Abstract
The sectorization problem is a particular case of partitioning problems occurring in cartography. The aim is to partition a territory into sectors such that the statistical activity measure of each sector is as close as possible to a given target value. We model this as a problem of minimizing the maximum deviation among all the sectors between their activity measure and their target value. We propose a mathematical programming formulation for the problem, we add some valid inequalities to restrict the solution space and develop a preprocessing procedure to reduce the number of variables. Computational results on different maps highlight the strong efficiency of this reduction procedure.
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Tang, X., Soukhal, A. & T’kindt, V. Preprocessing for a map sectorization problem by means of mathematical programming. Ann Oper Res 222, 551–569 (2014). https://doi.org/10.1007/s10479-013-1447-8
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DOI: https://doi.org/10.1007/s10479-013-1447-8