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\[\begin{aligned} \max_{\substack{q^{T \rightarrow D}_{tncbomy}, \\ q^{T \leftarrow P}_{tncomy}, \\ q^{T \rightarrow V}_{tncomy}, \\ q^{T \leftarrow V}_{tncomy}, \\ q^{T \rightarrow S}_{tncomy}, \\ q^{T \leftarrow S}_{tncomy}, \\ q^{T}_{tacomy}}} \quad & \sum_{y \in \mathcal{Y}} r_{y} \sum_{m \in \mathcal{M}} d_m \sum_{o \in \mathcal{O}} \sum_{c \in \mathcal{C}} \left[ \begin{aligned} \sum_{n \in \mathcal{N}} \left( \begin{aligned} {1}^{NC}_{tnc} \cdot \sum_{b \in \mathcal{DSB}} \tilde{P}^{T \rightarrow D}_{ncbmy}\biggl(Q^{T \rightarrow D}_{ncbmy}\biggr) \cdot q^{T \rightarrow D}_{tncbomy} \\ + \left( 1 - {1}^{NC}_{tnc} \right) \cdot \sum_{b \in \mathcal{DSB}} \pi^{T \rightarrow D}_{ncbmy} \cdot q^{T \rightarrow D}_{tncbomy} \end{aligned} \right) \\ + \sum_{n \in \mathcal{N}} \left( \pi^{T \rightarrow V}_{tncomy} \right) q^{T \rightarrow V}_{tncomy} \\ - \sum_{n \in \mathcal{N}}\left( \pi^{V \rightarrow T}_{tncomy} \right) q^{T \leftarrow V}_{tncomy} \\ + \sum_{n \in \mathcal{N}}\left( \pi^{T \rightarrow S}_{tncomy} \right) q^{T \rightarrow S}_{tncomy} \\ - \sum_{n \in \mathcal{N}}\left( \pi^{S \rightarrow T}_{tncomy} \right) q^{T \leftarrow S}_{tncomy} \\ - \sum_{a \in \mathcal{A} | (a,c) \in \mathcal{AC} }\left( \pi^{A}_{acmy} \right) q^{T}_{tacomy} \\ - \sum_{n \in \mathcal{N}_p(t)}\left( \pi^{P}_{ncomy} \right) q^{T \leftarrow P}_{tncomy}\\ \end{aligned} \right] \\ \text{s.t.} &\begin{aligned} \left(\begin{aligned} \sum_{a \in \mathcal{A}_s(n) | (a,c) \in \mathcal{AC} } (1+l^{A}_{ac}) q^{T}_{tacomy} \\ + \sum_{b \in \mathcal{DSB}} q^{T \rightarrow D}_{tncbomy}\\ + q^{T \rightarrow V}_{tncomy} \\ + q^{T \rightarrow S}_{tncomy} \end{aligned}\right) \\ \leq \left(\begin{aligned} \sum_{a \in \mathcal{A}_e(n) | (a,c) \in \mathcal{AC} } q^{T}_{tacomy} \\ + \sum_{n \in \mathcal{N}_p(t)} q^{T \leftarrow P}_{tncomy} \\ + q^{T \leftarrow V}_{tncomy} \\ + q^{T \leftarrow S}_{tncomy} \end{aligned}\right) \end{aligned} & \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} \quad &(\phi^{T}_{tncomy}) \\ % & \sum_{m \in \mathcal{M}} d_{m} \sum_{b \in \mathcal{DSB}} q^{T \rightarrow D}_{tncbomy} \leq \Lambda^{T}_{tncoy} \quad & \begin{aligned} \forall n \in \mathcal{N}, c \in \mathcal{C}, \\ o \in \mathcal{O}, y \in \mathcal{Y} \end{aligned} \quad & (\lambda^{T}_{tncoy}) \\ & \begin{aligned} q^{T \rightarrow D}_{tncbomy}, q^{T \leftarrow P}_{tncomy}, q^{T \rightarrow V}_{tncomy}, \\ q^{T \leftarrow V}_{tncomy}, q^{T \rightarrow S}_{tncomy}, q^{T \leftarrow S}_{tncomy}, q^{T}_{tacomy} \end{aligned} \geq 0 \quad & & \\ \end{aligned}\]