A Bus Subsidy Scheme Design Model Considering Competition between Bus Companies

The competition between bus companies plays an important role in the effects of bus subsidy schemes for operation-sharing networks. This paper presents a bi-level programming model considering the competition to design bus subsidy schemes. In the upper sub-model, a subsidy scheme is given with the target of minimizing the total social costs (TSC). Further, in the lower sub-model, each bus company competes with other companies under the subsidy scheme. The competition is portrayed as a non-cooperative game where each company changes the departure frequency of their lines separately to obtain the maximum profit. The subsidy schemes can minimize the TSC when all bus companies pursue the maximum profit. A specific approach combining genetic algorithm and best response dynamics is proposed to solve the model. To validate the constructed model, a real-world case study is conducted in Guangzhou. From the results, as the scheme is implemented, the bus companies will be inspired to increase the line departure frequency, leading to a reduction of the passenger waiting time and performing a higher level of service. The TSC are reduced by 28.6%, among which the total waiting time costs are reduced by 43.0%. The model can guide bus subsidy scheme design for operation-sharing bus networks.