# International Airline Alliance Network Design with Uncertainty
## 4 Case Study  
### Data Settings  
In this section, we selected a Chinese-based and US-based airline alliance network as a general example to examine the performance of the proposed models; the use case can be easily extended to other scenarios. We selected 10 cities in China and 8 cities in the US to form the route network and implement the airline alliance. The distribution of airports and relevant parameter configurations are presented in Table 1.  
The city airports marked with * are the regional hubs of the corresponding airlines. Transportation between these regional hubs is assumed to meet the traffic regulations. The crucial data, such as the passenger demands, are sourced from the Market Information Data Transfer Database and segment distance data [31].  
We applied the unit transportation cost function to measure the distance between the nodes (with \(C_{rr}=0\)). We used the cost per available seat kilometer (CASK) with the great circle distance between the relevant nodes for measuring the cost parameters [32] due to the variations in the CASK values according to the distance. Moreover, the uncertain factors could be conveniently integrated into CASK as the main indicator. For the three published aircraft categories, i.e., wide body, narrow body, and regional jets, the average CASK values were computed accordingly. The wide-body aircraft serve long-distance markets (distance \(>\) 5000 km); narrow-body aircraft serve distances between 1000 and 5000 km; regional jets are utilized in short-distance markets (distance \(<\) 1000 km). Similarly to [PERSON] et al. (2018) [32], the CASK values used in this research are presented in Table 2.  
To assess the impact of uncertainty in transportation cost on the design of an alliance network, we assume that the values of the CASK fluctuate within the interval \([-20\%,+20\%]\). We generated several scenarios by changing the CASK magnitudes, as shown in Table 3. As risk control is critical in the robust optimization, a boundary scenario should be considered in the robust optimization. There is no special requirement for the number of scenarios.  
As shown in Table 3, we generated nine different scenarios for a combination of the three CASK values, among which scenario 1 is called the base case. In each scenario \(s\in S\), we can get a set of values of the unit transportation cost.  
Based on the model formulation in Section 3.3, we know that this is a linear program. The model was coded on the AIMMS platform and solved by CPLEX12.5 with the CPLEX options set to their default values. All tests were executed using a personal computer running the Microsoft Windows 7 operating system and equipped with an Intel Core i5 CPU 6500 with 3.20 GHz and 4 GB RAM.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Node** & **Airport** & **Node** & **Airport** & **Node** & **Airport** \\ \hline
1 & PEK\({}^{\star}\)Beijing & 7 & CKG\(\backslash\)Chongqing & 13 & DTW\({}^{\star}\)Detroit \\ \hline
2 & CAN\(\backslash\)Guangzhou & 8 & \(\chi\)Y\({}^{\star}\)\(\backslash\)Xi’an & 14 & LAX\({}^{\star}\)\(\backslash\)Los Angeles \\ \hline
3 & PVG\({}^{\star}\)Shanghai & 9 & WUHF\({}^{\star}\)Wuhan & 15 & MSP\({}^{\star}\)\(\backslash\)Minneapolis \\ \hline
4 & CTU\(\backslash\)Chengdu & 10 & NKG\(\backslash\)Nanjing & 16 & SFO\(\backslash\)San Francisco \\ \hline
5 & SZ\(\backslash\)Shenzhen & 11 & ATL\({}^{\star}\)\(\backslash\)Atlanta & 17 & SEA\(\backslash\)Seattle \\ \hline
6 & KMG\({}^{\star}\)\(\backslash\)Kunming & 12 & JFK\({}^{\star}\)\(\backslash\)New York & 18 & ORD\(\backslash\)Chicago \\ \hline \hline \end{tabular}
\end{table}
Table 1: Citys airport.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Short Haul** & **Medium Haul** & **Long Haul** \\ \hline CNY per ASK & 0.3724 & 0.2894 & 0.2941 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Cost per available seat kilometer.