A predictive chance constraint rebalancing approach to mobility-on-demand services

This paper considers the problem of supply-demand imbalances in Mobility-on-Demand (MoD) services. These imbalances occur due to uneven stochastic travel demand and can be mitigated by proactively rebalancing empty vehicles to areas where the demand is high. To achieve this, we propose a method that takes into account uncertainties of predicted travel demand while minimizing pick-up time and rebalance mileage for autonomous MoD ride-hailing. More precisely, first travel demand is predicted using Gaussian Process Regression (GPR) which provides uncertainty bounds on the prediction. We then formulate a stochastic model predictive control (MPC) for the autonomous ride-hailing service and integrate the demand predictions with uncertainty bounds. In order to guarantee constraint satisfaction in the optimization under estimated stochastic demand prediction, we employ a probabilistic constraining method with user-defined confidence interval, using Chance Constrained MPC (CCMPC). The benefits of the proposed method are twofold. First, travel demand uncertainty prediction from data can naturally be embedded into the MoD optimization framework, allowing us to keep the imbalance at each station below a certain threshold with a user-defined probability. Second, CCMPC can be relaxed into a Mixed-Integer-Linear-Program (MILP) and the MILP can be solved as a corresponding Linear-Program, which always admits an integral solution. Our transportation simulations show that by tuning the confidence bound on the chance constraint, close to optimal oracle performance can be achieved, with a median customer wait time reduction of 4% compared to using only the mean prediction of the GPR.