Traffic network design problem with uncertain demand: A multi-stage bi-level programming approach∗

By exploring of the multi-stage network design problem of comprehensive traffic, the paper proposes a bi-level programming model with uncertain demand. The upper level problem is to maximize the consumer surplus of all demand scenarios with budget constraint. While under the network investment decisions of the upper level problem, the lower level problem is to maximize the consumer surplus of every demand scenario with consideration of the collaborations of transportation modes, traffic load balancing and capacity constraints. Then, a numerical example is given to verify the effectiveness of the multi-stage be-level programming model. Compared with the existing research, the proposed model can simultaneously optimize the final form of the comprehensive traffic network and construction timing. The model considers all the annual coordination between transportation infrastructure construction and demand. It reflects the cooperation and balanced development of transportation modes, and makes the decision support more effective for the gradual improvement of the comprehensive traffic network.