Route Duration Prediction in a Stochastic and Dynamic Vehicle Routing Problem with Short Delivery Deadlines

Abstract

Abstract We are facing a real-world vehicle routing problem where orders arrive dynamically over the day at an online store and have to be delivered within short time. Stochastic information in form of the expected number and weight of orders and the traffic congestion level is available upfront. The goal is to predict the average time needed to deliver an order for a given time and day. This information is desirable for both routing decisions in the short horizon and planning vehicle drivers’ shifts with just the right capacity prior to the actual day. We compare a white box linear regression model and a neural network based black box model on historic route data collected over three months. We employ a hourly data aggregation approach with sampling statistics to estimate the ground truth and features. The weighted mean square error is used as loss function to favor samples with less uncertainty. A mean validation R2 score over 10 x 5-fold cross-validations of 0.53 indicates a substantial amount of unexplained variance. Both predictors are slightly optimistic and produce median standardized absolute residuals of about one.