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

C^{\uparrow}_{OGW}(t) = \left[  (R_O(t) -  C^{\uparrow}_{O,p}) + (R_G(t) - C^{\uparrow}_{G,p}) \cdot  Y_{g,p}(t) \right]  \cdot (1- Y_{w,p}(t)) 
- C^{\uparrow}_{L,p} - C^{\uparrow}_{W,p} \cdot Y_{w,p}(t) 

q^{\uparrow}_{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}