## 4 Computational Experiments
### Results  
To validate our developed method, computational experiments are performed with different problem sizes and surgery durations. The arrival pattern for the ICU and ward is kept variable to generate scenarios of bottleneck resources among the operating room, ICU, and ward. As a first step, the patients are inserted into higher-level planning horizons based on their planned start time for the operating room and their arrival time for both the ICU and ward. After the higher-level of planning, the patients are allocated to different resources based on their requirements during their stay in the hospital. After the allocation of patients to all resources, based on the workload and utilization of the resources such as the operating room, ICU, and ward, the bottleneck resource with the highest utilization is identified. After identifying the bottleneck resource, the lower-level planning model for the bottleneck resource is run, and the schedule obtained is sent through a rope to be followed by the upstream departments. Table 4 represents the summary of results with average values for all samples based on the percentage utilization when the operating room, ICU, and ward are identified as a bottleneck. The resource with the highest percentage utilization is the bottleneck resource. The percentage utilization is related to the idle time as given in Equation (58) where _Idle_% is the percentage idleness of the resource. As the percentage utilization increases, the idle time decreases, which in turn leads to cost savings. \[Idle\%=1-UTL\% \tag{58}\]  
When the operating room is the bottleneck resource, the operating room's lower-level plan is operated, patients are allocated to operating rooms, and the optimal sequence of operating rooms is identified to minimize the makespan for all operating rooms. Table 5 represents the summary results of the lower-level plan when the operating room is the bottleneck resource. When the optimal sequence of patients in operating rooms is obtained, this sequence is followed by the ICU and ward such that the arrival times of patients in the ICU and ward are scheduled after the discharge times of patients from the operating room as represented by Equations (46) and (47). Table 6 represents the summary results of the lower-level plan when the ICU is identified as the bottleneck resource. When ICU becomes the bottleneck resource, the lower-level plan for the ICU is made, and it is followed by both the operating room and ward such that for the operating room, the discharge time of patients from the \begin{table}
\begin{tabular}{l l l} \hline \hline
**Problem Size** & **Poisson \(\lambda\) for ICU** & **Poisson \(\lambda\) for ward** \\ \hline Small & 2–3 & 5–6 \\ Medium & 5–7 & 10–12 \\ Large & 10–12 & 15–17 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Value of \(\lambda\) for different problem sizes. operating room is planned before the arrival time of the patients in the ICU as explained in Equation (49). In the same way, the patient's arrival time in the ward is planned after the patient's discharge from the ICU as given by Equation (50). Table 7 represents the summary results of the lower-level plan when the ward is the bottleneck resource.