---
title: Operating Room Scheduling Overview
url: https://www.emergentmind.com/topics/operating-room-scheduling-ors
type: topic
---

# Operating Room Scheduling Overview

Searching arXiv for recent and relevant work on operating room scheduling to ground the article in current literature.
Operating Room Scheduling (ORS) is the task of assigning surgical cases to operating rooms while determining when surgeries start, how they are sequenced, and how scarce resources are allocated under clinical, organizational, and stochastic constraints. In the formulations represented in recent arXiv work, ORS may include specialty compatibility, surgery durations, priority scores, operating room session durations, and the availability of beds for the entire length of stay both in the Intensive Care Unit and in the wards; broader integrated models additionally decide which ORs to open, which anesthesiologists to call in, and how to reschedule when the off-line schedule cannot be completed for some reason [2105.02283] [2204.11374]. The field therefore spans deterministic planning, stochastic and distributionally robust optimization, logic-based scheduling, reactive rescheduling, simulation-based decision support, and learning-enhanced hybrids.

## 1. Scope, decision layers, and empirical structure

ORS is not a single optimization task but a family of tightly coupled decisions. Depending on the formulation, it can include allocation, assignment, sequencing, scheduling, rescheduling, and bed management. One recent ASP formulation defines ORS as assigning patients to operating rooms while taking into account different specialties, lengths and priority scores of each planned surgery, operating room session durations, and the availability of beds for the entire length of stay both in the Intensive Care Unit and in the wards [2105.02283]. Another integrated formulation expands the scope further by simultaneously deciding which ORs to open, which on-call anesthesiologists to employ, how to assign an OR and an anesthesiologist to each surgery, and how to determine the order of surgeries and their scheduled start times in each OR [2204.11374].

A recurrent modeling assumption is that surgery duration is an input to OR allocation and surgery scheduling. Statistical evidence complicates that assumption. Using almost two years of data from a large hospital in China, one study examined both clinical and non-clinical effects on surgery duration and reported that surgery duration decreases with the number of surgeries a surgeon performs in a day, that there is a non-linear relationship between surgery duration and the number of surgeries allocated to an OR, and that a surgery’s duration is affected by its position in a sequence of surgeries performed by one surgeon. The paper modeled duration through \(\log(\text{DURATION})\) and represented the OR workload effect with the piecewise-linear term
\[
\beta_{41} \min\{\text{W\_OR}_i,TP\} + \beta_{42} \max\{\text{W\_OR}_i - TP,0\},
\]
with \(TP=4\). Numerically, each additional surgery a surgeon performs in a day reduces the average duration of each surgery by about 10 minutes; for up to 4 surgeries scheduled in an OR per day, each additional surgery allocated reduces procedure time by \(\sim 8\) minutes, whereas beyond 4 surgeries each extra surgery increases duration by \(\sim 12\) minutes. The same study explicitly states that it does not claim generalizability, but it shows that surgery duration may itself depend on scheduling context rather than functioning as a fixed exogenous parameter [1801.04110].

This empirical line of work clarifies a common misconception: ORS is not only a matter of placing fixed-duration jobs into OR blocks. In the available literature, duration estimation, resource congestion, order effects, and practitioner heterogeneity are all treated as operationally relevant.

## 2. Deterministic and integrated optimization formulations

Early deterministic ORS formulations often emphasized tractable allocation structures. An integer linear programming model for hospital operating theatre scheduling during peak and off peak time uses open scheduling, weekdays only, four main short-hour rooms, four main long-hour rooms, one Elective Outpatient Surgery short-hour room, and one Elective Outpatient Surgery long-hour room. Its decision variables \(X_{ijk}\) assign room type \(i\) to department \(j\) on day \(k\), and its objective is
\[
\min \sum_j s_j,
\]
where \(s_j\) denotes under-allocated hours for department \(j\). The model minimizes total relative under-allocation subject to room-type availability, departmental targets, and under-allocation limits, and was implemented with GLPK/AMPL; for the sample data of 10 rooms, 6 departments, and 5 days, the model solved to optimality in less than 2.0 seconds [1205.2108].

More elaborate deterministic models integrate upstream and downstream units rather than treating the OR in isolation. A 2019 formulation addresses uncertain surgery time in an integrated sequencing, planning and scheduling problem of the surgical ward by considering surgeon work times, patients' surgery priority, and preparation time of the operation room after each surgery. Its first model is a mixed-integer programming model that minimizes the total patient waiting time across three sections: Public Health Unit, Operating Rooms, and Post Anesthesia Care Unit. The formulation includes scheduling, allocating surgery personnel, and sequencing the groups of patients in each section. A second model introduces robust optimization to overcome uncertain surgery times, and the abstract reports that the robust model indicated that the fluctuations of solutions in the future are less than the deterministic model at an acceptable level [1909.07789].

