We study the elective surgery planning problem in a hospital with operation rooms shared by elective and emergency patients. This problem can be split in two distinct phases. First, a subset of patients to be operated in the next planning period has to be selected, and the selected patients have to be assigned to a block and a tentative starting time. Then, in the online phase of the problem, a policy decides how to insert the emergency patients in the schedule and may cancel planned surgeries. The overall goal is to minimize the expectation of a cost function representing the assignment of patient to blocks, case cancellations, overtime, waiting time and idle time. We model the offline problem by a two-stage stochastic program, and show that the second-stage costs can be replaced by a convex piecewise linear surrogate model that can be computed in a preprocessing step. This results in a mixed integer program which can be solved in a short amount of time, even for very large instances of the problem. We also describe a greedy policy for the online phase of the problem, and analyze the performance of our approach by comparing it to either heuristic methods or approaches relying on sampling average approximation (SAA) on a large set of benchmarking instances. Our simulations indicate that our approach can reduce the expected costs by as much as 30% compared to heuristic methods and is able to solve problems with $1000$ patients in about one minute, while SAA-approaches fail to obtain near-optimal solutions within 30 minutes, already for $100$ patients.
Handling Overtime Constraints in Mixed Integer Linear Programming for Surgical Scheduling: A Comparison of Neural Network and Classical Linearization Techniques
Erasmus University Medical Center（伊拉斯姆斯大学医学中心）；Delft Institute of Applied Mathematics, Delft University of Technology（代尔夫特理工大学应用数学研究所）
A Reinforcement-learning-based Column Generation Algorithm for Integrated Operating Room Planning and Scheduling
Concordia University（康科迪亚大学）；CIRRELT, Université de Montréal（蒙特利尔大学CIRRELT）；Université du Québec à Montréal（魁北克大学蒙特利尔分校）；Polytechnique Montréal（蒙特利尔理工学院）
Smart energy management: process structure-based hybrid neural networks for optimal scheduling and economic predictive control in integrated systems
School of Energy and Environment, Southeast University（能源与环境学院，东南大学）；Department of Chemical & Materials Engineering, University of Alberta（阿尔伯塔大学化学与材料工程系）；School of Chemistry, Chemical Engineering and Biotechnology, Nanyang Technological University（南洋理工大学化学、化学工程与生物技术学院）
A Two-Stage Operating Room Allocation Framework for Reducing Surgical Waiting Lists in Public Hospitals
Center for Mathematical Modeling, Universidad de Chile and CNRS (IRL 2807)（智利大学数学建模中心与法国国家科学研究中心（IRL 2807））；Universidad Nacional de Colombia（哥伦比亚国立大学）；Dr. Luis Calvo Mackenna Hospital（路易斯·卡尔沃·麦肯纳博士医院）；Department of Mathematical Engineering, Universidad de Chile（智利大学数学工程系）
