A center-based modeling approach to solve the districting problem

This article deals with the districting problem arising in applications such as political districting, police patrol area delineation and sales territory design. The aim of districting is to group basic areal units into geographic districts such that some set of criteria are satisfied, with basic criteria being district balance, compactness and contiguity. This article proposes a center-based mixed-integer linear programming model to solve the districting problem. Given the central units of districts, the model optimizes weighted objectives of district balance and compactness while satisfying contiguous constraints on districts. The performance of the model was tested using three study areas with 297, 324 and 1297 areal units, respectively. Experimentation shows that, using the district centers identified by a multistart weighted K-medoids algorithm, the model instances can be solved optimally or near-optimally. Compared with local search-based algorithms, the center-based approach outperforms metaheuristics such as simulated annealing, variable neighborhood descent, iterative local search and old bachelor acceptance search in terms of solution quality.