Prediction-failure-risk-aware online dial-a-ride scheduling considering spatial demand correlation via approximate dynamic programming and scenario approach

The dial-a-ride (DAR) service is a precursor to emerging shared mobility. Service providers expect efficient management of fleet resources to improve service quality without degrading economic viability. Most existing studies overlook possible future demands that could yield better matching opportunities and scheduling benefits, and therefore have short-sighted limitations. Moreover, the effects of correlated demand and potential prediction errors were ignored. To address these gaps, this paper investigates prediction-failure-risk-aware online DAR scheduling with spatial demand correlation. Request selection and cancellation are explicitly considered. We formulate the problem as a Markov decision process (MDP) and solve it by approximate dynamic programming (ADP). We further develop a demand prediction model that can capture the characteristics of DAR travel demand (uncertainty, sparsity, and spatial correlation). Deep quantile regression is adopted to estimate the marginal distribution of each OD pair. These marginals are combined into a joint demand distribution by constructing a Gaussian Copula to capture the spatial demand correlation. A prediction error correction mechanism is proposed to eliminate prediction errors and rectify policies promptly. Based on the model properties, several families of customized pruning strategies are devised to improve the computational efficiency and solution quality of ADP. We solve policies over time in the dynamic environment mixed with actual and stochastic future demands via the ADP algorithm and scenario approach. We propose the value function rolling method and multi-scenario exploration method, to address the deviation of the value function and identify the optimal policy from multiple future demand scenarios. Numerical results demonstrate the importance and benefits of incorporating demand forecasting and spatial correlation into the DAR operation. The improvement due to prediction is significant even when the prediction is imperfect, while the demand prediction can hedge against the negative effects of request cancellation. The real-world application result shows that compared to state-of-the-practice, the overall delivery efficiency can be substantially improved, along with better service quality and fleet size savings.