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, such as Uber or DiDi Rider. Such imbalances are due to uneven stochastic travel demand and can be prevented by proactively rebalance empty vehicles. To this end we propose a method that include estimated stochastic travel demand patterns into stochastic model predictive control (SMPC) for rebalancing of empty vehicles MoD ride-hailing service. More precisely, we first estimate passenger travel demand using Gaussian Process Regression (GPR), which provides demand uncertainty bounds for time pattern prediction. We then formulate a SMPC for the autonomous ride-hailing service and integrate demand predictions with uncertainty bounds into a receding horizon MoD optimization. In order to guarantee constraint satisfaction in the above optimization under estimated stochastic demand prediction, we employ a probabilistic constraining method with user defined confidence interval. Receding horizon MoD optimization with probabilistic constraints thereby calls for Chance Constrained Model Predictive Control (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. We show that for a given minimal fleet size the imbalance in each station can be kept below a certain threshold with a user defined probability. Second, CCMPC can further be relaxed into a Mixed-Integer-LP (MILP) and we show that the MILP can be solved as a corresponding Linear-Program which always admits a integral solution. Finally, we demonstrate through high-fidelity transportation simulations, that by tuning the confidence bound on the chance constraint close to optimal oracle performance can be achieved. The corresponding median customer wait time is reduced by 4% compared to using only the mean prediction of the GPR.