Robust surgical scheduling for nonoperating room anesthesia (NORA) under surgical duration uncertainty

Nonoperating room anesthesia (NORA) refers to the practice and administration of anesthesia or sedation outside the operating room (OR), which has been increasingly implemented in practice. The novelty of NORA is to separate the anesthesia preoperative stage from an OR for the sake of saving OR time and improving its efficiency. In this article, we study the scheduling problem for NORA considering both anesthetic rooms (ARs) and operating rooms (ORs) based on ambiguous information about surgical durations. Our goal is to devise a robust and efficient scheduling mechanism for NORA. To address this problem, we develop a two-stage mixed-integer Robust Optimization (RO) model that minimizes the total costs, including the sum of operating costs of opened ORs and ARs, delay cost of surgeries, and overtime cost of ORs. Decisions include the number of ARs and ORs to open, the allocation of patients to ARs and ORs, the sequence of surgeries, and the planned starting time for each surgery. Accordingly, a heuristic algorithm, so-called column-and-constraint generation (C&CG), is developed that renders a desirable performance. Some salient properties of the problem are also discussed. In addition, by leveraging practical data in conjunction with data reported in the extant research, the computational efficacy of the proposed algorithm is verified under various sets of parameters. Our numerical experiments reveal that (1) the implementation of NORA can reduce the OR overtime cost and the waiting time of patients; (2) our proposed Robust Optimization (RO) model possesses stronger robustness and computational efficiency than the distributionally robust model (DRO); and (3) while considering surgical duration uncertainty, the developed scheduling approach outperforms the corresponding deterministic setting in terms of decreasing the total cost and alleviating the surgery delay. Generally, the proposed approach is more adaptive to take the advantage of the surgical duration uncertainty to enhance its efficacy.