\begin{align}
\text { s. t. } & C_{\max } \geq 0, C_{\max } \geq C_{i}, \forall i \in[N] ; \\
& C_{i} \geq J T_{i n_{i}}+q_{i} \ell_{i} \sum_{m \in \mu_{i n_{i}}} p_{i m} A_{n_{i} m}^{i}, \forall i \in[N] ; \\
& J T_{i(j+1)} \geq J T_{i j}+q_{i} \ell_{i} \sum_{m \in \mu_{i j}} p_{i m} A_{j m}^{i}+T_{c}, \forall j \in\left[n_{i}-1\right], \forall i \\
& C_{i} \leq D_{i}, \forall i \in[N] ; \\
& J T_{h m} \geq J T_{i m}+q_{i} \ell_{i} p_{i m}+s_{i h m}-\tilde{M}\left(1-X_{i h}^{m}\right), \forall i, h \in \delta_{m} ; \\
& J T_{i m} \geq s_{0 i m}-\tilde{M} \sum_{h \in \delta} X_{h i}^{m}, \forall i \in \delta_{m} ; \\
& B_{i m}=\sum_{j} A_{j m}^{i}, \forall m \in[M], \forall i \in[N]
\end{align}