Multi-objective planning and scheduling of operating rooms and sterile section reusable surgical devices with a scenario-based robust optimization approach

Abstract

Planning and scheduling operating rooms and required equipment is very important for hospital managers from the perspective of cost, social, and health principles. Because operating rooms are one of the sources of income for hospitals that can provide the services needed by emergency patients who arrive randomly and elective patients whose surgery is preplanned. Since some tools used in operating rooms need to be sterilized each time, and in the real world, due to various reasons such as the physical condition of each patient, the duration of surgeries is uncertain, in this research, as well as considering the uncertainty of surgery times for emergency and elective patients, a robust scenario-based integrated mathematical model with two objective functions is presented. In this model, in addition to minimizing the cost of operating rooms, sterile section, and penalties for delay in surgery, the competition time of the last operation is minimized. Solving several problems and different sensitivity analyses confirmed the validation of the presented model from the viewpoint of the hospital managers. Introduction The healthcare system is one of the most important topics that has attracted the attention of researchers and hospital managers. Two significant elements of healthcare systems are patients and hospitals, and their planning and scheduling are necessary for providing better services. Hospital managers aim to minimize costs or maximize profits while considering service times. Operating rooms are often the most critical sections of the hospital. Since life and death issues are at stake in the operating rooms, even the slightest delay or lack of resources can endanger human lives. Therefore, careful planning and scheduling of operating rooms and their resources is especially important. Additionally, to prevent potential hospital infections, the sterilization of reusable medical instruments is essential for every operation. Furthermore, patients can be broadly categorized into two groups: emergency patients who arrive randomly, and elective patients whose surgeries are preplanned. Planning and scheduling operating rooms, along with the required equipment, is of utmost importance for hospital managers, taking into account cost, social factors, and health considerations. Some items used in operating rooms need to be sterilized after each use, which incurs both time and cost. Methodology Due to high fluctuations of the duration of surgery, the different condition of each patient, and in order to get as close as possible to the real conditions, the duration of each surgery is considered uncertain. In this research, in addition to considering selected patients, considering the uncertainty of the duration of surgery, emergency patients have also been investigated, and dealing with uncertainties, the robust optimization approach is used. This approach is stable against changes, and minimizes the fluctuation of changes and maintains optimal and feasible. Therefore, in this research, as well as considering the uncertainty of surgery times for emergency and elective patients, a robust scenario-based integrated mathematical model with two objective functions is presented. In this model, in addition to minimizing the cost of operating rooms, sterile section, and penalties for delay in surgery, the competition time of the last operation is minimized. There are costs for performing elective and emergency operations, and in order to give priority to emergency patients, the cost of performing the operation of these patients is lower than the cost of performing elective operations surgeries of emergency patients, such as those injured in accidents, must be performed as soon as possible and these patients should be paid less. Also, for emergency patients, a maximum waiting time is considered, which they should not wait more than it. Obviously, surgeries that cannot be scheduled during the working hours of the operating room are postponed. Every patient needs a number of reusable medical tools that require sterilization. The sterile duration of reusable tools and the capacity of each sterile machine are known. There are various techniques for solving multi-objective problems, one of which is the epsilon constraint method. In this method, one of the objective functions is considered as the main objective function and other objective functions are applied as constraints to the problem. Various developments for the epsilon constraint method have been presented to make it more efficient, among which we can mention the Augmented Epsilon Constrain (AEC) method. Moreover, in order to solve the bi-objective integrated mathematical model, Mulvey's robust method is implemented on the model, and its validation is carried out in the GAMS software with the AEC method. Results and Conclusion Different sensitivities all confirm the validity and accuracy of the model from the point of view of hospital managers. According to the obtained results, the changes of the three parameters of surgery delay cost, duration of surgery and sterile duration times have more effects on the both objective functions of the mathematical model than other parameters of the problem. Furthermore, the obtained results show that the first objective function, which includes the total cost, will have the highest value when the delay cost parameters and the duration of the surgical operations increase. For the second objective function, which shows the complete time of the last operation, the most challenging situation occurs when the parameters of the duration of surgical operations and the sterile duration increase. Therefore, the most ideal situation from the point of view of the hospital manager is to reduce all three parameters, which will reduce, the total cost and the completion time of the last operation; Moreover, the results show, the separate costs of planning and scheduling of the operating room and the sterile department are more than when the planning and scheduling of the operating rooms and the sterile department were examined in an integrated manner. The results of this research can be used for the integrated planning and scheduling of the operating rooms and sterilization department in all hospitals as a suitable management tool.

Keywords

• operating rooms
• sterilization section
• emergency operations
• elective operations
• robust optimization approach