Accelerated operating room scheduling using Lagrangian relaxation method and VNS meta-heuristic

Like any business that produces services, the hospital is part of a process of improving the quality of services provided to patients. As part of this, hospitals are faced with the daunting task of planning operating room patients with budget, time and personnel. Most of the scheduling problems are NP-hard, so researchers have favored the development of heuristics and meta-heuristics to the detriment of exact methods. In a context where high performance computers are in continuous improvement, it is once again interesting to explore exact methods. Here we focus on developing exact methods for solving the operating room planning and scheduling problem. Our contribution is to develop first an accelerated Integer Linear Program (ILP) using the Variable Neighborhood Search (VNS) meta-heuristic to optimize patient waiting time according to the priority of their surgeries. Afterwards, we expose a new lower bound obtained by optimizing the patient waiting time relaxed. The experimental results validated the performance of the accelerated ILP in comparison with the original ILP. Furthermore, we have shown that the Lagrangian relaxation of the original ILP produces a lower bound of good quality. © 2022 ACM.