Operating Room Scheduling Problem Research Articles

Operating room and surgical team members scheduling: A comprehensive review

Operating rooms (OR) are one of the most expensive parts of a hospital with complex processes, and the efficient use of resources is of utmost importance. Therefore, proper management and operation of operating rooms are extremely crucial. OR scheduling ensures that the surgeries are performed at the proper time, patients are treated effectively and safely, resources are used effectively, and staff is increased in work efficiency. Furthermore, accurately scheduled surgeries are safer for patients' healing processes. This is dependent on factors such as the availability of qualified personnel at the appropriate time, the readiness of surgical equipment, and the provision of proper sterilization and hygienic conditions. Surgical team scheduling ensures that surgeries begin on time, are completed effectively, and patients are treated safely. It is also critical to reduce employee fatigue and balance the workload. As a result, integrating surgical teams into operating room scheduling problems provides significant benefits. Accordingly, 29 research articles focusing on the problem of OR scheduling, within the scope of constraints on surgical team members, scheduling strategies, uncertainties, and solution methods, are thoroughly reviewed in this study.

A slack speed-up based discrete artificial bee colony algorithm for resource-constrained operating room scheduling problem

In today’s world, with the rapidly increasing demand for health care and the scarcity of health care resources, it is very important to provide more services under limited conditions. This paper focuses on a resource-constrained operating room scheduling (RCORS) problem with the characteristic of multi-stage. First, a mixed integrated programming model is presented to uncover the impact of no-wait and resources on the problem. Second, a slack speed-up based discrete artificial bee colony (SDABC) algorithm is devised to tackle varying configurations effectively. The solution is represented as a one-dimensional list, from which a complete schedule is derived by a decoding heuristic. Additionally, a speed-up evaluation procedure based on a slack-resource model is developed. In SDABC, an initial population with high quality and diversity is generated based on a problem-specific heuristic. Different strategies are employed in the three stages of SDABC to balance the local optimal, population optimal, and global optimal. A variable neighborhood search is introduced to enhance local exploration capabilities. Finally, we conduct a large number of experiments to verify the performance of the proposed algorithm. Numerical analysis proves that SDABC has significant advantages for solving the RCORS problem.

Genetic Algorithm for Solving the No-Wait Three-Stage Surgery Scheduling Problem.

In this research, we consider a deterministic three-stage operating room surgery scheduling problem. The three successive stages are pre-surgery, surgery, and post-surgery. The no-wait constraint is considered among the three stages. Surgeries are known in advance (elective). Multiple resources are considered throughout the surgical process: PHU (preoperative holding unit) beds in the first stage, ORs (operating rooms) in the second stage, and PACU (post-anesthesia care unit) beds in the third stage. The objective is to minimize the makespan. The makespan is defined as the maximum end time of the last activity in stage 3. Minimizing the makespan not only maximizes the utilization of ORs but also improves patient satisfaction by allowing treatments to be delivered to patients in a timely manner. We proposed a genetic algorithm (GA) for solving the operating room scheduling problem. Randomly generated problem instances were tested to evaluate the performance of the proposed GA. The computational results show that overall, the GA deviated from the lower bound (LB) by 3.25% on average, and the average computation time of the GA was 10.71 s. We conclude that the GA can efficiently find near-optimal solutions to the daily three-stage operating room surgery scheduling problem.

A comparative analysis of the efficient operating room scheduling models using robust optimization and upper partial moment

Operating room scheduling problems are difficult to solve due to the uncertainties inherent in operating time. This study develops a multi-stage linear mixed integer optimization model to optimize the operation time and resource assignment. The decision tree approach addresses the uncertainties in each level of the tree. The proposed model considers three optimistic, most probable, and pessimistic scenarios. Robust Optimization and Upper Partial Moments methods (UPM) are then applied to propose efficient solutions under uncertainty. A case study is presented to compare the solutions proposed by Robust Optimization and UPM methods. The results are compared according to the variance, solution time, and waiting time. We show that the UPM method is superior to the Robust Optimization method in terms of variance and waiting time, while it solves the problem slower.

