In the last two years, a new delivery paradigm has emerged for transporting goods on the socalled last mile to households, pioneered by such services as Google Shopping Express, Amazon Prime, Instacart, and Walmart To Go, among many others. Such services reduce the need for households to travel because one can simply order products online and have them delivered quickly to one's doorstep. However, it is not yet understood (or, more specifically, quantified) to what degree such services result in social benefits vis-a-vis congestion and carbon emissions.

A major complication in studying problems of this kind is the difficulty of creating a model that is mathematically tractable enough to give useful insights as well as faithful to the original phenomenon being modelled. For example, one complicating factor in modelling household behavior is the existence of multi-stop trips made by households: on a given day, a person will often visit multiple locations on one outing (such as running errands on the way to or from one's place of work), and each of these locations will usually have alternatives (e.g. there are usually multiple choices of which grocer or post office to use). Thus, the calculation of the cost of a multi-stop trip is more complicated than a mere direct trip to and from the various destinations and the household. In the current literature, this complication is handled by either simplifying the problem at hand or by introducing additional assumptions into the problem structure. This project applies tools from geospatial analysis, geometric probability theory, and mathematical optimization to develop an integrated model that predicts the changes in congestion and carbon footprint that result when households in a geographic region adopt (or reject) such delivery services.