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G = \sum_{y=1}^{N_y} \frac{AG_y}{(1+r)^y} \rightarrow \rm max

AG_y = \sum_{t=1+y_t}^{365+y_t} G_t = \sum_{t=1+y_t}^{365+y_t} 
\left( G_t^{+} - G_t^{-} \right)

G_t^{+} =  \sum_{k=1}^{N^{\uparrow}_P} \left[ R_O(t) \cdot q^{\uparrow}_{O, k}(t) + R_G(t) \cdot  q^{\uparrow}_{G, k}(t) \right] 

G_t^{-} = 
 \sum_{k=1}^{N^{\uparrow}_P} C^{\uparrow}_{L,k} \cdot q^{\uparrow}_{L, k}(t)
+\sum_{k=1}^{N^{\uparrow}_P} C^{\uparrow}_{O,k} \cdot q^{\uparrow}_{O, k} (t)
+\sum_{k=1}^{N^{\uparrow}_P} C^{\uparrow}_{G,k} \cdot q^{\uparrow}_{G, k} (t)
+\sum_{k=1}^{N^{\uparrow}_P} C^{\uparrow}_{W,k} \cdot q^{\uparrow}_{W, k}(t)
+\sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot q^{\downarrow}_{W, i}(t)
+\sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_{G,j} \cdot q^{\downarrow}_{G, j}(t)
+ C_{WS} \cdot q_{WS}(t)
+ C_{GS} \cdot q_{GS}(t)

q_{WS}(t) = \sum_{i=1}^{N^{\downarrow}_W}  q^{\downarrow}_{W, i}(t) - \sum_{k=1}^{N^{\uparrow}_P} q^{\uparrow}_{W, k}(t) 

C_{WS}(t)= \begin{cases} 
C^{\uparrow}_{WS}(t), & \mbox{if } q_{WS}(t)>0 
\\ 
C^{\downarrow}_{WS}(t), & \mbox{if } q_{WS}(t)<0 
\end{cases}

q_{GS}(t) = \sum_{j=1}^{N^{\downarrow}_G}  q^{\downarrow}_{G, j}(t) - \sum_{k=1}^{N^{\uparrow}_P} q^{\uparrow}_{G, k}(t)

C_{GS}(t)= \begin{cases} 
C^{\uparrow}_{GS}(t), & \mbox{if } q_{GS}(t) > 0 
\\ 
C^{\downarrow}_{GS}(t), & \mbox{if } q_{GS}(t) > 0 
\end{cases}