## 5 Conclusions, Limitations, and Future Research  
The planning and scheduling of hospital resources are significant for better service and profit generation. The current research proposed an integrated planning and scheduling problem at different levels for operating rooms, intensive care units, and recovery wards. The theory of constraints was applied, and a mixed integer linear programming model was developed for the integrated planning and scheduling of the operating room, considering the constraints of the downstream ward. Different models for planning and scheduling were made considering the shifting of the bottleneck resources of hospitals. The integrated models for planning at different levels when any one resource such as the operating room, ICU, or ward becomes a bottleneck were proposed for the first time in the literature. The proposed model for integrated planning and scheduling was solved using the CPLEX solver on different sizes of test problems. The small, medium, and large-sized test problems were made for each scenario where the operating room, ICU, or ward became the bottlenecked resource.  
The proposed model is significant for hospitals for effective and efficient planning and scheduling of their resources. This approach has practical significance in a hospital where the whole system's performance is affected by one bottleneck which keeps changing in different planning horizons. Planning based on the capacity of the bottleneck resource subordinates the rest of the resources to the bottleneck resource to achieve optimal hospital performance. The theory of constraints is significant to identify the bottleneck resource among all the critical resources of the hospital. Therefore, the mathematical models developed using the theory of constraints in the current study can be used to develop hospital planning systems in which planning is based on the capacity of bottleneck resources.  
Figure 6: CPU time for each category of problem: (**a**) operating room is the bottleneck, (**b**) ICU is the bottleneck, and (**c**) ward is the bottleneck.  
The current study has its limitation in using the CPLEX solver, which provides an exact method to solve the mathematical models. In the future, constraint-based heuristics can be developed to reduce the CPU time of the different sizes of the considered problems, particularly for larger-sized instances. In addition, the current study uses deterministic surgery durations and lengths of stay in downstream units. Further extension of the work includes the use of data mining and machine learning methods to predict patient arrivals and length of stay in the operating room and downstream units and using the predicted data as the inputs in the models developed in the current study.  
Conceptualization and supervision, S.U.; methodology, A.T.; validation, A.T. and T.M.; formal analysis, A.T.; writing--original draft preparation, A.T.; writing--review and editing, A.T., T.M., Y.Y.G., B.L. and H.A.; funding acquisition, H.A. All authors have read and agreed to the published version of the manuscript.  
Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2023R54), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.  
Not applicable.  
The study did not involve humans.  
The data used to support the findings of the study are available from the first author upon request.  
The authors are grateful to the Department of Industrial Engineering, University of Engineering and Technology, Taxila.  
The authors declare that they have no conflict of interest to report regarding the present study.