An integer linear programming problem is that of optimizing (let say maximizing ) a linear function cx over the set of the solutions of a finite number of linear inequalities and under the condition that the components of the solution have to take only integer values. In other words the set S of the feasible solutions of the problem is the intersection of the polyhedron P defined by the linear constraints of the problem and the integer lattice formed by the elements of Zn.
We may assume that all the data that define the instance are integer numbers.