An Improved Exact Algorithm for a Territory Design Problem with p-Center-Based Dispersion Minimization

Abstract: Territory design deals with the discrete assignment of geographical units into territories with restrictions dened by planning criteria. We propose an exact method of solution based on an integer programming model with the objective of minimizing a p-center dispersion measure. The solution approach is an iterative algorithm that uses dierent subproblems to validate if, for given values of the objective function of the original problem, it is possible to nd feasible solutions with at most p territories. This change allows testing various candidate distance values as lower bounds for the optimal solution of the original problem. The aim is to improve these lower bounds at each iteration as we add the necessary constraints to reach a feasible solution. The proposed algorithm performs significantly faster than existing methods with small and medium-sized instances.