Combined Stochastic and Robust Optimization for Electric Autonomous Mobility-on-Demand with Nested Benders Decomposition

Abstract: The electrification and automation of mobility are reshaping how cities operate on-demand transport systems. Managing Electric Autonomous Mobility-on-Demand (EAMoD) fleets effectively requires coordinating dispatch, rebalancing, and charging decisions under multiple uncertainties, including travel demand, travel time, energy consumption, and charger availability. We address this challenge with a combined stochastic and robust model predictive control (MPC) framework. The framework integrates spatio-temporal Bayesian neural network forecasts with a multi-stage stochastic optimization model, formulated as a large-scale mixed-integer linear program. To ensure real-time applicability, we develop a tailored Nested Benders Decomposition that exploits the scenario tree structure and enables efficient parallelized solution. Stochastic optimization is employed to anticipate demand and infrastructure variability, while robust constraints on energy consumption and travel times safeguard feasibility under worst-case realizations. We evaluate the framework using high-fidelity simulations of San Francisco and Chicago. Compared with deterministic, reactive, and robust baselines, the combined stochastic and robust approach reduces median passenger waiting times by up to 36% and 95th-percentile delays by nearly 20%, while also lowering rebalancing distance by 27% and electricity costs by more than 35%. We also conduct a sensitivity analysis of battery size and vehicle efficiency, finding that energy-efficient vehicles maintain stable performance even with small batteries, whereas less efficient vehicles require larger batteries and greater infrastructure support. Our results emphasize the importance of jointly optimizing predictive control, vehicle capabilities, and infrastructure planning to enable scalable, cost-efficient EAMoD operations.