Reformulation, linearization, and decomposition techniques for balanced distributed operating room scheduling

•We develop a mixed-integer nonlinear model for balanced distributed operating room scheduling.•We develop linearization techniques for the mixed-integer nonlinear model.•We develop uni- and bi-level logic-based Benders decompositions for the linearized models.•We develop Benders balancing cuts for each logic-based Benders decomposition approach.•Uni- and bi-level approaches converge to  ≈  2% optimality gap in 30 minutes.