A branch-and-price-and-cut algorithm for operating room scheduling under human resource constraints

In this paper, we address an integrated operating room planning and scheduling problem that includes, with fine detail, constraints commonly encountered in practice (i.e., sequence, capacity and due date constraints) and for human resources other than surgeons, i.e., nurses. A new model of the sequence-dependent operating room cleaning times that arise because of surgeries with different infection levels is considered. To solve this difficult integrated planning and scheduling problem, we devise a branch-and-price-and-cut algorithm based on the time-indexed formulation of the problem. The basic column generation scheme relies on a label-correcting algorithm that we purposely developed for solving the pricing problems that are modeled as single operating room scheduling problems with time-dependent costs and sequence-dependent cleaning times. The pricing problems are strongly NP-Hard. The efficiency of the label-correcting algorithm is ensured by dominance rules among labels and by two algorithms for computing the upper and lower bound of labels. An effective cutting procedure, inspired by Benders’ decomposition and based on duality theory for linear programming, is developed for tightening the linear relaxation of the problem. With instances from the literature and that we generated, we conduct a numerical study to demonstrate the computational effectiveness of the solution method.

Adapting duration categorical value to accommodate duration variability in a next-day operating room scheduling

Operating room scheduling is a complex problem since it involves the synchronization of multiple resources and uncertainty factors. The duration data is the significant input for scheduling, but it is naturally uncertain. We assume that the variability of duration in operating room scheduling can be represented by the categorical value. We use a time bin, a group of adjacent numerical values of duration, to represent a category value of duration. This study evaluates the impact of duration prediction using the categorical value on the operating room scheduling performance. For the scheduling model, we discuss a next-day operating room scheduling model considering surgeons' preferences for surgery starting time with limited resources and solve it using a priority dispatching rule-based heuristic algorithm. The numerical experiments using the data from a middle-scale university hospital in Indonesia show that the scheduling performance of the heuristic algorithm outperforms the actual schedule for most cases. The underestimated and overestimated duration predictions have no impact on increasing PACU beds, but underestimated surgery duration predictions have a significant impact on increasing surgeons' and patients’ waiting time. However, our results show the opportunity to use the categorical value of duration to accommodate the duration variability in the operating room scheduling problem.

An adaptive-learning-based genetic algorithm for collaborative scheduling of distributed operating rooms

To improve surgical services and hospital performance, collaborative operating room planning and scheduling across a network of hospitals has recently emerged as a new challenge in both healthcare industry and academic community. The paper considers a novel distributed operating room scheduling problem (DORSP), in which elective patients planned on a given day are scheduled for surgeries in the distributed operating rooms of collaborative hospitals. Since hospitals are different in terms of specialization and medical expertise, some complicated surgeries in this problem can only be performed in a subset of collaborative hospitals. Based on the similarities between healthcare delivery systems and production systems, DORSP is modelled as a distributed two-stage no-wait hybrid flow shop scheduling problem with factory eligibility. To deal with the NP-hardness of DORSP, an adaptive-learning-based genetic algorithm (ALBGA) is proposed to generate collaborative surgery schedules. In addition to traditional genetic operators, ALBGA also applies an adaptive learning operator to enhance the search ability by mimicking human learning behaviours. Computational results on both small-sized and large-sized test problems show that ALBGA is competitive among the compared algorithms.

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.

Evaluation of Operating Room Scheduling Processes by Analytic Network Process Method

Multiple performance criteria should be evaluated together in the operating room schedules. Therefore, the operating room scheduling problem is a complex and difficult problem. As a result, it is very difficult to get the best solution, even high-quality solutions, at a reasonable time. For this reason, the evaluation of the criteria that are effective in the scheduling and planning process of the operating room has been discussed. In this study, the analytical network process method which is one of multi-criteria decision-making methods has been used. Because this method considers the interaction of the criteria with each other and their relationships and dependencies. There are 24 sub-criteria under the 7 main criteria related to surgeons, operating room schedules, operating room resources, equipment and consumables, operating room staff, patients and other factors. The network structure of these criteria is created with the analytical network process method. Then, the significance levels of the criteria have been calculated. From the results obtained, the criteria for surgeons among the main criteria is in the foreground. The results show that resources in operating rooms should be used effectively. Therefore, it is necessary to pay attention to use resources effectively in the operating room scheduling processes.

