Modelling and inference for the travel times in vehicle routing problems

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

Active Trachoma and Ocular Chlamydia trachomatis Infection in Two Gambian Regions: On Course for Elimination by 2020?

Trachoma is the leading infectious cause of blindness worldwide, and is mainly found in tropical and poor countries. It is caused by infection of the eyes with the bacterium Chlamydia trachomatis. However, sometimes the clinical signs of disease can be present without infection being detected. Control efforts involve surgery, antibiotic treatment, face washing, and environmental improvement for better hygiene. Surveys of trachoma help countries to know whether and where they should implement control interventions. The Gambia is found in West Africa and has suffered from trachoma for decades. We conducted a survey of two Gambian regions to look at how much trachoma disease and C. trachomatis infection there is in the eyes. We found that although there was enough disease (≥10%) to warrant antibiotic treatment for everyone in the regions, there was nearly no infection (0.3%). This means that using clinical signs alone to make treatment decisions in low prevalence settings like The Gambia can lead to the waste of scarce resources. Our results also suggest that since less than 1% of children are infected with C. trachomatis, The Gambia is on course to achieve the World Health Organization's aim of eliminating blinding trachoma by the year 2020