A novel distributionally robust uncertain optimization method with application to bus bridging service under rail disruptions

Bus bridging service (BBS), as an effective means of evacuating passengers during rail disruptions, has received significant attention. However, the BBS network under rail disruptions involves complex uncertainty. In view of this, this paper innovatively defines an uncertainty distribution set to describe this uncertainty. Based on the defined uncertainty distribution set and the best-case scenario, this paper proposes a novel distributionally robust uncertain optimization method for the BBS network under rail disruptions, and constructs the corresponding model. To overcome the computational challenges of the model, this paper clarifies the specific structural characteristics of the uncertainty distribution set. By using uncertainty theory and dual techniques, the proposed model is equivalently transformed into either a mixed-integer linear programming formulation or a mixed-integer second-order cone programming formulation. The proposed method not only extends uncertainty theory under the ambiguity of the uncertainty distribution but also provides a theoretically derived computational formulation for the model. Finally, a real-world case validates the model, while sensitivity analysis and comparative experiments demonstrate the validity and advantages of the proposed method and model.