Taken together, these deterministic and integrated formulations show the range of admissible abstraction. At one extreme, ORS can be represented as weekly department-to-room assignment with under-allocation penalties; at the other, it becomes a multi-stage coordination problem coupling preoperative units, ORs, recovery resources, personnel allocation, and sequence-dependent setup or preparation effects.

## 3. Uncertainty, robustness, and decomposition

Uncertain durations, emergency arrivals, and recourse decisions have made stochastic and robust methods central to ORS. One important line concerns parallel processing, in which anesthesia induction and operating room turnover occur simultaneously. A two-stage stochastic mixed-integer programming model for multiple ORs and induction rooms sequences patients and sets appointment times in the first stage, assigns patients to induction rooms in the second stage, and minimizes the expected total cost of patient waiting time, OR idle time and IR idle time. The paper proves that an optimal myopic policy can be used for IR assignment decisions, strengthens the formulation with bounds on variables and symmetry-breaking constraints, and develops an Extended Progressive Hedging Algorithm. On real Mayo Clinic data, the proposed algorithm achieved solutions within 2.4% of optimal; adding a second induction room reduced the objective by about 45%; explicit stochastic modeling yielded a value of stochastic solution of 5–10%; and parallel processing reduced total OR closure times by 80–120 minutes at the expense of somewhat higher patient waiting times [2112.15203].

A second line addresses elective planning in flexible OR systems shared by elective and emergency patients. One two-stage stochastic program replaces second-stage costs with a convex piecewise linear surrogate model computed in preprocessing, yielding a compact mixed integer program. In simulation, this surrogate-based approach can reduce the expected costs by as much as 30% compared to heuristic methods and solve problems with \(1000\) patients in about one minute, while sample average approximation approaches fail to obtain near-optimal solutions within 30 minutes already for \(100\) patients [2304.13670]. This suggests that preprocessing-based approximation of recourse is one route to scaling ORS beyond the instance sizes that direct scenario-based methods can handle.

Distributional ambiguity motivates a further shift from stochastic programming to distributionally robust optimization. In flexible OR planning with emergency accommodation, one model constructs an ambiguity set using a 1-Wasserstein distance around the empirical distribution and solves a distributionally robust surgery assignment problem through an equivalent MILP reformulation. The objective combines fixed costs of scheduling or rejecting elective surgery with the maximum expected cost associated with OR overtime and idle time over all distributions in the ambiguity set. The numerical study reports superior out-of-sample operational performance over sample average approximation stochastic programming and moment-based DRO, especially when the available data is small or of poor quality, and derives policy comparisons between flexible and dedicated OR scheduling [2103.15221].

Integrated OR and anesthesiologist scheduling under uncertainty extends the same logic to staffing. One arXiv study proposes stochastic programming and distributionally robust optimization models with both risk-neutral and risk-averse objectives for combined OR opening, anesthesiologist call-in, surgery assignment, sequencing, and scheduling. Near-optimal solutions for the stochastic programming models are obtained using sample average approximation, while the DRO models are solved by a column-and-constraint generation method augmented by symmetry-breaking constraints. The reported out-of-sample evidence is that DRO models, especially DRO-CVaR, produce schedules with much lower worst-case costs and are less prone to disappointment than stochastic models under distributional misspecification, albeit with a tendency to open more ORs and call more anesthesiologists [2204.11374].

Distributed ORS introduces uncertainty across collaborating hospitals. In a stochastic distributed operating room scheduling model, uncertain surgery durations are handled through sample average approximation, and the recourse structure is exploited through logic-based Benders decomposition and Binary Decision Diagram based Benders cuts. Computational experiments on a hospital dataset show that the stochastic formulation generates robust schedules, nearly eliminates unnecessary cancellations relative to deterministic schedules, improves OR utilization, and benefits from enhanced decomposition frameworks that improve computational efficiency [1907.13265].

