Polyhedral results for discrete-time production planning MIP formulations for continuous processes

We derive polyhedral results for discrete-time mixed-integer programming (MIP) formulations for the production planning of multi-stage continuous chemical processes. We express the feasible region of the LP-relaxation as the intersection of two sets. The constraints describing the first set yield the convex hull of its integer points. For the second set, we show that for integral data the constraint matrix is κ-regular, and that the corresponding polyhedron is integral if the length of the planning period is selected appropriately. We use this result to show that for rational data, integer variables can also assume integral values at the vertices of the polyhedron. We also discuss how these results provide insight and can be used to effectively address large-scale problems. Finally, we present computational results for a series of example problems.