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This paper presents a two-person bargaining model in which railway company and its passenger community are the players in the train-scheduling problem. The fuel consumption cost and the total passenger-time constitute the payoff functions. First, the Pareto frontier is determined using the ∊-constraint method and then conflict resolution is performed using five particular resolution methodologies, namely the non-symmetric Nash solution, the non-symmetric Kalai-Smorodinsky solution, the non-symmetric area monotonic solution, the non-symmetric equal loss solution, and a one-shot solution concept. A numerical example is presented to illustrate the methodology.