A Combinatorial Benders' decomposition for the lock scheduling problem

This paper presents an exact algorithm for the Lock Scheduling Problem (LSP) based on a Combinatorial Benders decomposition. LSP consists of three strongly interconnected sub problems: scheduling the lockages, assigning ships to chambers, and positioning the ships inside the chambers. These three sub problems are interpreted resp. as a scheduling, an assignment, and a packing problem. By combining the first two problems into a master problem and using the packing problem as a sub problem, a decomposition is achieved which can be solved efficiently using a Combinatorial Benders approach. First the master problem is solved, thereby sequencing the ships into a number of lockages. Next, for each lockage, a packing sub problem is solved to verify its feasibility, possibly returning a number of combinatorial inequalities (cuts) to the master problem. Experiments are conducted on generated real world instances. The results indicate that our decomposition approach significantly outperforms other exact approaches previously presented in literature.