Modelling and inference for the travel times in vehicle routing problems

Wright, Chrissy and Tawn, Jonathan and Zografos, Konstantinos and Kourentzes, Nikos and Nunes, Matthew (2019) Modelling and inference for the travel times in vehicle routing problems. PhD thesis, Lancaster University.

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Abstract

Every day delivery companies need to select routes to deliver goods to their customers. A common method for the formulation and for finding the best route is the vehicle routing problem (VRP). One of the key assumptions when solving a VRP is that the input values are correct. In the case of travel time along a section of road, these values must be predicted in advance. Hence selecting the optimal solution requires accurate predictions. This thesis focuses upon the prediction of travel time along links, such that the predictions will be used in the defined VRP. The road network is split into links, which are connected together to form routes in the VRP. Travel time predictions are generated for each link. We predict the general behaviour of the travel times for each link, using time series forecasting models. These are tested both empirically, against the observed travel time, and theoretically, against the ideal characteristics of a VRP travel time input, including the resulting prediction uncertainty in the VRP. Small input variations are likely to have little impact upon the optimal solution. In contrast, infrequent and unpredicted large delays, e.g., from accidents, which occur outside the general travel time behaviour can change optimal routes. We study the delay behaviour and suggest a novel model consisting of three parts: the delay occurrence rate, length and size. We then suggest ways to input both the delay and the general travel time models to the VRP, which results in an optimal solution that is more robust to delays. Traffic moves from one link into the network, so if one link is busier then the same traffic will flow to the connecting links. We extend the single link model to incorporate information from the surrounding links using a network model. This produces better predictions than the single link models and hence better inputs for the VRP.