We start from the relaxation of the problem and solve it. If the optimal solution has all the first p components integer, then it is an optimal solution of the mixed integer problem and the methods stop. Otherwise one can consider all the components among the first p ones that are fractional in the current solution, find an equal number of cutting planes by solving the separation problem with respect to the corresponding polyhedra Pj(K) and add the found inequalities to the current formulation. Finally we solve the problem on the augmented set of constraints and move to the next iteration.
