Districting modeling with exact contiguity constraints

A classic problem in planning is districting, which aims to partition a given area into a specified number of subareas according to required criteria. Size, compactness, and contiguity are among the most frequently used districting criteria. While size and compactness may be interpreted differently in different contexts, contiguity is an unambiguous topological property. A district is said to be contiguous if all locations in it are ‘connected’—that is, one can travel between any two locations in the district without leaving it. This paper introduces a new integer-programming-based approach to districting modeling, which enforced contiguity constraints independently of any other criteria that might be additionally imposed. Three experimental models are presented, and tested with sample data on the forty-eight conterminous US states. A major implication of this paper is that the exact formulation of a contiguity requirement allows planners to address diverse sets of districting criteria.