Recursive logic-based Benders' decomposition for multi-mode outpatient scheduling.

•We address a complex, long term, outpatient appointment scheduling problem.•The problem is multi-modal, and integrates planning and scheduling.•A 3-level logic-based Benders’ decomposition solves the problem efficiently.•The approach is vastly superior to the corresponding 2-level decomposition.•Strengthening cuts by breaking symmetries, and strengthening each master, is critical.