A smart predict-then-optimize framework for vehicle rebalancing problem

Matching the imbalanced supply and demand through vehicle rebalancing is critical for enhancing the operational efficiency of ride-hailing platforms. However, the traditional two-stage Predict-then-Optimize (PO) framework suffers from a mismatch between the loss function of the upstream prediction model and the objective function used in downstream decision-making. To tackle this challenge, we propose a Smart Predict-then-Optimize (SPO) framework, in which the prediction model is trained to directly minimize decision loss. Firstly, we formulate the regional-level vehicle rebalancing problem as a mixed integer linear programming (MILP) model, aiming to maximize the Gross Merchandise Volume (GMV) of the ride-hailing platform. After that, the Spatial and Temporal Identity (STID) model is employed to predict future demand and supply. Instead of training the prediction model by minimizing fitting error, we adopt a decision-focused loss function determined by the solution of the optimization model. Considering that uncertain parameters appear in the constraints, we develop a penalty-augmented loss function along with a corresponding solution adjustment method. Moreover, we propose a perturbation-based method to address the challenge of gradient backpropagation through the non-differentiable optimization layer, which enables the gradients of the decision loss to be obtained via zeroth-order approximation. The theoretical properties are checked, showing that the method can yield an unbiased approximation of the gradient. We conduct extensive experiments on a real-world dataset from Didi Chuxing, including both numerical studies and simulation experiments. The results show that the proposed SPO framework improves the average GMV by 2.19% compared to rule-based rebalancing and by 0.28% compared to the PO strategy. In particular, the prediction model trained by the SPO method can learn the utility of each region, enabling more effective vehicle rebalancing by dispatching drivers from low-utility origins to high-utility destinations.