Objective Function

Optimal welfare will be reached by maximizing the sum of producer and consumer surplus, given by the integral of the aggregate demand curve less power production costs. The objective function is therefore expressed as:

$$Obj = \sum\_{n=1}^{|H|} \sum\_{i=k\_q}^{|E|} \int\_{q=0}^{\varepsilon\_k} \mathbb{C}\_k(q) dq - \sum\_{n=1}^{|H|} \sum\_{\psi=1}^{|\Psi|} \left( o\_{\psi^i} \cdot \upsilon^i \right) - \sum\_{\psi=1}^{|\Psi|} \left( \varphi^i \right) \tag{6}$$

Subject to

$$\sum\_{i=1}^{|E|} q\_{kn} \le \sum\_{\psi=1}^{|\Psi|} o\_{\psi} \uparrow 0 \le o\_n^i \le F(n, i) \,\,\forall 0 \le o\_n^i \le \overline{o^i}$$
