Collaborative airline revenue sharing game with grey demand data.

Airline alliances provide more flights, include different destinations, and maximize revenues. In an alliance, collaborating airlines can offer tickets for an identical flight plan, unlike the traditional single airline approach. In particular, due to epidemic/pandemic events, such as COVID-19, the available customer demands become highly uncertain across many real airline alliance problems, and maintaining stable revenue is as important as maximizing the revenue in the alliance. A critical question is how the independent airline companies of an alliance should collaborate to maintain reliable maximum revenue. Therefore, this question was studied using a grey mathematical programming model for small-sized airline alliances under grey demand data. Some cooperative game theoretical solution concepts, such as Shapley, equal revenue, Nucleolus, and minimax core, are presented. A numerical study of a small-sized alliance with three airline companies was used to interpret the results of the cooperative game theory concepts. Three cases were considered based on the grey passenger demand structure of airline collaborations to share extra revenues and maintain stable revenue distribution that would maximize the expected revenue. Based on the obtained results, the synergy of collaboration increased with the increase in the size coalition in all of the cases, except for the cases of lower (L) and upper (U) demand levels.