Predicting peak load of bus routes with supply optimization and scaled Shepard interpolation: A newsvendor model

The peak load of a bus route is essential to service frequency determination. From the supply side, there exist ineffective predicted errors of peak load for the optimal number of trips. Whilst many studies were undertaken to model demand prediction and supply optimization separately, little evidence is provided about how the predicted results of peak load affect supply optimization. We propose a prediction model for the peak load of bus routes built upon the idea of newsvendor model, which explicitly combines demand prediction with supply optimization. A new cost-based indicator is devised built upon the practical implication of peak load on bus schedule. We further devise a scaled Shepard interpolation algorithm to resolve discontinuities in the probability distribution of prediction errors arising from the new indicator, while leveraging the potential efficacy of multi-source data by adding a novel quasi-attention mechanism (i.e., scaling feature space and parameter optimization). The real-world application showed that our method can achieve high stability and accuracy, and is more robust to predicted errors with higher capacity. Our method can also produce a larger number of better trip supply plans as compared to traditional methods, while presenting stronger explanatory power in prioritizing the relative contribution of influential factors to peak load prediction.