); \(\mathrm{EOK}_{i}=\) productivity decreased rate during overtime per unit time (e.g., hour), normally \(20 \%\).