A network-based scheme for allocating the cost of empty railcar movements in railway systems

In the freight industry, allocating the cost of empty miles of rail cars to partners in coalition is an important pricing problem. This paper proposes an empty car movement cost allocation scheme based on the game theory that explicitly considers the level of participation and contribution from each partner, the costs generated before and after cooperation, and the overall benefits obtained by each partner due to cooperation. Characterization of cost at each level of cooperation is considered based on the empty miles generated or reduced through cooperation. Compared with other existing models, the proposed cost allocation scheme consistently yields reasonable results, even under the situation in which other models behave poorly. We also show that the proposed pricing scheme can enhance the stability of a coalition such that the subgroup of a coalition will not be better off if the members of the subgroup choose to break away from the coalition.