Operating Room Overtime Research Articles

Robust Operating Room Scheduling Model with Violation Probability Consideration under Uncertain Surgery Duration.

This paper proposes an operating room (OR) scheduling model to assign a group of next-day patients to ORs while adhering to OR availability, priorities, and OR overtime constraints. Existing studies usually consider OR scheduling problems by ignoring the influence of uncertainties in surgery durations on the OR assignment. In this paper, we address this issue by formulating accurate patient waiting times as the cumulative sum of uncertain surgery durations from the robust discrete approach point of view. Specifically, by considering the patients’ uncertain surgery duration, we formulate the robust OR scheduling model to minimize the sum of the fixed OR opening cost, the patient waiting penalty cost, and the OR overtime cost. Then, we adopt the box uncertainty set to specify the uncertain surgery duration, and a robustness coefficient is introduced to control the robustness of the model. This resulting robust model is essentially intractable in its original form because there are uncertain variables in both the objective function and constraint. To make this model solvable, we then transform it into a Mixed Integer Linear Programming (MILP) model by employing the robust discrete optimization theory and the strong dual theory. Moreover, to evaluate the reliability of the robust OR scheduling model under different robustness coefficients, we theoretically analyze the constraint violation probability associated with overtime constraints. Finally, an in-depth numerical analysis is conducted to verify the proposed model’s effectiveness and to evaluate the robustness coefficient’s impact on the model performance. Our analytical results indicate the following: (1) With the robustness coefficient, we obtain the tradeoff relationship between the total management cost and the constraint violation probability, i.e., a smaller robustness coefficient yields remarkably lower total management cost at the expense of a noticeably higher constraint violation probability and vice versa. (2) The obtained total management cost is sensitive to small robustness coefficient values, but it hardly changes as the robustness coefficient increases to a specific value. (3) The obtained total management cost becomes increasingly sensitive to the perturbation factor with the decrease in constraint violation probability.

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

AbstractNonoperating 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.

Data-driven distributionally robust surgery planning in flexible operating rooms over a Wasserstein ambiguity

We study elective surgery planning in flexible operating rooms (ORs) where emergency patients are accommodated in the existing elective surgery schedule. Specifically, elective surgeries can be scheduled weeks or months in advance. In contrast, an emergency surgery arrives randomly and must be performed on the day of arrival. Probability distributions of the actual durations of elective and emergency surgeries are unknown, and only a possibly small set of historical realizations may be available. To address distributional uncertainty, we first construct an ambiguity set that encompasses all possible distributions of surgery durations within a 1-Wasserstein distance from the empirical distribution. We then define a distributionally robust surgery assignment (DSA) problem to determine optimal elective surgery assignment decisions to available surgical blocks in multiple ORs, considering the capacity needed for emergency cases. The objective is to minimize the total cost consisting of the fixed cost related to scheduling or rejecting elective surgery plus the maximum expected cost associated with OR overtime and idle time over all distributions defined in the ambiguity set. Using the DSA model’s structural properties, we derive an equivalent mixed-integer linear programming (MILP) reformulation that can be implemented and solved efficiently using off-the-shelf optimization software. In addition, we extend the proposed model to determine the number of ORs needed to serve the two competing surgery classes and derive a MILP reformulation of this extension. We conduct extensive numerical experiments based on real-world surgery data, demonstrating our proposed model’s computational efficiency and superior out-of-sample operational performance over two state-of-the-art approaches. In addition, we derive insights into surgery scheduling in flexible ORs.

