Commercial Territory Design for a Distribution Firm with New Constructive and Destructive Heuristics

Territory design problems appear in many real-world cases from diverse fields such as political districting or sales and service territory design. The problem consists of grouping small geographic areas into larger geographic clusters called territories in such a way that the latter are acceptable according to relevant planning criteria. This paper addresses a case of the territory design problem arising from a real-world application in a beverage distribution firm. In this specific application, requirements of compactness, contiguity, and multiple balancing are considered. In this work, we propose four new heuristics based on Greedy Randomized Adaptive Search Procedure within a location-allocation scheme. The proposed heuristic procedures are called GRLH1, GRLH2, GRDL, and SLA, respectively. SLA builds the territories one at a time, while the others build the territories simultaneously. The construction phase in the simultaneous creation consists of two parts: a location phase where p territory seeds are identified, and an allocation phase where the remaining basic units (BUs) are iteratively assigned to a territory. In contrast, the construction phase of SLA consists of locating a territory seed and allocate the unassigned BUs to this territory. When the territory size reaches an upper limit, the territory is closed and another seed is located to open a new territory. This process is repeated until all territories are partially filled, then the unassigned BUs are allocated to these partial territories by evaluating a merit function. The post-processing phase is the same for all procedures and it consists of a local search that attempts to improve both a dispersion-based objective function and the violation of some soft constraints. Empirical results reveals that GRLH1 and GRLH2 find near-optimal or optimal solutions to relatively small instances, where exact solutions could be found. The proposed procedures require short time to provide an approximate solution. We carried out a comparison between the proposed heuristic procedures and the existing method in larger instances. It was observed the proposed heuristic GRLH1 produced very competitive results with respect to the existing approach.