Hibrit Genetik Algoritma Kullanarak Ameliyat Odası Çizelgeleme

Hospitals are among the most important institutions of today. For hospitals, efficient use of operating rooms is of great importance. Efficient use of operating rooms is a problem that needs to be solved. The operating room scheduling problem is a very complex problem with large number of constraints. This type of problem called as NP-Hard type problem. NP-Hard type problems do not consist of polynomial values. Therefore, the solution of these problems is very complex and difficult. Solutions consisting of polynomial values can be solved effectively with existing mathematical methods. However, more effective algorithms were needed to solve NP-hard type problems. As a result of the studies, many heuristic, meta-heuristic algorithms such as Genetic Algorithm, Particle Swarm Optimization, Simulated Annealing, Taboo Search Algorithm have been developed to solve the complexity of NP-Hard problems. In this article, the operating room scheduling problem solved with a hybrid genetic algorithm. In this solution, it shows how the algorithm affects the solution area in the changes in the number of surgeons, operating rooms and operating room reservations, which are among the operating room parameters. In the developed software, C# programming language has been preferred in order to provide comfortable use of the end user.

Operating Room Scheduling Optimization Based on a Fuzzy Uncertainty Approach and Metaheuristic Algorithms

Today, planning and scheduling problems are the most significant issues in the world and make a great impact on improving organizational productivity and serving systems such as medical and healthcare providers. Since operating room planning is a major problem in healthcare organizations, the optimization of medical staff and equipment plays an essential role. Thus, this study presents a multi-objective mathematical model with a new categorization (preoperative, intraoperative, and postoperative) to minimize operating room scheduling and the risk of using equipment. Time constraints in healthcare systems and medical equipment limited capacity are the most significant considered limitation in the present study. In this regard, since the duration of patient preparation and implementation of treatment processes occur in three states of optimistic, pessimistic, and normal, the introduced parameters are examined relying on a fuzzy uncertainty analysis of the problem. Hence, the model is measured in a real numerical solution sample in a medical center to evaluate and confirm the proposed mathematical model. Then, two meta-heuristic algorithms (NRGA and NSGAII) are implemented on the mathematical model to analyze the proposed model. Finally, the research results indicate that the NSGA-II is more efficient in the operating room scheduling problem.

Dealing with uncertain surgery times in operating room scheduling

The operating theater is one of the most expensive units in the hospital, representing up to 40% of the total expenses. Because of its importance, the operating room scheduling problem has been addressed from many different perspectives since the early 1960s. One of the main difficulties that has reduced the applicability of the current results is the high variability in surgery duration, making schedule recommendations hard to implement.In this work, we propose a time-indexed scheduling formulation to solve the operational problem. Our main contribution is that we propose the use of chance constraints related to the surgery duration’s probability distribution for each surgeon to improve the scheduling performance. We show how to implement these chance constraints as linear ones in our time-indexed formulation, enhancing the performance of the resulting schedules significantly.Through data analysis of real historical instances, we develop specific constraints that improve the schedule, reducing the need for overtime without affecting the utilization significantly. Furthermore, these constraints give the operating room manager the possibility of balancing overtime and utilization through a tuning parameter in our formulation. Finally, through simulations and the use of real instances, we report the performance for four different metrics, showing the importance of using historical data to get the right balance between the utilization and overtime.

Increased Surgical Capacity without Additional Resources: Generalized Operating Room Planning and Scheduling

