Districting Problems

Abstract: Districting is the problem of grouping small geographic areas, called basic units, into larger geographic clusters, called districts, such that the latter are balanced, contiguous, and compact. Balance describes the desire for districts of equitable size, for example with respect to workload, sales potential, or number of eligible voters. A district is said to be geographically compact if it is somewhat round-shaped and undistorted. Typical examples for basic units are customers, streets, or zip code areas. Districting problems are motivated by very diverse applications, ranging from political districting over the design of districts for schools, social facilities, waste collection, or winter services, to sales and service territory design. Despite the considerable number of publications on districting problems, there is no consensus on which criteria are eligible and important and, moreover, on how to measure them appropriately. Thus, one aim of this chapter is to give a broad overview of typical criteria and restrictions that can be found in various districting applications as well as ways and means to quantify and model these criteria. In addition, an overview of the different areas of application for districting problems is given and the various solution approaches for districting problems that have been used are reviewed.