Using mixed integer programming and constraint programming for operating rooms scheduling with modified block strategy

Operating room (OR) planning and scheduling is a highly complex combinatorial optimization problem that involves patient assignment, OR allocation, and surgical sequencing within a constrained planning horizon. This study addresses the OR scheduling problem by incorporating downstream bed availability in both hospital wards and intensive care units (ICUs), aiming to improve operational efficiency and patient outcomes. A mixed-integer programming (MIP) model is developed to minimize the total completion time across all operating rooms during the planning period. Given the NP-hard nature of the problem, a novel Genetic Engineering Algorithm (GEA) is proposed as an advanced extension of the traditional Genetic Algorithm (GA). The GEA incorporates three innovative search strategies inspired by genetic engineering principles, refining the crossover and mutation operators to improve solution quality and convergence speed. To evaluate the effectiveness of the proposed algorithm, GEA and its variants are tested on 18 benchmark instances of varying problem sizes for the proposed OR planning and scheduling problem. A real-world case study from a hospital in Pakistan illustrates the practical applicability of the proposed approach using different real-world criteria. The results demonstrate that GEA consistently outperforms state-of-the-art metaheuristic algorithms. Its robustness and accuracy are further validated using 10 standard mathematical benchmark functions. The results confirm the GEA’s effectiveness and efficiency in addressing complex OR planning and scheduling problems and underscore its potential for advancing metaheuristic algorithm design in combinatorial optimization.

Operating Room (OR) scheduling is crucial to allow efficient use of ORs. Currently, the predicted durations of surgical procedures are unreliable and the OR schedulers have to follow the progress of the procedures in order to update the daily planning accordingly. The OR schedulers often acquire the needed information through verbal communication with the OR staff, which causes undesired interruptions of the surgical process. The aim of this study was to develop a system that predicts in real-time the remaining procedure duration and to test this prediction system for reliability and usability in an OR. The prediction system was based on the activation pattern of one single piece of equipment, the electrosurgical device. The prediction system was tested during 21 laparoscopic cholecystectomies, in which the activation of the electrosurgical device was recorded and processed in real-time using pattern recognition methods. The remaining surgical procedure duration was estimated and the optimal timing to prepare the next patient for surgery was communicated to the OR staff. The mean absolute error was smaller for the prediction system (14 min) than for the OR staff (19 min). The OR staff doubted whether the prediction system could take all relevant factors into account but were positive about its potential to shorten waiting times for patients. The prediction system is a promising tool to automatically and objectively predict the remaining procedure duration, and thereby achieve optimal OR scheduling and streamline the patient flow from the nursing department to the OR.

Operating room (OR) scheduling is a critical challenge in healthcare, directly impacting patient outcomes and hospital efficiency. Traditional methods often struggle with the complex, multi-level constraints and uncertainties inherent in OR scheduling, such as resource limitations, variable surgery durations, and emergency cases. This study aims to develop a novel hybrid framework that optimizes OR scheduling by integrating multi-level optimization with reinforcement learning and column generation techniques. The proposed framework decomposes the OR scheduling problem into strategic, tactical, and operational levels, enabling focused optimization at each layer while ensuring cohesive decision-making across the hierarchy. Reinforcement learning guides the column generation process, learning policies that identify promising scheduling options to enhance solution quality and computational efficiency. Robust uncertainty handling mechanisms are incorporated to manage variability in surgery durations and resource availability without compromising tractability. Experiments were conducted using three years of real-world data from Shanxi Provincial People's Hospital, complemented by large-scale synthetic datasets to evaluate scalability and robustness of the framework. The framework demonstrates meaningful improvements in key operational metrics compared to traditional approaches. Analysis of three years of implementation shows consistent enhancements in operational efficiency, including a reduction in average patient waiting time by 15.8% (from 10.1 to 8.5 days), an increase in OR utilization by 5.4 percentage points (from 73.8% to 79.2%), and improved workload balance among surgeons. The framework maintains robust performance under uncertainty, achieving a 92.5% feasibility rate and reducing schedule disruptions by 26.2%. The proposed hybrid framework offers a practical and scalable solution for optimizing OR scheduling, demonstrating improvements in healthcare delivery and operational performance in real hospital environments. By effectively balancing multiple operational objectives while handling practical constraints and uncertainties, the framework provides a viable approach for healthcare systems seeking incremental yet sustainable improvements in efficiency and patient care.

