Constrained integer linear programming

An integer linear programming problem in which the integer solution is constrained to satisfy any h out of n additional constraint sets (not necessarily convex polyhedrons), is studied in the present paper. An algorithm is developed, which obtains optimal integer solution in a finite number of steps. Ranking as well as scanning of all the integer points of a convex polyhedron has also been discussed. A numerical illustration is included in support of the proposed methodology.