An algorithm for the two-stage robust optimization surgery-to-operating room allocation problem is presented. The second-stage problem is an integer linear program whose convex hull is approximated using three types of specialized valid inequalities and Chvátal-Gomory cuts. The resulting linear relaxation of the second-stage problem is then dualized and integrated into the first-stage problem. The resulting mixed integer linear program, which is an approximation of the original problem, is then solved using a commercial solver. If the solution of this model is not optimal for the second-stage problem, valid inequalities for the second-stage problem are generated, yielding a type of column-generation based approach that we refer to as the sequential follower refinement (SFR) algorithm. Data from an academic medical center are used to compare the computational performance of SFR with the constraint and column generation (C&CG) algorithm, which is the only exact approach that has been specifically applied for this problem in the literature. An extensive numerical study of SFR and its computational characteristics is presented that shows that SFR yields better-quality solutions compared with C&CG, even as the termination criterion of SFR is met much sooner, especially for problems involving higher number of surgeries. History: Accepted by Paul Brooks, Area Editor for Applications in Biology, Medicine, & Healthcare. 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.2022.0191 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0191 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

This paper presents a new model for online decision making. Motivated by the healthcare delivery application of dynamically allocating patients to procedure rooms in outpatient procedure centers, the online stochastic extensible bin-packing problem is described. The objective is to minimize the combined costs of opening procedure rooms and utilizing overtime to complete a day’s procedures. The dynamic patient-allocation decisions are made in an uncertain environment where the number of patients scheduled and the procedure durations are not known in advance. The resulting optimization model’s tractability focuses the paper’s attention on approximation methods and a special case that is amenable to decomposition-based solution methods. Theoretical performance guarantees are presented for list-based approximation methods as well as an approximation that is common in practice, where procedure rooms are reserved for patient groups in advance. Numerical results based on a real outpatient procedure center demonstrate the favorable results of the list-based approximations based on their average and worst case performances, as well as their computational requirements. Further, the numerical experiments show that the policy of reserving procedure rooms for patient groups in advance can perform poorly. These results are contrary to common practice and favor alternative, and still easy-to-implement, policies. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0750 .