Math-heuristic for a territory design problem

Abstract

In this work, we study a territory design problem. This type of problem consists of dividing a geographic area into territories that meet certain characteristics or planning criteria. The problem studied in this paper considers the division of a geographical area into compact, contiguous and balanced territories, with respect to one or several measures of activity. To find feasible solutions for the problem, we propose a math-heuristic. The method first constructs solutions, using a minisum objective as measure of dispersion, that are balanced with respect to the different activity measures. Subsequently, the solutions are modified so that they satisfy the contiguity constraints. To test the performance of the proposed method, we use a set of test instances available in the literature. The results obtained are compared with the optimal solutions of the test instances. According to this comparison, the proposed method provides optimal solutions or solutions very close to the optimal solution with a reasonable computational effort compared to that required by an exact solution method.