A Multi-Objective Optimization Framework for a Schedule-Aware Transit System with Dynamic Bus Assignment

Abstract

Traditional fixed-route systems provide structure and scalability but rely on static route assignments and homogeneous fleets, limiting their ability to respond to variations in passenger demand. In contrast, demand-responsive transportation (DRT) systems incorporate passenger-specific information and adapt routing decisions, but typically rely on smaller vehicles and fully flexible routing that is challenging to scale to large transit networks. This work proposes an intermediate approach that maintains the structure of fixed-route systems while introducing flexibility through dynamic bus-route assignments that adapt to passenger demand over time. The problem is formulated as a multi-objective mixed-integer linear program for a schedule-aware bus transportation system operating over a finite discrete-time planning horizon. A heterogeneous fleet of buses operates on predefined routes and is dynamically assigned across routes based on evolving passenger demand. The optimization problem minimizes a weighted combination of passenger travel time cost and bus operating cost. Passenger travel time cost is modeled asymmetrically to encourage punctual service. The proposed system enables several key behaviors. By allowing dynamic assignment of buses to different routes, a limited fleet can effectively serve more routes than available vehicles, improving overall system coverage. This flexibility is complemented by coordinated transfer synchronization, where buses are dispatched in advance to facilitate seamless passenger transfers. At the same time, the model incorporates cost-aware utilization of a heterogeneous fleet, prioritizing lower-cost vehicles while still respecting operational requirements such as capacity. The system also prioritizes passengers with tighter deadlines, and responds systematically to objective function weighting, shifting between service-oriented and cost-efficient solutions. In high-demand scenarios, capacity-aware allocation ensures that larger buses are assigned where they are most effective. Finally, the discrete-time formulation enables direct animation and visualization of system operations, providing clear and interpretable insight into system behavior. To isolate the impact of dynamic route assignment, the proposed framework is compared against a fixed-route baseline that retains the key behaviors of the proposed system but restricts buses to fixed route assignments. Simulation results show that dynamic bus assignment translates into significant performance gains. Relative to the fixed-route baseline, passenger travel time cost is reduced by 67%, with only a 14% increase in operating cost. Overall, this work shows that meaningful improvements in transit performance can be achieved not by abandoning fixed-route structures, but by introducing targeted flexibility in how buses are assigned within them.