A hybrid K-means and integer programming method for commercial territory design: a case study in meat distribution

The objective of territorial design for a distribution company is the definition of geographic areas that group customers. These geographic areas, usually called districts or territories, should comply with operational rules while maximizing potential sales and minimizing incurred costs. Consequently, territorial design can be seen as a clustering problem in which clients are geographically grouped according to certain criteria which usually vary according to specific objectives and requirements (e.g. costs, delivery times, workload, number of clients, etc.). In this work, we provide a novel hybrid approach for territorial design by means of combining a K-means-based approach for clustering construction with an optimization framework. The K-means approach incorporates the novelty of using tour length approximation techniques to satisfy the conditions of a pork and poultry distributor based in the region of Valparaíso in Chile. The resulting method proves to be robust in the experiments performed, and the Valparaíso case study shows significant savings when compared to the original solution used by the company.