The allocation of facilities and customers is a key problem in the design of supply chains of companies. In this paper, this issue is approached by partitioning the territory in areas where the distribution points are allocated. The demand is modelled through a set of continuous functions based on the population density of the geographic units of the territory. Because the partitioning problem is NP hard, it is necessary to use heuristic methods to obtain reliable solutions in terms of quality and response time. The Neighborhood Variable Search and Simulated Annealing heuristics have been selected for the study because of their proven efficiency in difficult combinatorial optimization problems. The execution time is the variable chosen for a factorial experimental design to determine the best-performing heuristics in the problem. In order to compare the quality of the solutions in the territorial partition, we have chosen the execution time as the common parameter to compare the two heuristics. At this point, we have developed a factorial statistical experimental design to select the best heuristic approaches to this problem. Thus, we generate a territorial partition with the best performing heuristics for this problem and proceed to the application of the location-allocation model, where the demand is modelled by a set of continuous functions based on the population density of the geographical units of the territory.