Designing a new operating room (OR) suite is a difficult process owing to the number of caregivers involved and because decision-making managers try to minimize the direct and indirect costs of operating the OR suite. In this study, we devised a computer simulation flow model to calculate, first, the minimum number of beds required in the postanesthesia care unit (PACU). In a second step, we evaluated the relationship between the global performance of the OR suite in terms of OR scheduling and number of staffed PACU beds and porters. We designed a mathematical model of OR scheduling. We then developed a computer simulation flow model of the OR suite. Both models were connected; the first one performed the input flows, and the second simulated the OR suite running. The simulations performed examined the number of beds in the PACU in an ideal situation or in the case of reduction in the number of porters. We then analyzed the variation of number of beds occupied per hour in the PACU when the time spent by patients in the PACU or the number of porters varied. The results highlighted the strong impact of the number of porters on the OR suite performance and particularly on PACU performances. Designing new operating room (OR) facilities implies many decisions on the number of ORs, postanesthesia care unit (PACU) beds, and on the staff of nurses and porters. To make these decisions, managers can use rules of thumb or recommendations. Our study highlights the interest of using flow simulation to validate these choices. In this case study we determine the number of PACU beds and porter staff and assess the impact of decreasing the number of porters on PACU bed requirements.

Maximizing Operating Room Performance Using Portfolio Selection

It may be very difficult to achieve the optimal shift schedule in call centers which have highly uncertain and peaked demand during short time periods. Overlapping shift systems are usually designed for such cases. This paper studies shift scheduling and rostering problems for inbound call centers where overlapping shift systems are used. An integer programming model that determines which shifts to be opened and how many operators to be assigned to these shifts is proposed for the shift scheduling problem. For the rostering problem both integer programming and constraint programming models are developed to determine assignments of operators to all shifts, weekly days-off, and meal and relief break times of the operators. The proposed models are tested on real data supplied by an outsource call center and optimal results are found in an acceptable computation time. An improvement of 15% in the objective function compared to the current situation is observed with the proposed model for the shift scheduling problem. The computational performances of the proposed integer and constraint programming models for the rostering problem are compared using real data observed at a call center and simulated test instances. In addition, benchmark instances are used to compare our Constraint Programming (CP) approach with the existing models. The results of the comprehensive computational study indicate that the constraint programming model runs more efficiently than the integer programming model for the rostering problem. The originality of this research can be attributed to two contributions: (a) a model for shift scheduling problem and two models for rostering problem are presented in detail and compared using real data and (b) the rostering problem is considered as a task-resource allocation and considerably shorter computation times are obtained by modeling this new problem via CP.

Optimizing Operating Room Scheduling

Objective:This study examines the 2009 patient operating room (OR) length of stay data for a medical center in Taipei City. Using a statistical method based on regression analysis, the crucial factors that influence OR efficiency and performance were identified. The analytical results indicated that surgical procedures with general anesthesia and high surgical complexity incurred high surgical fees. Additionally, the anesthesia fees, operating time, and operating time variance rises as the squared number of surgical procedures increases. Therefore, for the hospitals 2010 OR scheduling management strategy, we adjusted the priority regulations for daily OR use to enhance the safety and quality of surgical patient health care and improve OR efficiency.Method:We collected 11 case ORs, that is, 9 inpatient and 2 outpatient ORs, for this study. The pre-implementation data were collected between January 1, 2009, and December 31, 2009. The post-implementation data were collected between January 1, 2010, and December 31, 2010; both forms of data included patients OR length of stay information. Furthermore, the indicators that were compared and analyzed for this study included variances in the number of cases in which general anesthesia was administered, the number of scheduled surgical procedures, the number of emergency surgical procedures, and OR use rates.Results:A total of 20,731 surgical operations were performed in 2009, among which general anesthesia was administered 6,925 times, 10,122 scheduled surgical procedures were performed, 1,305 emergency surgical procedures were performed, and the OR use rate was 70.30%. A total of 21,105 surgical operations were performed in 2010, among which general anesthesia was administered 7,106 times, 10,549 scheduled surgical procedures were performed, 1,319 emergency surgical procedures were performed, and the OR use rate was 71.05%.

