*3.2. Objective Function*

The optimization model formulation is performed in a way for keeping the level of the road performance at an acceptable level by using strategies of cost-effective maintenance. This constitutes using a multi-objective function in decision making to obtain the optimal maintenance plan.

As aforementioned, the PCR was used to evaluate the pavement condition in this study then one of the objective functions is maximizing the PCR value as shown in Equation (4). The other function is minimizing the cost to attain the optimal solution with minimum cost as possible as shown in Equation (5). In this study, the establishment of pavement maintenance strategies were constrained by the available budget for maintenance and the desired level of performance. The annual budget *Bt* constrains the objective function as in Equation (6). The Equation (7) is the constraint of the pavement performance. Only applying of one treatment is taken into account for each road section in each year as in Equation (8).

$$\mathbf{Max} \sum\_{s=1}^{S} \sum\_{j=1}^{m} PCR\_{s,t}(X\_{s,j}) \tag{4}$$

$$\mathbf{M} \text{in} \sum\_{s=1}^{S} \sum\_{j=1}^{m} \mathbb{C}(X\_{s,j}) L\_s \mathcal{W}\_S \tag{5}$$

Subjected to

$$\sum\_{s=1}^{S} \mathbb{C} \left( \mathbf{X}\_{s,j} \right) \times L\_s \times W\_s \le B\_{t\prime} \qquad \quad \forall \text{ s} = 1 \text{ to } S \tag{6}$$

$$\sum\_{s=1}^{S} \mathbb{C} \left( X\_{s,j} \right) \times L\_s \times W\_s \le B\_{t\prime} \qquad \quad \quad \quad \quad \quad \forall \, s = 1 \; \; to \; S \tag{7}$$

$$\sum\_{j=1}^{m} X\_{s,j} = 1,\qquad\qquad\qquad\forall\,s=1\text{ to }S\tag{8}$$

where, *Xs*,*<sup>j</sup>* maintenance application (option) for section *s* and treatment *j*, *C* is the cost of maintenance activity, *Ls*, and *Ws* are the length and width of the roadway section. The total maintenance cost of all sections is calculated as in (6).