We study a generalized operating room planning and scheduling (GORPS) problem at the Toronto General Hospital (TGH) in Ontario, Canada. GORPS allocates elective patients and resources (i.e., operating rooms, surgeons, anesthetists) to days, assigns resources to patients, and sequences patients in each day. We consider patients’ due‐date, resource eligibility, heterogeneous performances of resources, downstream unit requirements, and lag times between resources. The goal is to create a weekly surgery schedule that minimizes fixed‐ and over‐time costs. We model GORPS using mixed‐integer and constraint programming models. To efficiently and effectively solve these models, we develop new‘ multi‐featured logic‐based Benders decomposition approaches. Using data from TGH, we demonstrate that our best algorithm solves GORPS with an average optimality gap of 2.71% which allows us to provide our practical recommendations. First, we can increase daily OR utilization to reach 80%—25% higher than the status quo in TGH. Second, we do not require to optimize for the daily selection of anesthetists—this finding allows for the development of effective dominance rules that significantly mitigate intractability. Third, solving GORPS without downstream capacities (like many papers in literature) makes GORPS easier to solve, but such OR schedules are only feasible in 24% of instances. Finally, with existing ORs’ safety capacities, TGH can manage 40% increase in its surgical volumes. We provide recommendations on how TGH must adjust its downstream capacities for varying levels of surgical volume increases (e.g., current urgent need for more capacity due to the current Covid‐19 pandemic).

Operating Room (Re)Scheduling with Bed Management via ASP

AbstractThe Operating Room Scheduling (ORS) problem is the task of assigning patients to operating rooms (ORs), taking into account different specialties, lengths, and priority scores of each planned surgery, OR session durations, and the availability of beds for the entire length of stay (LOS) both in the Intensive Care Unit (ICU) and in the wards. A proper solution to the ORS problem is of primary importance for the healthcare service quality and the satisfaction of patients in hospital environments. In this paper we first present a solution to the problem based on Answer Set Programming (ASP). The solution is tested on benchmarks with realistic sizes and parameters, on three scenarios for the target length on 5-day scheduling, common in small–medium-sized hospitals, and results show that ASP is a suitable solving methodology for the ORS problem in such setting. Then, we also performed a scalability analysis on the schedule length up to 15 days, which still shows the suitability of our solution also on longer plan horizons. Moreover, we also present an ASP solution for the rescheduling problem, that is, when the offline schedule cannot be completed for some reason. Finally, we introduce a web framework for managing ORS problems via ASP that allows a user to insert the main parameters of the problem, solve a specific instance, and show results graphically in real time.

Solving Operating Room Scheduling Problem Using Artificial Bee Colony Algorithm

Many healthcare institutions are interested in reducing costs and in maintaining a good quality of care. The operating room department is typically one of the most costly units in a hospital. Hospital managers are always interested in finding effective ways of using operating rooms to minimize operating costs. In this research, we study the operating room scheduling problem. We consider the use of a weekly surgery schedule with an open scheduling strategy that takes into account the availabilities of surgeons and operating rooms. The objective is to minimize the total operating cost while maximizing the utilization of the operating rooms but also minimizing overtime use. A revised mathematical model is proposed that can provide optimal solutions for a surgery size up to 110 surgical cases. Next, two modified heuristics, based on the earliest due date (EDD) and longest processing time (LPT) rules, are proposed to quickly find feasible solutions to the studied problem. Finally, an artificial bee colony (ABC) algorithm that incorporates the initial solutions, a recovery scheme, local search schemes, and an elitism strategy is proposed. The computational results show that, for a surgery size between 40 and 100 surgical cases, the ABC algorithm found optimal solutions to all of the tested problems. For surgery sizes larger than 110 surgical cases, the ABC algorithm performed significantly better than the two proposed heuristics. The computational results indicate that the proposed ABC is promising and capable of solving large problems.

Vehicle Routing Problems with Synchronized Visits and Stochastic Travel and Service Times: Applications in Healthcare

This paper, for the first time, studies vehicle routing problems with synchronized visits (VRPS) and stochastic travel and service times. In addition to considering a home healthcare scheduling problem, we introduce an operating room scheduling problem with stochastic durations as a novel application of VRPS. We formulate VRPS with stochastic times as a two-stage stochastic integer programming model that, unlike the deterministic models in the VRPS literature, does not have any big-M constraints. This advantage comes at the cost of a large number of second-stage integer variables. We prove that the integrality constraints on second-stage variables can be relaxed, and therefore, we can apply the L-shaped algorithm and its branch-and-cut implementation to solve the problem. We enhance the model by developing valid inequalities and a lower bounding functional. We analyze the subproblems of the L-shaped algorithm and devise a specialized algorithm for them that is significantly faster than standard linear programming algorithms. Computational results show that the branch-and-cut algorithm optimally solves stochastic home healthcare scheduling instances with 15 patients and 10%–30% of synchronized visits. It also finds solutions with an average optimality gap of 3.57% for instances with 20 patients. Furthermore, the branch-and-cut algorithm optimally solves stochastic operating room scheduling problems with 20 surgeries.