The surgery department is required to improve its performance by efficient usage of its available resources. Surgery department interdependencies with other hospital functions and departments are numerous and complex, which causes some restrictions on surgery ward performance and consequently hospital performance. Operating room (OR) schedule determines day to day operations that take a place at the surgery department. Creating such a schedule is a complex task, due to a multitude of constraints, preferences and objectives that planners need to take into account. Meanwhile, the schedule has major effects on the performance of surgery department and the hospital. This paper provides a review of recent operational research on operating room planning and scheduling with focus on multi-objective simulation optimization with use meta-heuristic method: in operating room, as a practical suggestion for hospitals. Recent researches were collected based on some keywords including simulation optimization, and operating room by google scholar, Scopus, and Pubmed. The findings showed that, there are not much practical suggestion in this case and still there is a gap and needs to be discovered.

Enhancement opportunities in operating room utilization; with a statistical appendix

We solve the flexible job shop scheduling problems (F-JSSPs) to minimize makespan. First, we compare the constraint programming (CP) model with the mixed-integer programming (MIP) model for F-JSSPs. Second, we exploit the decomposable structure within the models and develop an efficient CP–logic-based Benders decomposition (CP-LBBD) technique that combines the complementary strengths of MIP and CP models. Using 193 instances from the literature, we demonstrate that MIP, CP, and CP-LBBD achieve average optimality gaps of 25.50%, 13.46%, and 0.37% and find optima in 49, 112, and 156 instances of the problem, respectively. We also compare the performance of the CP-LBBD with an efficient Greedy Randomized Adaptive Search Procedure (GRASP) algorithm, which has been appraised for finding 125 optima on 178 instances. CP-LBBD finds 143 optima on the same set of instances. We further examine the performance of the algorithms on 96 newly (and much larger) generated instances and demonstrate that the average optimality gap of the CP increases to 47.26%, whereas the average optimality of CP-LBBD remains around 1.44%. Finally, we conduct analytics on the performance of our models and algorithms and counterintuitively find out that as flexibility increases in data sets the performance CP-LBBD ameliorates, whereas that of the CP and MIP significantly deteriorates.

In this study, the U-type assembly line balancing problem (UALBP) with assignment restrictions (AR-UALBP) is considered. Linked and incompatible distance and station restrictions are taken into account. New mathematical programming (MP) and constraint programming (CP) models are proposed. The objective function of the models is minimizing the cycle time for a given number of workstations. In addition to this objective, line efficiency and CPU time are also considered as other performance measurements. Numerical experiments on some problems from the literature are performed to evaluate the effectiveness of the proposed models. The results are compared with the results of the CP model of the straight ALBP with assignment restrictions and also the results from MP and CP models are compared with each other. The numerical results indicate that the proposed CP and MP models are more effective in obtaining better and optimal results when solving the AR-UALBP.

Traditional vehicle routing problems implicitly assume that only one crew operates a vehicle for the entirety of its journey. However, this assumption is violated in many applications arising in humanitarian and military logistics. This paper considers a joint vehicle and crew routing and scheduling problem in which crews are able to interchange vehicles, resulting in space and time interdependencies between vehicle routes and crew routes. The problem is formulated as a mixed integer programming (MIP) model and a constraint programming (CP) model that overlay crew routing constraints over a standard vehicle routing problem. The constraint program uses a novel optimization constraint to detect infeasibility and to bound crew objectives. This paper also explores methods using large neighborhood search over the MIP and CP models. Experimental results indicate that modeling the vehicle and crew routing problems jointly and supporting vehicle interchanges for crews may bring significant benefits in cost reduction compared with a method that sequentializes these decisions.

Creutzfeldt-Jakob Disease Operating Room Protocols: Turning Published Recommendations into Reality

We develop algorithms for a stochastic two-machine single-server sequencing problem with waiting time, idle time and overtime costs. Scheduling surgeries for a single surgeon operating in two parallel operating rooms (ORs) motivates the work. The basic idea is that staff perform cleanup and setup in one OR while the surgeon is operating in the other. The benefit is less waiting time for the surgeon between surgeries, but may also result in added idle time for staff if cleanup and set-up are completed prior to completion of surgery in the other OR. When surgeries are long relative to cleanup and setup times, parallel OR scheduling is not attractive as significant OR and staff idle time will result. The problem we address consists of assigning surgeries to ORs and sequencing them, and is formulated as an integer stochastic program using sample average approximation. A decomposition based solution approach is developed. Computational testing based on real data shows that the proposed methods solve the problems to optimality in acceptable processing times. Using the solution methodology, we conduct additional experiments to provide insight as to the conditions when scheduling a single surgeon in parallel operating rooms is cost effective.