A revenue management model for airline and railway transportation considering cooperative and competitive games

Simultaneous optimization of pricing and seat-allocation brings about revenue management improvement. Thus, recently, some researchers have accentuated the joint optimization of pricing and quantity decisions. Investigating customer choice behavior leads to a more precise grasp of this issues. This paper presents a game-theoretic framework, in which a rail transport company and an airline company are participants of the game. This paper’s primary incentive is to study two heterogeneous participants’ behavior under competition and cooperation, considering the joint optimization of pricing and quantity decisions. To that aim, firstly, two separate mixed-integer non-linear programming models are developed. The models are linked through their demand functions, and each company’s demand acts based on its price and quality, as well as the competitor’s price and quality. The objective functions of both models aim at maximizing the total revenue. Companies’ performance is studied under both non-cooperative and cooperative games. The equal profit method and Shapley value are employed to build a coalition between participants. Ultimately, the analyses’ findings indicate that both companies yield more revenue as they form a coalition rather than competing with each other. Moreover, results show that passengers may find longer train journeys inconvenient or exhausting compared to faster alternatives like flights; hence, the airline company gains more revenue in large-size instances. Furthermore, revenue increases for both airline and rail transport companies with rising demand. Besides, it turned out that price elasticity is inversely related to revenue. On the other hand, quality elasticity has a direct relation with revenue.