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\[ \begin{aligned} \min \quad & \sum_{P \in S} c_P \cdot y_P + \sum_{(u,v) \in \hat A} M \cdot z_{uv}& \\ \text{s.t.} \quad & z_{uv} + \sum_{P \in S, (u, v) \in P} y_P \geq 1 &\quad \forall (u,v) \in \hat{A} \\ & -x_{uv} + \sum_{P \in S, (u, v) \in P} y_P = 0 &\quad \forall (u,v) \in A \\ & \sum_{P \in S} x_p \leq k \\ & y_{P} \geq 0 &\quad \forall P \in S \\ & z_{uv} \geq 0 &\quad \forall (u,v) \in \hat A \\ & x_{uv} \in \{0,1\} &\quad \forall (u, v) \in A \\ \end{aligned} \]
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Thu, 22 Mar 2018 15:29 GMT