Time-Cost-Quality Tradeoff Modeling based on Resource Allocation

Implementation of the PTCQTP Model

The PTCQTP model is to minimize the project overall time while conforming to the requirements of construction quality standards within a specified budget, which can be stated as follows:

$\begin{array}{ll}\min & Z_{1}=T, \\ \text { s.t. } & C \cdot X \leq A ; Q \cdot X \geq B, \end{array}$          (14)

where $A=$ the specified maximum cost; $B=$ the minimum requirements of construction quality;

$\mathrm{X}=\left[\mathrm{DPK}_{(1)} \cdots \mathrm{DPK}_{(n)} \mathrm{LQ}_{(1)} \cdots \mathrm{LQ}_{(n)} \mathrm{MQ}_{(1)} \cdots \mathrm{MQ}_{(n)} \mathrm{EQ}_{(1)} \cdots \mathrm{EQ}_{n} \mathrm{AQ}_{(1)} \cdots \mathrm{AQ}_{(n)}\right]_{1 \times 5 n}^{T}$,

a vector of all variables in the PTCQTP model.

In order to solve this comprehensive time-cost-quality tradeoff problem, a global optimization algorithm is necessary. The genetic algorithm is widely applied in optimization solution and pattern search is one of direct search methods, both methods can solve global optimization problems. Tests of different algorithms developed for this model reveal that the pattern search algorithm cannot solve this complex nonlinear programming problem by direct search which often falls into local optimization, but the genetic algorithm can find out a global optimization though solutions are not precise but acceptable.

The genetic algorithm has been widely applied in previous works of the literature; thereafter the development process of genetic algorithm for the PTCQTP model is not worthy of detailing here.