New Models for Commercial Territory Design

Abstract: In this work we present an exact procedure to solve a commercial territory design problem. The problem is motivated from a real-world case in the beverage distribution industry. Different versions of this problem have been studied before, particularly from a heuristic perspective due to its NP-completeness. In this case, the firm wants to create a specific number of territories and it requires compactness, connectivity and balance according to the number of costumers and sales volume on each territory. A common practice to guarantee compactness is the minimization of dispersion measures, the most usual measures being the objective functions of that p-center and p-median problems. We have included a performance analysis of these dispersion measures. In addition, we are introducing a quadratic formulation to the problem that reduces the number of binary variables and it permits to solve larger instances than the linear model. Experimental work reveals that the solution of the quadratic model produces high quality solutions in relatively small computational effort.