Monoidal Cut Strengthening and Generalized Mixed-Integer Rounding for Disjunctive Programs∗

This article investigates cutting planes for mixed-integer disjunctive programs. In the early 1980s, Balas and Jeroslow presented monoidal disjunctive cuts exploiting the integrality of variables. For disjunctions arising from binary variables, it is known that these cutting planes are essentially the same as Gomory mixed-integer and mixed-integer rounding cuts. In this article, we investigate the relation of monoidal cut strengthening to other classes of cutting planes for general twoterm disjunctions. In this context, we introduce a generalization of mixed-integer rounding cuts. We also demonstrate the effectiveness of monoidal disjunctive cuts via computational experiments on instances involving complementarity constraints.