## 4. Logic-based scheduling, reactive rescheduling, and digital twins

Answer Set Programming has been used to represent ORS as a combinatorial optimization problem with explicit logical constraints. An ASP formulation models registrations through predicates such as `registration(R,P,SU,LOS,SP,ICU,A)`, master surgical schedule information through `mss(O,S,SP,D)`, session durations through `duration(N,O,S)`, and bed availability through `beds(SP,AV,D)`. The output predicate `x(R,P,O,S,D)` encodes assignment of a registration to an OR, session, and day. The encoding has 13 rules, uses hard constraints to require that all priority 1 patients must be assigned, uses weak constraints to minimize unassigned lower-priority patients, incorporates ward and ICU occupancy constraints for the entire length of stay, and remains suitable on scheduling horizons up to 15 days. The same work also presents an ASP solution for the rescheduling problem and a web framework that allows a user to insert the main parameters of the problem, solve a specific instance, and show results graphically in real-time [2105.02283].

Reactive ORS frameworks address the fact that schedules are disrupted continually. A real-time reactive framework for the multiple operating room surgical case sequencing problem models the task as equivalent to a resource-constrained parallel-machine scheduling problem with identical machines, machine eligibility restrictions, and machine release dates. It introduces constructive heuristics based on modified block scheduling and open scheduling, both designed to generate feasible solutions in under one second, and classifies seven disruption types: non-elective arrival, OR breakdown, surgery runs under-time, surgery runs over-time, patient cancellation, anticipated OR underutilization, and anticipated OR overtime. The reaction set consists of do nothing, repair, and reschedule strategies, and updating can be periodic, continuous, or adaptive. In the reported experiments, each update required less than 0.1 seconds, and full weekly schedules were computed in under 5–25 seconds, compared with 6,000 seconds for an exact daily solve [1808.10133].

Scenario-based restoration is particularly explicit in pediatric ORS. A disruption-restoration MILP for elective surgical scheduling in a children's hospital constructs a nominal schedule together with back-up schedules for emergencies and no-shows. The approach enumerates a representative subset of possible emergency and no-show scenarios, assigns emergencies through an as-soon-as-possible policy, and computes back-up schedules in advance so that OR activity immediately recovers in case of disruption. For the largest test instances, the average total time to generate all schedules, nominal plus back-ups, is reported as approximately 16 minutes, while the price of robustness is only moderately higher than that of the purely nominal plan [2408.12518].

Digital-twin decision support systems generalize reactive scheduling into prospective and retrospective analysis. One recent prototype uses a relational database as input, implements discrete-event simulation in FlexSim Healthcare®, and supports prospective analysis through five steps—feasibility assessment, performance evaluation, robustness analysis, resilience testing, and full stochastic simulation—as well as retrospective analysis through constraint compliance check, performance evaluation, and discrepancy analysis. Outputs include dashboard visualizations of OR utilization, staff overtime, patient waiting time, and Gantt chart diagrams showing the status of each OR. In a one-day case inspired by a real French hospital with eight ORs, the real-life, First Fit, Best Fit, and Worst Fit strategies yielded the same OR utilization of 77.3% and the same staff overtime of 9.6% for the specific urgent cases considered, illustrating how simulation can make the rationale for equivalent outcomes explicit [2509.03094].

## 5. Learning-enhanced, hybrid, and neuro-symbolic approaches

Recent ORS research increasingly combines predictive models with exact or symbolic schedulers. One neuro-symbolic approach augments ASP-based ORS with machine learning predictions of surgery duration. Multiple regressors were evaluated on historical data from ASL1 Liguria, and XGBoost achieved a Mean Absolute Error of 12.36 minutes and an \(R^2\) of 0.79. Prediction quality is encoded through the Absolute Percentage Error,
\[
\text{APE} = \frac{|\hat{y} - y|}{y} \times 100,
\]
which is discretized into four confidence levels: High Confidence, Moderate Confidence, Low Confidence, and Very Low Confidence. Over 65% of predictions were classified as High or Moderate confidence. Predicted durations replace static estimates in ASP facts, and new weak constraints distribute confidence more evenly across day, OR, and shift. On historical data, the confidence-aware method produced schedules with OR occupancy close to the ideal 100% and the lowest or nearly lowest number of overbooked and underbooked operating rooms relative to baselines based on average durations by department or procedure type [2507.16454].

Hybrid optimization is also being pushed inside large-scale integrated planning and scheduling. A reinforcement-learning-based column generation algorithm for integrated operating room planning and scheduling formulates mandatory and elective surgeries over multiple days in a mixed integer program with overtime and surgeons' daily availability limits. Column generation is strengthened by a hybrid algorithm that integrates a Reinforcement Learning Algorithm and the Genetic Algorithm to generate initial columns. On synthetic data, the reported average optimality gap is 1.23%; on real-world cases from Naples, Italy, it is 1.49%. Under 20% variability in surgery durations, incorporating a 120-minute buffer time minimizes the overall cost. For synthetic instances, the inclusion of emergency surgeries increased the total rescheduling cost by 4.13%, whereas in the real-world Naples cases, priority escalation led to only a 0.11% increase [2604.22977].

