## 4 Computational Experiments
### The Data  
For the arrival of elective surgery patients, it is assumed that the elective patients follow a discrete uniform distribution derived from historical data. The data collected from the case hospital consisted of 10,664 patients in operating rooms. Out of these patients, 95% require a ward after surgery and 5% require the ICU after surgery. For each type of patient, the underlying distribution is derived, and the number of patients for each type for the planning horizon is randomly generated using Equation (56) based on the relative frequencies of each type of patient in the historical data where \(NP_{e}\) is the total number of surgery patients of specialty, \(e\ NP\) is the total number of surgery patients for all specialties \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Problem Size** & **No. of OR** & **No. of Beds in ICU** & **No. of Beds in Ward** \\ \hline Small & 3–4 & 7–10 & 25–35 \\ Medium & 6–8 & 11–15 & 45–55 \\ Large & 10–12 & 16–18 & 80–100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the different-sized problems. in the considered planning horizon, and \(f_{e}\) is the frequency of patients for each specialty in the historical data. \[NP_{e}=f_{e}\times NP\ \forall e\in E \tag{56}\]  
The numerical experiments in this section were carried out on a laptop Intel(r) CoreTM i3-500 SU CPU @ 2.00 GHz with a memory of 8.0 GB. The developed models were implemented in the IBM ILOG CPLEX 12.10 optimization studio. Patient arrivals in the ICU and ward are assumed to follow a Poisson distribution with a known mean [1]. Patients' length of stay in the operating room, ICU, and ward follows lognormal distribution [9; 36]. The binomial distribution is used to find the number of patients visiting the ICU and ward after surgery. The probability that out of total surgery P patients who had surgery on a given day, the p patients in the ICU or ward can be calculated using the binomial distribution [57]. The formula for binomial distribution is given by Equation (57), where p is the probability that a patient will go to the ICU or ward after surgery. Using Equation (57), the number of patients from each specialty who will move to the ICU after surgery is determined. \[\Pr_{NP_{e}}=\binom{NP}{NP_{e}}p^{NP_{e}}q^{NP-NP_{e}} \tag{57}\]  
It is considered that 98% of the patients might follow one of the following paths after surgery. About 95% of patients are admitted to the ward before discharge and around 5% go to the ICU and ward before discharge. Only about 1% are discharged directly from the operating room [13; 37]. After generating the number of patients arriving and length of stay data in the operating room, ICU, and ward, the elective surgery patient list is generated by assigning random arrivals and due dates to the patients within the planning horizon. \begin{table}
\begin{tabular}{l l l l l} \hline
**Sr. No.** & **Problem Size** & **Surgery Duration** & **Bottleneck Resource** & **Number of Instances** \\ \hline
1 & Small & Small & OR & 10 \\
2 & Small & Medium & OR & 10 \\
3 & Small & Large & OR & 10 \\
4 & Small & Small & ICU & 10 \\
5 & Small & Medium & ICU & 10 \\
6 & Small & Large & ICU & 10 \\
7 & Small & Small & Ward & 10 \\
8 & Small & Medium & Ward & 10 \\
9 & Small & Large & Ward & 10 \\
10 & Medium & Small & OR & 10 \\
11 & Medium & Medium & OR & 10 \\
12 & Medium & Large & OR & 10 \\
13 & Medium & Small & ICU & 10 \\
14 & Medium & Medium & ICU & 10 \\
15 & Medium & Large & ICU & 10 \\
16 & Medium & Small & Ward & 10 \\
17 & Medium & Medium & Ward & 10 \\
18 & Medium & Large & Ward & 10 \\
19 & Large & Small & OR & 10 \\
20 & Large & Medium & OR & 10 \\
21 & Large & Large & OR & 10 \\
22 & Large & Small & ICU & 10 \\
23 & Large & Medium & ICU & 10 \\
24 & Large & Large & ICU & 10 \\
25 & Large & Small & Ward & 10 \\
26 & Large & Medium & Ward & 10 \\
27 & Large & Large & Ward & 10 \\ \hline \end{tabular}
\end{table} 
Table 2: Matrix of experiments.