The alternating current optimal transmission switching (ACOTS) problem incorporates line switching decisions into the alternating current optimal power flow framework, offering well-known benefits in reducing operational costs and enhancing system reliability. ACOTS optimization models contain discrete variables and nonlinear, nonconvex constraints, which make them difficult to solve. In this work, we develop strengthened quadratic convex (QC) relaxations for ACOTS, in which we tighten the relaxation with several new valid inequalities, including a novel kind of on/off cycle–based polynomial constraints by taking advantage of the network structure. We linearize the sum of on/off trilinear terms in the relaxation using extreme-point representation, demonstrating theoretical tightness, and efficiently incorporate on/off cycle–based polynomial constraints through disjunctive programming–based cutting planes. Combined with an optimization-based bound-tightening algorithm, this results in the tightest QC-based ACOTS relaxation to date. We additionally propose a novel maximum spanning tree–based heuristic to improve the computational performance by fixing certain lines to be switched on. Our extensive numerical experiments on medium-scale power grid library instances show significant improvements on relaxation bounds, whereas tests on large-scale instances with up to 2,312 buses demonstrate substantial performance gains. To our knowledge, this is the first ACOTS relaxation-based approach to demonstrate near-optimal switching solutions on realistic large-scale power grid instances. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: The authors gratefully acknowledge support from the U.S. Department of Energy through Los Alamos National Laboratory’s directed research and development program [Grant 20230091ER: Learning to Accelerate Global Solutions for Non-Convex Optimization]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0236 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0236 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

The distributed operating room (OR) scheduling problem aims to find an assignment of surgeries to ORs across collaborating hospitals that share their waiting lists and ORs. We propose a stochastic extension of this problem where surgery durations are considered to be uncertain. In order to obtain solutions for the challenging stochastic model, we use sample average approximation and develop two enhanced decomposition frameworks that use logic-based Benders (LBBD) optimality cuts and binary decision diagram based Benders cuts. Specifically, to the best of our knowledge, deriving LBBD optimality cuts in a stochastic programming context is new to the literature. Our computational experiments on a hospital data set illustrate that the stochastic formulation generates robust schedules and that our algorithms improve the computational efficiency. Summary of Contribution: We propose a new model for an important problem in healthcare scheduling, namely, stochastic distributed operating room scheduling, which is inspired by a current practice in Toronto, Ontario, Canada. We develop two decomposition methods that are computationally faster than solving the model directly via a state-of-the-art solver. We present both some theoretical results for our algorithms and numerical results for the evaluation of the model and algorithms. Compared with its deterministic counterpart in the literature, our model shows improvement in relevant evaluation metrics for the underlying scheduling problem. In addition, our algorithms exploit the structure of the model and improve its solvability. Those algorithms also have the potential to be used to tackle other planning and scheduling problems with a similar structure.