## 4 Computational Experiments
### Results
\begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline
**Problem** & **Surgery** & **No. of Patients** & **Workload** & **Utilization** & **No. of Patients** & **Utilization** & **No. of Patients** & **Utilization** \\
**Size** & **Duration** & **in the OR** & **of OR** & **of OR** & **in the ICU** & **of ICU** & **in the Ward** & **of Ward** \\ \hline \hline \multicolumn{10}{c}{The operating room becomes a Bottleneck} \\ \hline Small & Small & 16 & 1695 & 93\% & 5 & 60\% & 22 & 72\% \\ Small & Medium & 11 & 1452 & 84\% & 5 & 59\% & 10 & 66\% \\ Small & Large & 9 & 1413 & 76\% & 5 & 58\% & 18 & 61\% \\ Medium & Small & 33 & 3542 & 92\% & 8 & 69\% & 41 & 82\% \\ Medium & Medium & 22 & 3017 & 83\% & 8 & 68\% & 36 & 73\% \\ Medium & Large & 21 & 3190 & 84\% & 9 & 72\% & 36 & 71\% \\ Large & Small & 43 & 4905 & 87\% & 11 & 71\% & 61 & 68\% \\ Large & Medium & 35 & 5067 & 88\% & 12 & 72\% & 59 & 66\% \\ Large & Large & 28 & 5188 & 90\% & 11 & 70\% & 67 & 75\% \\ \hline \multicolumn{10}{c}{ICU becomes Bottleneck} \\ \hline Small & Small & 12 & 1397 & 79\% & 7 & 87\% & 21 & 71\% \\ Small & Medium & 9 & 1224 & 71\% & 7 & 90\% & 19 & 63\% \\ Small & Large & 9 & 1302 & 74\% & 7 & 88\% & 21 & 69\% \\ Medium & Small & 26 & 2933 & 76\% & 11 & 92\% & 37 & 75\% \\ Medium & Medium & 20 & 2882 & 76\% & 11 & 91\% & 34 & 68\% \\ Medium & Large & 17 & 3155 & 82\% & 11 & 91\% & 34 & 68\% \\ Large & Small & 33 & 3843 & 68\% & 15 & 91\% & 68 & 76\% \\ Large & Medium & 28 & 3947 & 71\% & 15 & 95\% & 63 & 70\% \\ Large & Large & 22 & 4023 & 70\% & 15 & 91\% & 63 & 70\% \\ \hline \multicolumn{10}{c}{Ward becomes Bottleneck} \\ \hline Small & Small & 14 & 1550 & 85\% & 6 & 70\% & 28 & 94\% \\ Small & Medium & 10 & 1360 & 71\% & 5 & 59\% & 28 & 92\% \\ Small & Large & 7 & 1313 & 68\% & 5 & 68\% & 27 & 91\% \\ Medium & Small & 23 & 2617 & 71\% & 8 & 66\% & 45 & 90\% \\ Medium & Medium & 20 & 2901 & 76\% & 9 & 71\% & 43 & 87\% \\ Medium & Large & 16 & 2877 & 75\% & 8 & 70\% & 43 & 86\% \\ Large & Small & 34 & 3919 & 73\% & 12 & 76\% & 82 & 91\% \\ Large & Medium & 28 & 4017 & 74\% & 11 & 72\% & 82 & 91\% \\ Large & Large & 23 & 4151 & 74\% & 12 & 77\% & 85 & 94\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of results. \begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline \multirow{2}{*}{**PS**} & \multirow{2}{*}{**SD**} & \multicolumn{2}{c}{**Operating Room**} & \multicolumn{2}{c}{**ICU**} & \multicolumn{2}{c}{**Ward**} & \\ \cline{3-10}  & & **PP** & **Makespan** & **POR** & **OB** & **EP** & **POR** & **PICU** & **OB** & **EP** \\ \hline Small & Small & 16 & 1347 & 1 & 2 & 2 & 15 & 0 & 4 & 3 \\ Small & Medium & 11 & 1242 & 1 & 2 & 2 & 10 & 1 & 5 & 4 \\ Small & Large & 9 & 1386 & 0 & 2 & 2 & 8 & 1 & 5 & 4 \\ Medium & Small & 33 & 2858 & 2 & 1 & 5 & 31 & 0 & 0 & 10 \\ Medium & Medium & 22 & 2624 & 1 & 4 & 4 & 21 & 1 & 4 & 11 \\ Medium & Large & 21 & 2620 & 1 & 3 & 5 & 20 & 1 & 4 & 11 \\ Large & Small & 43 & 3930 & 2 & 1 & 8 & 41 & 2 & 2 & 16 \\ Large & Medium & 35 & 4710 & 2 & 1 & 9 & 33 & 1 & 11 & 14 \\ Large & Large & 28 & 4521 & 1 &When the ward becomes the bottleneck resource, the lower-level plan for the ward is made, and it is followed by both the operating room and ICU such that for the operating room, the discharge time of patients from the operating room is planned before the arrival time of the patients in the ward, as explained in Equation (52). In the same way, the patient's discharge time from ICU is planned before the patient's arrival time in the ward as given by Equation (53). The average CPU time in seconds for each category of problem for one planning horizon is shown in Figure 6. The CPU time is proportional to the size of the problem in cases when the operating room and ward are the bottlenecks. While in the scenario where the ICU is the bottleneck, the trend in the CPU time for the medium-sized problem is random. It is proposed that the CPU time can be reduced using heuristic algorithms without compromising the solution's optimality.