Multi-Criteria MILP Model Integrating Kirchhoff’s Current Law for Optimal Green Feeder Bus Network Design: A Case Study of Ho Chi Minh City Metro Line 1

Integrating an efficient feeder bus network is critical to maximizing the passenger-carrying capacity of urban mass transit systems. This study proposes a Kirchhoff’s Current Law-based Network Flow Model (KCL-NFM) that integrates Mixed-Integer Linear Programming (MILP) formulations—ranging from fundamental to advanced multi-objective levels—to optimize feeder bus fleet size and the number of operational routes for Ho Chi Minh City Metro Line 1 across various planning horizons from 2024 to post-2040. By systematically optimizing operational frequency and route length constraints, the analysis identifies a practical operating point with a vehicle rotation rate of 2.5 round trips per hour and a maximum round trip length of 5 km. Experimental simulations demonstrate that the Advanced MILP model achieves a significant fleet size reduction of 53.6% to 55.4%—equivalent to eliminating over 200 redundant units in long-term scenarios. This efficiency translates into a 128% increase in revenue per bus and substantial capital savings of 740 billion VND (~29.1 million USD), representing a 58.7% reduction in capital expenditure (CAPEX), while maintaining vehicle load factors within a realistic operational threshold of 95% to 113%. Furthermore, sensitivity analysis reveals that transitioning to a 100% medium-sized electric bus fleet completely eliminates direct operational (tailpipe) carbon dioxide (CO2) emissions. This green transition not only mitigates urban congestion but also indicates the framework’s potential to support transport planners in designing economically viable and environmentally sustainable multi-modal transit systems.