Applying Topological Data Analysis to Logistics Systems Analysis

The purpose of this project is to apply computational tools from topological data analysis (TDA) to study the logistics systems in the state of California and the USA, with an emphasis on freight networks. TDA is a relatively nascent research area that allows one to describe geometric properties of a data set, such as connectivity, existence of holes, or clustering, in a way that imposes minimal assumptions on parametric structures like coordinate systems or forms of probability distributions. In recent years, TDA has been successfully applied to many different scientific domains, such as aviation, path planning, and time series analysis. To the best of our knowledge, this project will be the first to apply TDA to the logistics domain. The basic principle that we will exploit is that TDA excels at identifying coarse features in datasets using a technique called persistence, and is not sensitive to more localized phenomena. The fundamental data structure in TDA is called a simplicial complex, which is a generalization of a network structure that allows one to identify not only pairwise relationships (i.e. arcs or links in a network”), but also relationships between three or more entities (e.g., “these four cities are all part of the same metropolitan region). The research team will use these tools to study datasets taken from the Bureau of Transportation Statistics, and possibly real‐time load boards, to make descriptive insights as well as prescriptive recommendations, such as identifying key regions where LTL freight can potentially be aggregated, finding bottleneck regions where the network is most sensitive to disruption, and determining where new lanes or hubs should be built in order to improve system efficiency and sustainability.

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