## 4 Case Study and Discussion
### Comparison among Different Configurations Using Design Methods  
Table 8 compares the design results from three different design methods: (1) the robust optimal design, (2) the uncertainty-based design (i.e., developed in Reference [9]), and (3) the conventional design. The combination with one variable-speed chiller (1100 kW cooling capacity) and four constant-speed chillers (1300 kW cooling capacity) is selected as the optimal design to achieve the lowest annual total cost. By comparing with uncertainty-based and conventional designs, the total cost of robust optimal design (\(4222\times 10^{3}\) HKD) is reduced about 26% and 11.4%, respectively, when the penalty ratio is 10 HKD/kW. To better demonstrate the impact of different design methods and configurations on design results, the operation cost, initial cost, and availability risk cost of eight optimum design options are shown in Figure 10. Among these eight design options, six options are using robust optimal design method with different total capacities. It can be observed that the total costs of six robust optimal design options are obviously lower than that of uncertainty-based and  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Penalty Ratio (HKD/kW)** & \multicolumn{2}{c}{**1**} & \multicolumn{2}{c}{**10**} & \multicolumn{2}{c}{**100**} \\ \hline
**Option (Size(kW) \(\times\) Number)** & \(RC\) & \(TC\) & \(RC\) & \(TC\) & \(RC\) & \(TC\) \\ \hline \(3200\times 1\text{CSD}+2800\times 1\text{VSD}\) & 102 & 3978 & 1021 & 4897 & 10,210 & 14,085 \\ \(2100\times 2\text{CSD}+1800\times 1\text{VSD}\) & 39 & 3977 & 387 & 4326 & 3871 & 7810 \\ \(1550\times 3\text{CSD}+1350\times 1\text{VSD}\) & 25 & 4140 & 247 & 4362 & 2468 & 6583 \\ \(1600\times 2\text{CSD}+1400\times 2\text{VSD}\) & 25 & 4053 & 254 & 4282 & 2542 & 6570 \\ \(1250\times 4\text{CSD}+1000\times 1\text{VSD}\) & 19 & 4070 & 185 & 4237 & 1851 & 5903 \\ \(1300\times 3\text{CSD}+1050\times 2\text{VSD}\) & 28 & 4084 & 275 & 4331 & 2755 & 6811 \\ \(1050\times 5\text{CSD}+750\times 1\text{VSD}\) & 15 & 4135 & 145 & 4265 & 1451 & 5571 \\ \(1050\times 4\text{CSD}+900\times 2\text{VSD}\) & 22 & 4165 & 216 & 4331 & 2161 & 6276 \\ \hline \hline \end{tabular} Remarks: RC: availability risk cost, TC: total cost.  
\end{table}
Table 6: Annual availability risk cost (\(10^{3}\) HKD) and total cost (\(10^{3}\) HKD) of different design options.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Total Cooling** & **Best Option (Size (kW) \(\times\) Number)** & **Availability Risk Cost (10\({}^{3}\) HKD)** & **Operation Cost** & **Total Cost** \\
**Capacity (kW)** & **Number)** & **Cost (10\({}^{3}\) HKD)** & **(10\({}^{3}\) HKD)** & **(10\({}^{3}\) HKD)** \\ \hline
5100 & \(1050\times 4\text{CSD}+900\times 1\text{VSD}\) & 490 & 3397 & 4469 \\
5400 & \(1100\times 4\text{CSD}+1000\times 1\text{VSD}\) & 343 & 3412 & 4350 \\
5700 & \(1150\times 4\text{CSD}+1100\times 1\text{VSD}\) & 246 & 3421 & 4274 \\
6000 & \(1250\times 4\text{CSD}+1100\times 1\text{VSD}\) & 185 & 3436 & 4237 \\
6300 & \(1300\times 4\text{CSD}+1100\times 1\text{VSD}\) & 131 & 3463 & 4222 \\
6600 & \(2300\times 2\text{CSD}+2000\times 1\text{VSD}\) & 253 & 3501 & 4231 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Best design options under different total cooling capacities (penalty ratio: 10 HKD/kW).  
conventional design methods while the total cost differences among the six robust optimal design options are not significant. This indicates that the proposed design method can provide a more robust and more cost-effective design option than existing design methods.