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q^{\uparrow}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}

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

q^{\uparrow}C_{WS}(t) = \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot q^begin{cases} 
C^{\uparrow}_{WS}(t), & \mbox{if } q_{WS}(t) > 0 
\\ 
C^{\downarrow}_{W, iWS}(t), -& \sum_{k=1}^{N^{\uparrow}_P} C^{\uparrow}_{W,k} \cdot q^{\uparrow}_{W, k}(t)mbox{if } q_{WS}(t) > 0 
\end{cases}

q^{\uparrow}q_{WSGS}(t) = \sum_{ij=1}^{N^{\downarrow}_WG}  q^{\downarrow}_{WG, ij}(t) - \sum_{k=1}^{N^{\uparrow}_P} q^{\uparrow}_{WG, k}(t) > 0

q^{\uparrow}C_{GS}(t)= \begin{cases} 
C^{\uparrow}_{GS}(t), & \mbox{if } q_{GS}(t)  >  =0 \sum_{j=1}^{N^{\downarrow}_G}  q^
\\ 
C^{\downarrow}_{G, jGS}(t), -& \sum_{k=1}^{N^{\uparrow}_P} q^{\uparrow}_{G, kmbox{if } q_{GS}(t)  >  0 
\end{cases}