On the allocation of new lines in a competitive transit network with uncertain demand and scale economies

This paper proposes a new model for investigating the allocation of new lines in a competitive transit network in which transit operations are subject to demand uncertainty and scale economies. Scale economies imply that the operating cost of each operator per unit of transit line decreases with the number of lines operated. The proposed model explicitly considers the interactions among three types of players: transit authority, transit operators, and transit passengers. The transit authority aims to maximize the total social welfare for a given confidence level (or probabilistic guarantee) by optimizing the allocation of new lines tobidding operators. For a given allocation scheme, each of the operators determines the associated frequencies and fares to maximize its own profit at a certain confidence level while accounting for the responses of transit passengers to their strategies. The proposed line allocation model is formulated as a robust 0-1 integer programming problem that can be solved by an implicit enumeration algorithm. A numerical example is presented to illustrate the effects on the transit system of the allocation of new lines, the scale economies, the level of variation in passenger demand, and the risk attitude of transit operators toward uncertainty.