We consider the multiple depot vehicle scheduling problem (MDVSP) and propose a branch-and-bound algorithm for solving it that combines column generation, variable fixing, and cutting planes. We show that the solutions of the linear relaxation of the MDVSP contain many “odd cycles.” We derive a class of valid inequalities by extending the notion of odd cycle and describe a lifting procedure for these inequalities. We prove that the lifted inequalities represent, under certain conditions, facets of the underlying polytope. Finally, we present the results of a computational study comparing several strategies (variable fixing, cutting planes, mixed branching, and tree search) for solving the MDVSP.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.