An Integer Programming Approach to Sectorization with Compactness and Equilibrium Constraints

The process of sectorization aims at dividing a dataset into smaller sectors according to certain criteria, such as equilibrium and compactness. Sectorization problems appear in several different contexts, such as political districting, sales territory design, healthcare districting problems and waste collection, to name a few. Solution methods vary from application to application, either being exact, heuristics or a combination of both. In this paper, we propose two quadratic integer programming models to obtain a sectorization: one with compactness as the main criterion and equilibrium constraints, and the other considering equilibrium as the objective and compactness bounded in the constraints. These two models are also compared to ascertain the relationship between the criteria.

Automated summary

The process of sectorization involves dividing a dataset into smaller sectors based on specific criteria. This paper proposes two quadratic integer programming models for sectorization, one focusing on compactness with equilibrium constraints, and the other considering equilibrium as the objective with compactness bounded in the constraints. The relationship between the criteria is also compared.