A bi-objective programming model for designing compact and balanced territories in commercial districting

Abstract

In this paper, we address a territory design problem arising from a bottled beverage distribution company. We propose a bi-objective programming model where dispersion and balancing with respect to the number of customers are used as performance criteria. Constraints such as connectivity and balancing with respect to sales volume are considered in the model. Most of the work in territory design has been developed for single-objective models. To the best of our knowledge, this is the first multi-objective approach for this commercial territory design problem, and in particular, for territory design with connectivity constraints. We propose an improved ε-constraint method for generating the optimal Pareto front. Empirical evidence over a variety of instances shows that the improved method is well suited for finding optimal Pareto fronts with no more computational effort than the traditional method. Instances of up to 150 units and 6 territories are solved in relatively short amount of time. For this problem, the improved method finds practically the same fronts than those found by the traditional ε-constraint method. In addition, we observe that when the firm reduces the tolerance in the imbalance of sales volume the efficient fronts change and when the number of territories increases, the balance with respect to the number of customers becomes harder to achieve.