Natural Intersection Cuts for Mixed-Integer Linear Programs

Intersection cuts are a family of cutting planes for pure and mixedinteger linear programs, developed in the 1970s. Most papers on them consider only cuts that come from so-called maximal lattice-point-free polyhedra. We define a completely different family of intersection cuts, called “natural”. Their key property is that they can be generated very quickly and easily from a simplex tableau. In many cases, one can also easily strengthen them, using an idea of Balas and Jeroslow. We show that the strengthened cuts are a generalisation of Gomory mixed-integer cuts, and then show how to tailor the cuts to problems with special structure (such as knapsack, packing, covering and partitioning problems, or problems with complementarity constraints or fixed charges). Our computational results are encouraging.