MP 2 SPLPO mathematical programming formulation.

$$\begin{array}{ccc}\hfill minZ& =& \sum _{i\in I}\sum _{j\in J}{c}_{ij}{x}_{ij}+\sum _{j\in J}{f}_j{y}_j,\hfill \end{array}$$ (2) $$\begin{array}{ccc}\hfill \mathrm{subject}\mathrm{to}\sum _{j\in J}{x}_{ij}& =& 1,\forall i\in I,\hfill \end{array}$$ (3) $$\begin{array}{ccc}\hfill x_{ij}& \le & y_j,\forall i\in I,j\in J,\hfill \end{array}$$ (4) $$\begin{array}{ccc}\hfill \sum _{k\in \overline{W_{ij}}}{x}_{ik}& \ge & y_j,\forall i\in I,j\in J^i,\hfill \end{array}$$ (5) $$\begin{array}{ccc}\hfill x_{ij}& \ge & 0,\forall i\in I,j\in J,\hfill \end{array}$$ (6) $$\begin{array}{ccc}\hfill y_j& \in & \{0,1\},\forall j\in J.\hfill \end{array}$$ (7)