A continuous approach to the design of physical distribution systems

The optimization model presented in this paper sets the district boundaries and seeks the best fleet of vehicles as to minimize total daily transport costs. Both vehicle time and vehicle load are treated probabilistically. Each district is related to a characteristic function that takes into account distribution costs, time and capacity constraints, distribution effort, and shape considerations (district slenderness). In a previous work (Novaes and Graciolli, European Journal of Operational Research, forthcoming) the region under analysis was represented by a rectangular grid structure. A continuous approach, however, provides more accurate results and reduces the data preparing effort. The mathematical model developed to solve this problem is a combination of a gradient method with random perturbations, and a hybrid genetic algorithm. This method was reported in the literature and has been applied successfully to solve topological design problems in civil and mechanical engineering. The results of the model, applied to a parcel delivery problem in the city of São Paulo, Brazil, are compared with previous findings.