Facets and Reformulations for Solving Production Planning With Changeover Costs

We study a scheduling problem with changeover costs and capacity constraints. The problem is NP-complete, and combinatorial algorithms for solving it have not performed well. We identify a general class of facets that subsumes as special cases some known facets from the literature. We also develop a cutting-plane-based procedure and reformulation for the problem, and we obtain optimal solutions to problem instances with up to 600 integer variables without resorting to branch-and-bound procedures.