Stronger Cuts from Weaker Disjunctions

We discuss an enhancement of the Balas-Jeroslow procedure for strengthening disjunctive cuts for mixed 0-1 programs. It is based on the paradox that sometimes weakening a disjunction helps the strengthening procedure and results in sharper cuts. When applied to a split cut derived from a source row of the simplex tableau, the enhanced procedure yields, besides the Gomory Mixed Integer cut (GMI), also inequalities that cut deeper in certain directions.