A Multi-Objective Decomposition Model for Integrated Urban Transit Line Planning and Passenger Routing

: Urban public transport networks must balance traveler convenience with tight budgetary and capacity constraints. This study develops a comprehensive multi-objective integer programming framework that unifies line selection, frequency setting, and passenger routing to minimize door-to-door travel time and operating cost while respecting vehicle capacities and limiting transfers. The model is solved using a Dantzig–Wolfe decomposition approach with linear-programming relaxation, which enables tractable solutions on realistically scaled networks. To reflect real-world commuting behavior, three increasingly sophisticated formulations are proposed: a Basic Line Planning Model, a Direct Connection Capacity Model, and a Change-and-Go Model that embeds walking and waiting penalties. On a six-edge, four-node network with 6,000 passenger trips, the Change-and-Go Model emerges as the most effective, reducing average travel time by 47%, halving transfers, and increasing cost by only 11% compared to the incumbent plan. Sensitivity analysis reveals that the model remains robust under varying demand levels and cost–time priorities. The proposed framework thus offers a scalable and passenger-friendly decision-support tool that significantly improves public transport efficiency with moderate investment, making it especially valuable for urban transit agencies seeking to modernize their services.