Operating Rooms efficiency: leveraging data to improve management of elective surgery

Abstract Background Careful scheduling of elective surgery Operating Rooms (ORs) is crucial for their efficient use, to avoid low/over utilization and staff overtime. Accurate estimation of procedures duration is essential to improve ORs scheduling. Therefore analysis of historical data about surgical times is fundamental to ORs management. We analyzed the effect, in a real setting, of an ORs scheduling model based on estimated optimum surgical time in improving ORs efficiency and decreasing the risk of overtime. Methods We studied all the 2014-2019 elective surgery sessions (3,758 sessions, 12,449 interventions) of a district general hospital in Siena's Province, Italy. The hospital had3 ORs open 5 days/week 08:00-14:00. Surgery specialties were general surgery, orthopedics, gynecology and urology. Based on a pilot study conducted in 2016, which estimated a 5 times greater risk of having an OR overtime for sessions with a surgical time (incision-suture)>200 minutes, from 2017 all the ORs were scheduled using a maximum surgical time of 200 minutes calculated summing the mean surgical times for intervention and surgeon (obtained from 2014-2016 data). We carried out multivariate logistic regression to calculate the probability of ORs overtime (of 15 and 30 minutes) for the periods 2014-2016 and 2017-2019adjusting for raw ORs utilization. Results The 2017-2019 risk of an OR overtime of 15 minutes decreased by 25% compared to the 2014-2016 period (OR = 0.75, 95%CI=0.618-0.902, p = 0.003); the risk of a OR overtime of 30 minutes decreased by 33% (OR = 0.67, 95%CI= 0.543-0.831, p < 0.001). Mean raw OR utilization increase from 62% to 66% (p < 0.001). Mean number of interventions per surgery sessions increased from 3.1 to 3.5 (p < 0.001). Conclusions This study has shown that an analysis of historical data and an estimate of the optimal surgical time per surgical session could be helpful to avoid both a low and excessive use of the ORs and therefore to increase the efficiency of the ORs. Key messages An accurate analysis of surgical procedures duration is crucial to optimize operating room utilization. A data-based approach can improve OR management efficiency without extra resources.

A Decomposition Algorithm for the Two-Stage Chance-Constrained Operating Room Scheduling Problem

The required time for surgical interventions in operating rooms (OR) may vary significantly from the predicted values depending on the type of operations being performed, the surgical team, and the patient. These deviations diminish the efficient utilization of OR resources and result in the disruption of projected surgery start times. This paper proposes a two-stage chance-constrained model to solve the OR scheduling problem under uncertainty. The goal is to minimize the costs associated with OR opening and overtime as well as reduce patient waiting times. The risk of OR overtime is controlled using chance constraints. Numerical experiments show that the proposed model provides a better trade-off between minimizing costs and reducing solution variability when compared to two existing models in the literature. It is also shown that the three models converge as the overtime probability threshold approaches one. Moreover, it is observed that the individual chance constraints result in the opening of fewer rooms, lower waiting times, and shorter solution times when compared to that of joint chance constraints. A decomposition algorithm is applied that solves large test instances of the OR scheduling problem, that of which is known to be NP-hard. Strong valid inequalities are derived in order to accelerate the convergence speed. The proposed approach outperformed both a commercial solver and a basic decomposition algorithm after solving all test instances with up to 89 surgeries and 20 ORs in less than 48 minutes.

Time Is Money: Can Punctuality Decrease Operating Room Cost?

Inefficient operating room (OR) use wastes resources. Studies have suggested "first case on-time starts" (FCOTS) reduce OR "idle time," yet no direct association between FCOTS and markers of OR efficiency, like "last case on-time end" (LCOTE) or overtime costs, have been reported. We performed this study to evaluate factors associated with FCOTS, LCOTE, and OR overtime costs. In April 2017, our medical center launched an FCOTS improvement initiative. Prospectively collected data concerning cases performed in the 6-month pre- (October 2016 to March 2017) and post-intervention (October 2017 to March 2018) periods were retrospectively analyzed. Elective, nontraumatic cases performed by orthopaedics, gynecology, urology, minimally invasive surgery, or colorectal surgery were eligible. Univariate and multivariable analyses were used to evaluate 3 outcomes of interest: the association between FCOTS and LCOTE (primary), the change in FCOTS rates after intervention implementation (secondary), and estimated overtime cost savings associated with FCOTS (secondary). We analyzed 12,073 cases (6,095 pre- vs 5,978 post-intervention) performed over 2,631 OR days (1,401 pre vs 1,230 post). The FCOTS rate increased after intervention (76.1% vs 86.6%, p <0.001), with post-intervention cases twice as likely to start on time (adjusted odds ratio [aOR] 2.07; 95% CI 1.73 to 2.46, p < 0.001). Additionally, starting on time was associated with a higher likelihood of LCOTE (aOR 1.76; 95% CI 1.38 to 2.24, p < 0.001) and 21.8 fewer overtime minutes (95% CI 13.7 to 29.8, p < 0.001) per OR day. Post-intervention estimated savings of $87,954 in direct OR costs over 6 months were associated with the FCOTS initiative. The FCOTS initiative was associated with higher frequency of FCOTS, which was independently associated with LCOTE. This achieved an estimated 6-month cost savings of more than $80,000 in direct OR expenditures.

