Market Clearing

\[\begin{aligned} \left[\begin{aligned} q^{P \rightarrow T}_{p(n)comy} - q^{T \leftarrow P}_{t(n)ncomy} \end{aligned}\right] \geq 0 & \perp \pi^{P}_{ncomy} \geq 0 & \begin{aligned} \forall n \in \mathcal{N}, c \in \mathcal{C}, \\o \in \mathcal{O}, m \in \mathcal{M}, \\ y \in \mathcal{Y} \end{aligned} \\ \left[\begin{aligned} \pi^{T \rightarrow D}_{ncbmy} - \tilde{P}^{T \rightarrow D}_{ncbmy}\biggl( \sum_{o \in \mathcal{O}} \sum_{t \in \mathcal{T}}q^{T \rightarrow D}_{tncbomy}\biggr) \end{aligned}\right] \geq 0 & \perp \pi^{T \rightarrow D}_{ncmy} \geq 0 & \begin{aligned} \forall n \in \mathcal{N}, c \in \mathcal{C}, \\ b \in \mathcal{DSB}, m \in \mathcal{M}, \\ y \in \mathcal{Y} \end{aligned} \\ \left[\begin{aligned} \sum_{c' \in \mathcal{C} | (c,c') \in \mathcal{VT}}fi^{V}_{cc'} q^{V}_{v(n)tcc'omy} - q^{T \rightarrow V}_{tncomy} \end{aligned}\right] \geq 0 & \perp \pi^{T \rightarrow V}_{tncomy} \geq 0 & \begin{aligned} \forall t \in \mathcal{T}, n \in \mathcal{N}, \\ c \in \mathcal{C}, o \in \mathcal{O}, \\ m \in \mathcal{M}, y \in \mathcal{Y} \end{aligned} \\ \left[\begin{aligned} \sum_{c \in \mathcal{C} | (cc') \in \mathcal{VT}}q^{V }_{v(n)tcc'omy} - q^{T \leftarrow V}_{tncomy} \end{aligned}\right] \geq 0 & \perp \pi^{V \rightarrow T}_{tncomy} \geq 0 & \begin{aligned} \forall t \in \mathcal{T}, n \in \mathcal{N}, \\ c' \in \mathcal{C}, o \in \mathcal{O}, \\ m \in \mathcal{M}, y \in \mathcal{Y} \end{aligned} \\ \left[\begin{aligned} q^{A}_{acmy} - \sum_{o \in \mathcal{O}} \sum_{t \in \mathcal{T}}q^{T}_{tacomy} \end{aligned}\right] \geq 0 & \perp \pi^{A}_{acmy} \geq 0 & \begin{aligned} \forall (a,c) \in \mathcal{AC}, \\ m \in \mathcal{M}, y \in \mathcal{Y} \end{aligned} \\ \left[\begin{aligned} q^{S_{in}}_{s(n)tcomy} - q^{T \rightarrow S}_{tncomy} \end{aligned}\right] \geq 0 & \perp \pi^{T \rightarrow S}_{tncomy} \geq 0 & \begin{aligned} \forall t \in \mathcal{T}, n \in \mathcal{N}, \\ c \in \mathcal{C}, o \in \mathcal{O}, \\ m \in \mathcal{M}, y \in \mathcal{Y} \end{aligned} \\ \left[ q^{S_{out}}_{s(n)tcomy} - q^{T \leftarrow S}_{tncomy} \right] \geq 0 & \perp \pi^{S \rightarrow T}_{tncomy} \geq 0 & \begin{aligned} \forall t \in \mathcal{T}, n \in \mathcal{N}, \\ c \in \mathcal{C}, o \in \mathcal{O}, \\ m \in \mathcal{M}, y \in \mathcal{Y} \end{aligned} \end{aligned}\]