Constructing Efficient Commercial Territory Design Plans for a Beverage Distribution Firm with a Bi-objective Programming Model

Abstract: In this paper, we address a territory design problem arising from a beverage distribution company. This problem belongs to the family of territory design problems. 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 the sales volume are considered in the model. Most of the work in territory design have been developed for single-objective models. A very few works have addressed multi-objective territory design problems. To the best of our knowledge, this is the first multi-objective approach for this commercial territory design problem, and in particular, for a territory design with connectivity constraints. In this paper, we introduce a bi-objective mixed-integer programming model for this problem and propose an improved epsilon-constraint method for generating the optimal Pareto front. This method is based on a recent improved technique by Ehrgott and Ruzika to assure properly efficient solutions. Empirical evidence over a variety of instances shows that the improved method finds indeed better fronts than those found by the traditional epsilon-constraint method. This comes at no extra computational effort. In addition, we observe that when the firm reduces the tolerance in the unbalance of sales volume the efficient fronts make a dramatic change.