Chance-Constrained Surgery Planning Under Conditions of Limited and Ambiguous Data

Surgery planning decisions include which operating rooms (ORs) to open, allocation of surgeries to ORs, sequence, and time to start each surgery. They are often made under uncertain surgery durations with limited data that lead to unknown distributional information. Moreover, cost parameters for criteria such as overtime and surgery delays are often difficult or impossible to estimate in practice. In this paper, we formulate distributionally robust (DR) chance constraints on surgery waiting and OR overtime, which recognize practical limitations on data availability and cost parameter accuracy. We use [Formula: see text]-divergence measures to build an ambiguity set of possible distributions of random surgery durations, and derive a branch-and-cut algorithm for optimizing a mixed-integer linear programming reformulation based on finite samples of the random surgery durations. We test instances generated from real hospital-based surgery data. The results show computational efficacy of our approaches, and provide insights for DR surgery planning.

Solving 0–1 semidefinite programs for distributionally robust allocation of surgery blocks

We allocate surgery blocks to operating rooms (ORs) under random surgery durations. Given unknown distribution of the duration of each block, we investigate distributionally robust (DR) variants of two types of stochastic programming models using a moment-based ambiguous set. We minimize the total cost of opening ORs and allocating surgery blocks, while constraining OR overtime via chance constraints and via an expected penalty cost in the objective function, respectively in the two types of models. Following conic duality, we build equivalent 0–1 semidefinite programming (SDP) reformulations of the DR models and solve them using cutting-plane algorithms. For the DR chance-constrained model, we also derive a 0–1 second-order conic programming approximation to obtain less conservative solutions. We compare different models and solution methods by testing randomly generated instances. Our results show that the DR chance-constrained model better controls average and worst-case OR overtime, as compared to the stochastic programming and DR expected-penalty-based models. Our cutting-plane algorithms also outperform standard optimization solvers and efficiently solve 0–1 SDP formulations.

Solving 0-1 Semidefinite Programs for Distributionally Robust Allocation of Surgery Blocks

We consider the problem of allocating surgeries in operating rooms (ORs) under random surgery durations. We minimize the cost of opening ORs and surgery assignments, while restricting OR overtime risk via distributionally robust (DR) chance constraints using the first two moments to construct an ambiguous set of the unknown distribution of surgery durations. Following the conic duality, the DR chance-constrained model is equivalent to a 0-1 semidefinite program (SDP) and that is solved by a cutting-plane algorithm. We also propose a 0-1 second-order conic program (SOCP) reformulation that approximates the result with a less conservative solution. We conduct numerical studies to show the performance of each method on randomly generated instances. The 0-1 SDP outperforms the 0-1 SOCP and a benchmark Sample Average Approximation approach in terms of CPU time and the out-of-sample reliability of having no overtime.

A sample gradient-based algorithm for a multiple-OR and PACU surgery scheduling problem

ABSTRACTIn this article, we study a surgery scheduling problem in multiple Operating Rooms (ORs) constrained by the Post-Anesthesia Care Unit (PACU) capacity within the block-booking framework. With surgery sequences predetermined in each OR, a Discrete-Event Dynamic System (DEDS) is devised for the problem. A DEDS-based stochastic optimization model is formulated in order to minimize the cost incurred from patient waiting time, OR idle time, OR blocking time, OR overtime, and PACU overtime. A sample gradient-based algorithm is proposed for the sample average approximation of our formulation. Numerical experiments suggest that the proposed method identifies near-optimal solutions and outperforms previous methods. We also show that considerable cost savings (11.8% on average) are possible in hospitals where PACU beds are a constraint.

