# International Airline Alliance Network Design with Uncertainty
## 5 Conclusions  
International alliances are built on the extensions of existing bilateral relationships and are implemented to allow the largest international carriers in the world to link their routes  
Figure 3: Alliance route network optimization design.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(p=2\) & \(p=3\) & \(p=4\) & \(p=5\) \\ \hline \(\alpha=0.2\) & \(3,14\) & \(3,12,14\) & \(1,3,12,14\) & \(1,3,12,13,14\) \\ \hline \(\alpha=0.4\) & \(1,14\) & \(1,12,14\) & \(1,3,12,14\) & \(1,3,12,13,14\) \\ \hline \(\alpha=0.6\) & \(1,14\) & \(1,12,14\) & \(1,3,12,14\) & \(1,3,12,14,15\) \\ \hline \(\alpha=0.8\) & \(1,14\) & \(1,12,14\) & \(1,3,12,14\) & \(1,3,12,14,15\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Optimal results for different numbers of international gateways.  
and frequent flyer programs to make international networks. The rational construction of an alliance route network is important for the airlines to maximize the use of the alliance network's resources and to expand their network.  
In this paper, we constructed an alliance route network based on an HS airline network. Uncertainties were taken into account in the design of the alliance network. We built an alliance route network optimization model that considers the uncertainty in unit transportation costs by modifying a three-subscript model of an HS network. To date, this has not been proposed in the literature. The proposed model was tested on a real-world dataset of a China-based airline and a US-based airline. The optimal alliance route network showed that the two airlines achieved inter-area transport through their international gateways. The calculation results indicated that the optimal solutions were sensitive to the unit transportation costs, and it was better to adopt the solution obtained with the robust model instead of adopting the solution of a particular scenario. By evaluating the impact of the number of gateways on the robust solutions, we concluded that the model proposed in this paper can reduce the total transportation costs compared with those of previous studies.  
The proposed model and method enabled the design of a route network with the capability of being resistant to risks and economic decisions. The model was extended from a three-subscript route network model, which is promising for addressing airline alliance problems.  
The methodology developed in this paper shows potential for other alliance network optimization problems with more complicated structures, such as the capacity limitations among hub airports with the consideration of passenger demands and cost uncertainties. Dynamic and flexible costs impact the optimization performance, and the real-time estimation of costs also demands further investigation.  
Conceptualization, supervision, and funding acquisition, W.Y.; methodology, W.Y., J.S. and Y.J.; software and validation, J.S. and Y.J.; writing--original draft preparation, W.Y., J.S. and Y.J.; writing--review and editing, W.Y., Z.X. and A.T. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the \(<\)Fundamental Research Funds for the Central Universities \(\backslash\)\(\#1>\) under grant number NS2016063; \(<\)2018 Graduate Innovation Base (Lab) Open Fund Project \(\backslash\)\(\#2>\) under grant number kfjj20180716.  
Not applicable.  
The authors declare no conflict of interest.