# International Airline Alliance Network Design with Uncertainty
## 2 Literature Review  
Regarding the multiple airline alliance models, several works have been done. [PERSON], [PERSON], and [PERSON] [14] investigated alliances using a complementary and a parallel model, with the conclusion of better economic performance with the complementary alliance model. [PERSON] [7] examined hybrid alliances whose members have complementary and overlapping routes, and discussed the implications of hybrid alliances for international airline alliances. From the alliance cooperation perspective, [PERSON], [PERSON], [PERSON], and [PERSON] [15] grouped alliances into high-level and low-level categories according to the degree of participation in the cooperation. A high-level alliance involves network-level collaboration, representing that the allied airlines connect their route networks, while the low-level collaboration considers the route-level cooperation, neglecting the network topology considerations. Some research has been done on designing and optimizing airline alliance networks. [PERSON] and [PERSON] [16] took factors of the flight frequency and cost into consideration for the alliance network design, where a multi-objective function was presented based on the code sharing among member airlines for the purpose of maximizing the overall profits. [PERSON] and [PERSON] [12] investigated international alliances and mergers in a competitive environment. The results revealed that the optimal international gateway choices vary depending on the number of competitors remaining in the market. [PERSON], [PERSON], and [PERSON] [17] focused on a reliability analysis of the three typical network models for an alliance network, and proposed an alternative node selection strategy to evaluate their robustness and vulnerability. [PERSON] and [PERSON] [18] analyzed the vulnerability of member airlines for exiting the alliance. Their results suggested that Oneworld is the most vulnerable alliance, with SkyTeam ranked as the second and Star Alliance as the third. For designing optimized networks, some works have been done. [PERSON] [19] firstly applied an HS network to address the minimization of the cost of designing hub networks. [PERSON] [20,21] proposed an integer-linear-program-based method with the consideration of single and multiple allocation schemes. [PERSON] and [PERSON] [22,23] proposed variants oriented from hub-location-allocation problems with fewer variables. The above typical linear formulations were adjusted according to unique specifications, along with the processing of some distinguished features. Among them, the parameter uncertainty was studied in order to address HS network design problems. After their investigations, [PERSON] and [PERSON] obtained the conclusion that the hub-and-spoke network structure remains advantageous with higher congestion costs in the hubs [24]. To build route networks with the consideration of market competition, [PERSON] and [PERSON] considered the long-term impact resulting from the competition of high-speed rail with airlines, and developed an analytical model to investigate the airlines' impact on networks, as well as the impacts on markets when the competition of high-speed rail in trunk lines exists [25]. [PERSON] and [PERSON] discussed airline models operating in a competitive environment in order to select a network structure. In order to capture the interaction between competing airlines in the selection, the impacts of price, flight frequency, seat accessibility, and route length on product differentiation were thoroughly studied [26]. For network optimization with uncertainties, some studies were carried out. [PERSON] [27] formulated the deviation and robust optimization problem and designed an optimization algorithm to convert the original problem, whose objective function was MinMax, into a deterministic objective function.