Optimal scheduling of mixed conventional and modular autonomous bus fleets for sustainable urban transit

Abstract

Modular autonomous vehicles (MAVs) are considered a promising solution to mitigating the mismatch between travel demand and service capacity in public transit systems. However, integrating them into existing fleets of conventional human-driven buses (CHBs) introduces a complex scheduling problem that remains unsolved under real-world operational constraints. This study develops a novel optimization framework for mixed fleets comprising CHBs and MAVs on a single route, jointly optimizing bus departure times, vehicle type assignments, and MAV configurations to minimize total cost. The mixed-integer nonlinear programming (MINLP) model explicitly incorporates vehicle resource limitations, redeployment requirements, and MAV penetration thresholds that reflect regulatory and societal acceptance. Through exact linearization, the MINLP is transformed into a tractable mixed-integer linear programming formulation and solved to global optimality. Numerical results show that the optimal mixed-fleet schedule significantly outperforms CHB-only operations, achieving a total cost reduction of 57.7%. Comprehensive sensitivity analyses quantify the effects of critical factors on optimal results. The findings reveal that: (i) marginal returns to additional modules diminish beyond an optimal threshold, enabling precise inventory planning; (ii) optimal fleet composition depends critically on demand, with MAVs most cost-effective at moderate levels and CHBs preferable under high demand; and (iii) even under a conservative 10% MAV penetration threshold, the mixed fleet outperforms CHB-only operations. These insights confirm the efficacy of the proposed model as a strategic tool for transit agencies in making informed decisions on fleet composition and service design across diverse operational contexts.