# International Airline Alliance Network Design with Uncertainty
## 1 Introduction  
An international airline alliance, which is composed of airlines, is a joint collaboration of airline companies with the aim of establishing a unified global route system for improving competitiveness through code sharing or joint operations. Differently from typical airline operation modes, the airlines in the alliances are coordinated and treated equally to maximize the profits. For the implementation of an international airline alliance, diverse airports provide services to support the alliance, although there are multiple restrictions in practice. Some benefits of having an international alliance, i.e., a collaboration between airline companies among different countries, have been highlighted. For instance, limitations in the regulatory or legal barriers between countries can be released [1], airlines' passenger capacity can be increased, and the chance of improving profits is improved by having a larger number of airline destinations. Moreover, an international airline alliance benefits the passenger experience by way of having access to larger networks, having convenient services, having more choices of carriers, and being connected to more flyer points [2]. An international airline alliance enables an effective coordination of flight schedules so as to minimize the travelers' waiting time and provide a sufficient usage of time between flights [3]. The handover of passenger loads among airports can be simplified, and the same aircraft maintenance services can be shared to reduce the maintenance time within an airline alliance network. An international airline alliance also facilitates the quality of service (QoS)--for instance, by establishing a flexible price negotiation model, optimizing the airline routes, and reducing airlines' running expenses. For international airline alliances, there are three typical categories, which are grouped in accordance with the topologies among airline members, i.e., Star Alliance, Oneworld, and SkyTeam, which have initial partners located in the major geographic regions and are often involved in bilateral partnerships with other founders. The scheduled passenger volumes of the three major alliances account for more than 50% of the global civil aviation industry [4]. Distinct from domestic airline alliances, international alliances are more challenging due to some practical considerations, such as the large number of uncertain factors, docking through separate gateways, the uncertainties in agile policies, changeable economic and social factors, and the Snyder effect in uncertainties [5]. To address the airline alliance problem, the problem is separated into two specific issues [6], i.e., the selection of an alliance model and the route network design. Some typical alliance models of the partial connection type have been highlighted, such as competition model and strategic model. The authors of [7] evaluated and discussed the performance of applying a strategic model for the alliance problem, where three alliance types were classified in accordance with their alliance strategies; these were a complementary alliance (also called the vertical competition model), parallel alliance (also called the horizontal competition model), and hybrid alliance. Among them, the complementary model has been widely used for airline alliances owing to its elimination of the negative externalities between routes [8] and the benefits of reducing the connection fare and improvement of social welfare. It is possible to significantly shorten the connection time for flight transfers with the complementary alliance model, leading to the potential possibility of having seamless transfer (one ticket to the end at the place of the departure, with a direct luggage hanging service [9]). Consequently, this paper implements the complementary model as the prototype for addressing the model selection issue. The route network is the foundation of airline operation.