Producer

\[\begin{aligned} \max_{\substack{q^{I}_{pibmy}, \\ q^{P \rightarrow T}_{pcomy}, \\ \Delta^{I}_{piby}, \\ \Delta^{P}_{pcoy}}} \quad & \sum_{y \in \mathcal{Y}} r_{y} \left[ \begin{aligned}\sum_{m \in \mathcal{M}} d_m \left( \begin{aligned} \sum_{o \in \mathcal{O}} \sum_{c \in \mathcal{C}} \left(\pi^{P}_{n(p)comy} - c^{P}_{pcoy} \right) q^{P \rightarrow T}_{pcomy} \\ - \sum_{i \in \mathcal{I}} \sum_{b \in \mathcal{IOB}} \left(c^{I_{l}}_{pibmy} q^{I}_{pibmy} + \frac{1}{2} c^{I_{q}}_{pibmy} \left(q^{I}_{pibmy}\right)^{2} \right) \end{aligned} \right) \\ - \sum_{i \in \mathcal{I}} \sum_{b \in \mathcal{IOB}} \frac{1}{ \| \Delta \|_{y}} c^{\Delta^{I}}_{piby} \Delta^{I}_{piby} \\ - \sum_{c \in \mathcal{C}} \sum_{o \in \mathcal{O}} \frac{1}{ \| \Delta \|_{y}} c^{\Delta P}_{pcoy} \Delta^{P}_{pcoy} \end{aligned} \right] \\ \text{s.t.} \quad & \sum_{o \in \mathcal{O}} \sum_{c \in \mathcal{C}} fi^{P}_{cio} q^{P \rightarrow T}_{pcomy} \leq \sum_{b \in \mathcal{IOB}} q^{I}_{pibmy} \quad &\begin{aligned} \forall i \in \mathcal{I}, \\ m \in \mathcal{M}, y \in \mathcal{Y} \end{aligned} \quad &(\phi^{P}_{pimy}) & \\ % & q^{I}_{pibmy} \leq av^{I}_{pibm} \left( \begin{aligned} \Lambda^{I}_{piby} \\ + \sum_{ y' \in \mathcal{Y} | (y-L^{I}_{i} \leq y' < y ) } \Delta^{I}_{piby} \end{aligned} \right) & \begin{aligned} \forall i \in \mathcal{I}, b \in \mathcal{IOB},\\ m \in \mathcal{M}, y \in \mathcal{Y} \end{aligned} \quad &( \Lambda^{I}_{piby}) & \\ % & q^{P \rightarrow T}_{pcomy} \leq \left( \begin{aligned} \Lambda^{P}_{pcoy} \\ + \sum_{ y' \in \mathcal{Y} | (y-L^{P}_{co} \leq y' < y ) } \Delta^{P}_{pcoy} \end{aligned} \right) \quad & \begin{aligned} \forall c \in \mathcal{C}, \forall o \in \mathcal{O},\\ m \in \mathcal{M}, y \in \mathcal{Y} \end{aligned} \quad &(\lambda^{P}_{pcomy}) & \\ % & \Delta^{P}_{pcoy} \leq \Omega^{P}_{pcoy} \quad &\begin{aligned} \forall c \in \mathcal{C}, \\ o \in \mathcal{O}, y \in \mathcal{Y} \end{aligned} \quad &(\omega^{P}_{pcoy}) & \\ % & \sum_{ y' \in \mathcal{Y} | (y-L^{I}_{i} \leq y' < y ) } \Delta^{I}_{piby'} \leq \Omega^{I}_{piby} \quad & \begin{aligned} \forall i \in \mathcal{I}, \\b \in \mathcal{IOB}, y \in \mathcal{Y} \end{aligned} \quad &(\omega^{I}_{piby}) & \\ % & q^{I}_{pibmy}, q^{P \rightarrow T}_{pcomy}, \Delta^{I}_{piby}, \Delta^{P}_{pcoy} \geq 0 \quad & & & \end{aligned}\]