The objective function minimizes the total cost.

${\displaystyle \sum {\displaystyle \sum c_{ij}{x}_{ij}}}$

$i\in I$ , $j\in J$

Constraint (1)

${\displaystyle \sum x_{ij}}=1$ , $\forall j\in J$

$i\in I$

Constraint (2)

$x_{ij}\le {\gamma }_i$ , $\forall i\in I$ , $\forall j\in J$

Constraint (3)

${\displaystyle \sum {\gamma }_i}=p$

$i\in I$

Constraint (4)

$x\in B^{\left|I\right|\left|J\right|},y\in B^{\left|I\right|}$