Bilevel Optimization of Regular Bus-Subway-Shared Bicycle Cooperative Operation considering Dual Uncertainties

The primary objective of this paper is to minimize the overall travel costs for passengers while simultaneously maximizing the operational revenue for the transportation company. This is achieved through the optimization and adjustment of various factors, such as the intervals between regular bus and subway services, the duration of vehicle stops at each station, and the pricing structure for subway and shared bicycle usage. By enhancing the efficiency of passenger travel, we have successfully bolstered the company’s operational profits. In contrast to prior research, this paper comprehensively considers the dual uncertainties associated with both bus operations and shared bicycle operations within a cooperative system. By establishing a coordinated dual-level optimization model for regular bus, subway, and bike-sharing networks under dual uncertainty conditions, we employed convex combination techniques to unify the dual uncertain variables into a single objective, which was then incorporated into a chance-constrained bilevel programming model. Ultimately, we utilized KKT conditions to transform the model from a bilevel to a single level for resolution. This paper centers its research on the collaborative system comprising the Nanchang Metro Line 1, Bus Route 520, Bus Route 211, and the adjacent region hosting a cluster of shared bicycles. By leveraging Python programming, optimization models, empirical data on traffic flow and stoppage times, and OD data, we conducted an optimization analysis to solve the problem at hand. According to the optimization results, passenger waiting time, passenger transfer time, and passenger on board time are effectively reduced by 6.81%, 18.29%, and 23.92%. At a confidence level of 95%, the resulting time level results in a 12.44% reduction in total travel time. The average subway fare increased by 18.12%, the average shared bicycle fare decreased by 19.12%, and the total cost of travel expenses increased by 16.68%. The final total cost of travel was reduced by 4.06%, and the business operating income was increased by 13.10%. The comprehensive optimization results have effectively fulfilled the objectives of the bilevel optimization model, thereby confirming the rationality and practicality of the optimization approach. The research outcomes hold significant practical implications for facilitating the efficient and cooperative development of urban transportation networks, ultimately enhancing the convenience of residents’ travel experiences.