Coordinating clinic and surgery appointments to meet access service levels for elective surgery

Providing timely access to surgery is crucial for patients with high acuity diseases like cancer. We present a methodological framework to make efficient use of scarce resources including surgeons, operating rooms, and clinic appointment slots with a goal of coordinating clinic and surgery appointments so that patients with different acuity levels can see a surgeon in the clinic and schedule their surgery within a maximum wait time target that is clinically safe for them. We propose six heuristic scheduling policies with two underlying ideas behind them: (1) proactively book a tentative surgery day along with the clinic appointment at the time an appointment request is received, and (2) intelligently space out clinic and surgery appointments such that if the patient does not need his/her surgery appointment there is sufficient time to offer it to another patient. A 2-stage stochastic discrete-event simulation approach is employed to evaluate the six scheduling policies. In the first stage of the simulation, the heuristic policies are compared in terms of the average operating room (OR) overtime per day. The second stage involves fine-tuning the most-effective policy. A case study of the division of colorectal surgery (CRS) at the Mayo Clinic confirms that all six policies outperform the current scheduling protocol by a large margin. Numerical results demonstrate that the final policy, which we refer to as Coordinated Appointment Scheduling Policy considering Indication and Resources (CASPIR), performs 52% better than the current scheduling policy in terms of the average OR overtime per day under the same access service level. In conclusion, surgical divisions desiring stratified patient urgency classes should consider using scheduling policies that take the surgical availability of surgeons, patients’ demographics and indication of disease into consideration when scheduling a clinic consultation appointment.

A Progressive Hedging Approach for Surgery Planning Under Uncertainty

We propose a multistage stochastic mixed-integer programming formulation for the assignment of surgeries to operating rooms over a finite planning horizon. We consider the demand for and the duration of surgery to be random variables. The objective is to minimize three competing criteria: expected cost of surgery cancellations, patient waiting time, and operating room overtime. We discuss properties of the model and an implementation of the progressive hedging algorithm to find near-optimal surgery schedules. We conduct numerical experiments using data from a large hospital to identify managerial insights related to surgery planning and the avoidance of surgery cancellations. We compare the progressive hedging algorithm to an easy-to-implement heuristic for practical problem instances to estimate the value of the stochastic solution. Finally, we discuss an implementation of the progressive hedging algorithm within a rolling horizon framework for extended planning periods.

Dynamic Surgery Assignment of Multiple Operating Rooms With Planned Surgeon Arrival Times

This paper addresses the dynamic assignment of a given set of surgeries to multiple identical operating rooms (ORs). Surgeries have random durations and planned surgeon arrival times. Surgeries are assigned dynamically to ORs at surgery completion events. The goal is to minimize the total expected cost incurred by surgeon waiting, OR idling, and OR overtime. We first formulate the problem as a multi-stage stochastic programming model. An efficient algorithm is then proposed by combining a two-stage stochastic programming approximation and some look-ahead strategies. A perfect information-based lower bound of the optimal expected cost is given to evaluate the optimality gap of the dynamic assignment strategy. Numerical results show that the dynamic scheduling and optimization with the proposed approach significantly improve the performance of static scheduling and First Come First Serve (FCFS) strategy.

Chance-Constrained Surgery Planning Under Uncertain or Ambiguous Surgery Duration

Surgery planning include decisions of which operating rooms (ORs) to open, allocation of surgeries to ORs, sequence and time to start each surgery. The decisions are often made under uncertain surgery durations with limited data that leads to unknown distributional information; furthermore, cost data for criteria such as overtime and surgery delays are often difficult or impossible to estimate in practice. In this paper, we consider a distributionally robust (DR) formulation that recognizes practical limitations on data availability and obviates the need to provide accurate cost parameters for surgery planning. We minimize the cost of opening ORs for completing a set of surgeries, subject to a joint DR chance constraint on OR overtime. We use statistical $\phi$-divergence measures to build an ambiguity set of possible distributions of random surgery durations, and derive a branch-and-cut algorithm for optimizing a mixed-integer linear programming reformulation of the DR chance-constrained model formulated based on a finite sample of scenarios. We compute instances generated from real hospital-based surgery data, demonstrate the computational efficacy of our approach, and provide insights for DR surgery planning.