Modeling patient preference in an operating room scheduling problem

When a patient needs plastic surgery and there are multiple available surgeons, the patient selects the surgeon based on different criteria. Accommodating patient preference while scheduling such surgeries is important as it is related to patient satisfaction. In this study, we propose a framework for integrating patient preference in an operating room (OR) scheduling problem. To model patient preference to a surgeon, we propose nine criteria: responsive and caring, reputation, professional experiences, communication skills, same ethnicity, same gender, age, same language, and online rating. Fuzzy TOPSIS (namely, Technique for Order of Preference by Similarity to Ideal Solution) is then employed to quantify patient preference to surgeons. The outcomes of fuzzy TOPSIS are then fed into a multi-objective mixed-integer linear programming (MILP) model to optimize daily surgery schedule. The proposed study is based on a real-life case study that was conducted in a plastic surgery department at a partner hospital. The computational results show that when patient preference to surgeon is considered, more than 70% of patients are assigned to their most preferred surgeons, and less than 5% are assigned to their least preferred surgeons. However, when patient preference is not considered, less than 20% of patients are assigned to most preferred surgeons, and the others are assigned to less preferred surgeons. When it comes to the total costs, the two scenarios results are similar. This concludes that the proposed framework is robust and able to increase patient satisfaction in OR scheduling without sacrificing the total OR operational costs.

A Comprehensive Review and Analysis of Operating Room and Surgery Scheduling

A comprehensive review and analysis of operating room (OR) theatre scheduling problems as well as a comparison of solution approaches along with suggestions for future studies are presented in this work. A detailed scientometric analysis was performed, which is a powerful tool for conducting bibliometric analyses and comprehensive reviews. OR scheduling problems were categorized into three decision levels, including strategical, tactical, and operational levels. Since optimization of OR problems is an NP-hard optimization problem, we evaluated research studies that employed different mathematical and metaheuristic methods to address OR optimization problems. The comprehensive review presented in this work is divided into two sections. The first section is focused on mathematical modeling, including deterministic and uncertainty modeling, and the second section is focused on solution approaches. The latter section reviews single and multi-objective solution methods. An additional section of this paper is focused on application software that are developed to address the previously mentioned problems. The final section of the paper presents conclusions of this work.

A simulated annealing for a daily operating room scheduling problem under constraints of uncertainty and setup

This article addresses the daily scheduling of surgeries in an operating theatre. The problem consists of a set of surgical operations that have to be scheduled in identical operating rooms. The operations have uncertain durations, require setup activities before and after the surgical act and are assigned to surgeons who have to perform the surgical part. The objective is to find the best sequence of operations in each room in order to minimize the theatre’s opening duration (makespan) and the surgeons’ waiting times. A stochastic mathematical model and a simulated annealing-based algorithm, where the uncertainty is represented using the sample average approximation technique, are provided. An experimental study carried out on real-sized instances shows that the method’s solutions have respectable relative gaps in comparison with lower bounds and optimal solutions.

A Two-Stage Approach for Resource Allocation and Surgery Scheduling With Assistant Surgeons

The high costs of operating rooms (ORs) make surgery scheduling decisions critical for hospitals, which refer to resource allocations and determining the start time of each surgery. We take into account an important issue that could affect surgery scheduling decisions, ie., assistant surgeons. The operating room scheduling problem is considered as a two-stage problem. The first stage refers to resource allocations, including allocating surgeries into ORs and assigning assistant surgeons to surgeries, while the start time of each surgery is determined in the second stage. The robustness of the model is considered in a tractable way. We develop a bound-based algorithm to solve the model with the objective of minimising the total cost in the two stages. Numerical studies show the good performances of the proposed algorithm. Sensitivity analysis is conducted to examine the effects of the key parameters. An easy-to-implement policy for decisions in the first stage is inspired by the results of the experiments.