Intraday ORS under uncertainty has also been framed as a cooperative Markov game. In one multi-agent reinforcement learning framework, each OR is an agent trained with centralized training and decentralized execution, all agents share a PPO policy, and a within-epoch sequential assignment protocol constructs conflict-free joint schedules across ORs. A mixed-integer pre-schedule provides reference starting times for electives, and the reward uses type-specific quadratic delay penalties and a terminal overtime penalty:
\[
\max_{\pi} \;\; \mathbb{E}_{\pi} \left[\sum_{i\in\mathcal{I}} \left(u_{k_i} - c_{k_i}\omega_i^2\right) - C_o \cdot \mathrm{OT}\right].
\]
In simulations with six ORs, eight surgery types, and random urgent and emergency arrivals, the learned policy outperformed six rule-based heuristics across seven metrics and three evaluation subsets. Policy analytics showed prioritization of emergencies, batching of similar cases to reduce setups, and deferral of lower-value electives [2512.04918].

Metaheuristic work has likewise moved toward unified decoders that can represent rich hospital resource interactions. A Random-Key Optimizer models integrated OR scheduling as a variant of the Flexible Job Shop Problem, including multi-room scheduling, equipment scheduling, surgeon and staff availability, business hours, cleaning and moving times, and a blocking time constraint \(\Phi\) of 15 minutes. The framework uses a single decoder and supports Biased Random-Key Genetic Algorithm with \(Q\)-Learning, Simulated Annealing, and Iterated Local Search. The reported results show significant lower and upper bound improvements on literature instances and one proved optimal result, while the best-proposed metaheuristic efficiently generates schedules for new real-world inspired instances [2501.10243].

## 6. Objectives, trade-offs, and persistent research issues

Across formulations, ORS objectives are multi-criteria and often conflicting. The literature represented here includes minimization of total patient waiting time, expected total cost of patient waiting time, OR idle time and IR idle time, total relative under-allocation, overtime, postponement, and cancellations, together with maximization of OR utilization or reward-weighted service. The importance of objective choice is visible in empirical trade-offs: parallel processing can reduce total OR closure times while increasing patient waiting times [2112.15203]; distributionally robust models can improve out-of-sample performance but may open more ORs and call more anesthesiologists [2204.11374]; and dedicated ORs for emergencies can schedule more surgeries but exhibit more idle time and lower utilization if emergencies do not materialize, whereas flexible ORs hedge better against overtime and unpredictable arrivals [2103.15221].

A second persistent issue is decentralization. A bilevel approach to integrated surgeon scheduling and surgery planning models a head surgeon who allocates time blocks and individual surgeons who independently choose surgical case plans. The target solution is an optimal Nash equilibrium that optimizes the objectives of the surgeon head while ensuring that no individual surgeon can improve their own objective within the allocated time blocks. The computational study evaluates the price of stability and the price of decentralisation and reports that, when leader and follower objectives are misaligned, these ratios can become larger than \(1.2\), up to several hundred in some synthetic instances. This result formalizes a long-standing practical concern: schedules that are optimal under centralized criteria may be unstable once decentralized clinical actors respond strategically [2509.24806].

A third issue is the status of duration estimation. Statistical modeling shows that clinical and non-clinical factors, sequencing, workload, and practitioner identity all affect duration, and the same paper explicitly notes the need for future work to ensure that faster surgery under high workload does not compromise outcomes [1801.04110]. This suggests that ORS cannot be reduced to a purely combinatorial packing problem without potential loss of behavioral realism.

Current work therefore points toward integrated predictive-prescriptive systems in which duration prediction, confidence estimation, exact or symbolic optimization, reactive rescheduling, and simulation-based validation are all linked. That trajectory is visible in ASP plus machine learning, in reinforcement-learning-assisted column generation, and in digital twins that unify prospective planning with retrospective discrepancy analysis. A plausible implication is that the central scientific question of ORS is no longer only how to construct a feasible schedule, but how to construct a schedule whose feasibility, efficiency, and robustness survive uncertainty, decentralized response, and real-time disruption.

Source: https://www.emergentmind.com/topics/operating-room-scheduling-ors