A Study of Operating Room Scheduling That Integrates Multiple Quantitative and Qualitative Objectives

Most operating room (OR) scheduling is done by scheduling personnel based on experience or heuristics. Such often results in excessive overtime for medical personnel and poor resource-use efficiencies. This study was designed to employ an integrated OR scheduling performance evaluation model (IOSPEM), which integrates quantitative and qualitative multiple objectives, to the improvement of OR scheduling quality. The fuzzy Delphi method was used to obtain the weight values of time factor, cost factor, and risk factor. The fuzzy set theory was applied to transform qualitative risk measures into quantitative values. The desirability function was utilized to integrate time, cost, and risk factors to develop the IOSPEM. The simulated annealing algorithm was used to develop the scheduling system and test proposed model performance. The proposed IOSPEM successfully integrated the quantitative and qualitative indices into a sole quantitative index. Experiment results show that the IOSPEM incorporating the simulated annealing algorithm is able to obtain the most efficient OR schedule and is helpful in reducing costs and fatigue risks. Operating room scheduling will be made more objective and efficient if OR scheduling personnel can simultaneously consider the cost, fatigue risk, and other factors in scheduling. Cost of each OR room should be considered to set appropriate cost coefficients in practical application of the IOSPEM. It is also suggested that other indices (e.g., OR overtime costs and OR nurse fatigue risks) also be considered in the proposed model so as to better reflect the actual scheduling environment. The procedure and methods implemented in this study may be used as the basis for further developing more effective and efficient OR scheduling systems.

The effect of scheduling policies on operating room overtime performance

The Operating Room (OR) overtime performance depends on two sources of variability. The uncontrollable case-specific variability includes such factors as the patient's characteristics, the type of operation and the surgeon. There is an additional source of variability that arises from the sharing of hospital resources and can be controlled to an extent. Most operational surgery-scheduling approaches determine short-term case schedules in two phases: assignment of cases to ORs and subsequent sequencing decision. In this study, we consider the effect of sequencing decisions on the overtime performance under different surgery start time policies and resource coupling levels. We provide both analytical and numerical results based on a simulation study. Our results conform to the common practice and indicate that scheduling highly variable cases early on leads to better overtime performance. In addition, we conclude that reducing the level of resource coupling across multiple ORs and/or scheduling coupled cases early on significantly reduces overtime.

A pre-assignment heuristic algorithm for the Master Surgical Schedule Problem (MSSP)

In this paper a 0–1 linear programming model and a solution heuristic algorithm are developed in order to solve the so-called Master Surgical Schedule Problem (MSSP). Given a hospital department made up of different surgical units (i.e. wards) sharing a given number of Operating Rooms (ORs), the problem herein addressed is determining the assignment among wards and ORs during a given planning horizon, together with the subset of patients to be operated on during each day. Different resource constraints related to operating block time length, maximum OR overtime allowable by collective labour agreement and legislation, patient length of stay (LOS), available OR equipment, number of surgeons, number of stay and ICU beds, are considered. Firstly, a 0–1 linear programming model intended to minimise a cost function based upon a priority score, that takes into proper account both the waiting time and the urgency status of each patient, is developed. Successively, an heuristic algorithm that enables us to embody some pre-assignment rules to solve this NP-hard combinatorial optimisation problem, is presented. In particular, we force the assignment of each patient to a subset of days depending on his/her expected length of stay in order to allow closing some stay areas during the weekend and hence reducing overall hospitalisation cost of the department. The results of an extensive computational experimentation aimed at showing the algorithm efficiency in terms of computational time and solution effectiveness are given and analysed.