Solving integrated operating room planning and scheduling: Logic-based Benders decomposition versus Branch-Price-and-Cut

Abstract

Integrated operating room planning and scheduling (IORPS) allocates patients optimally to different days in a planning horizon, assigns the allocated set of patients to ORs, and sequences/schedules these patients within the list of ORs and surgeons to maximize the total scheduled surgical time. The state-of-the-art model in the IORPS literature is a hybrid constraint programming (CP) and integer programming (IP) technique that is efficiently solved by a multi-featured Branch-Price-&Cut (BP&C) algorithm. We extend the IORPS literature in two ways: (i) we develop new mixed-integer programming (MIP) and CP models that improve the existing CP-IP model and (ii) we develop various combinatorial Benders decomposition algorithms that outperform the existing BP&C algorithm. Using the same dataset as used for the existing methods, we show that our MIP model achieves an average optimality gap of 3.84%, outperforming the existing CP-IP model that achieves an average optimality gap of 11.84%. Furthermore, our MIP model is 54–92 times faster than the CP-IP model in some of the optimally solved instances of the problem. We demonstrate that our best Benders decomposition approach achieves an average optimality gap of 0.88%, whereas the existing BP&C algorithm achieves an average optimality gap of 2.81%.