Algorithm 1: FMP algorithm

Step 0: Form the initial c-set family $\mathcal{C}:=\mathcal{C}(\mathcal{B})$ (where $\mathcal{C}(\mathcal{B})=\{c(v):v\in \mathcal{B}\}$).        Step 1: Solve the master MP($\mathcal{C},\mathsf{\Delta }$), i.e., the linear relaxation of FMP($\mathcal{C},\mathsf{\Delta }$) formulated in (3), to obtain the optimal dual variables ${\lambda }^{*}={({\lambda }_{vu}^{*})}_{v\in \mathcal{B},u\in \mathcal{R}(v)}$ and ${\theta }^{*}$.        Step 2: Solve the pricing problem (8) for parameters ${\lambda }^{*}$ and ${\theta }^{*}$. If the maximum of the objective function P is strictly positive, then $\mathcal{C}:=\mathcal{C}\cup \left\{c^{*}\right\}$ (where $c^{*}$ is defined in (9)) and go to Step 1.        Step 3: Solve the original MIP version of FMP($\mathcal{C},\mathsf{\Delta }$) and stop.