An Attempt to Synthesise Predictive Modelling with Optimal Transport for Resource Allocation Problems in Large-Scale Construction

Sammanfattning

This report presents a novel approach for combining predictive methods, in particular, Gaussian Processes (GPs) with the Optimal Transport (OT) framework in large-scale construction settings handled by the Swedish Transport Administration (STA). The aim is to explore the possibility to forecast excavations and demands on multiple construction sites and formulate this as a mass allocation problem. The methods used are presented in a breadth-first style, providing an overview rather than a deep introduction. Given the large topic of OT, the major part of this thesis consists of the presentation of this and some of its measure theoretic prerequisites. First we develop a GP regression model to individually forecast excavated resource supply and landfill demand at a collection of construction sites, leveraging a feature engineered and generated dataset mimicking the structure of the real dataset in the STA's young data collection project ELSA. The model shows potential to predict quite well in comparison to prior fictively generated estimates made by the contractor and the STA -- generated via variances multiplied with true function and some white noise added to it to include heteroscedastic estimates -- while also providing uncertainty quantification. Secondly, we formulate the OT problem as an Unbalanced Optimal Transport (UOT) problem with entropic regularisation, allowing for so called mass destruction and teleportation. This entropic UOT is then solved using the Sinkhorn algorithm. The results shows the forecasted system can be modelled using OT and illustrates how supply and demand efficiently can be satisfied. Finally, implementing both predictive methods and OT as well as the combination to real data is recommended to the STA as the findings shows it can be a useful addition to their existing estimation methods. In particular, an exploration of extended methods such as combining predictive models, uncertainty quantification and robust optimisation in UOT is recommended for future work.