Two maps of Georgia based on solving semi-discrete optimal transport problems: congressional districts and power plants maps

Our goal in this work is to adopt the framework of semi-discrete optimal transport problems to obtain two maps of the state of Georgia. The first map will give a subdivision of the 14 congressional districts of the state of Georgia. The second map will produce a subdivision of the state of Georgia in 14 regions to be served by the existing power plants in the state. We will introduce a new measure of cost, and our goal will be to minimize this cost, while maintaining stringent constraints: be them those of equal population or equal access to power supply. Our main scope in this work is to exemplify how, in a very inexpensive way, sound mathematical principles can be used to provide viable maps that can be used by policy makers in order to make decisions or as a basis for further refinements.