View article

Many problems in the Operations Research/Management Science literature can be formulated with both zero-one and continuous variables. However, the exact optimization of such mixed zero-one models remains a computational challenge. In this paper, we propose to study mixed problems from a mathematical point of view that is similar in spirit to recent research on purely combinatorial problems that has investigated systems of defining linear inequalities (or facets of the underlying polytope). At least two numerical studies have validated this line of research computationally, and the advances in the problem-solving capabilities are considerable. We expect that similar gains are possible for the mixed zero-one problem. More precisely, we consider the mixed integer programs whose feasible region X is composed of (i) a simple additive constraint in the continuous variables x_j, for j = 1, 2, …, n and (ii) constraints 0 …