Designing multi-vehicle delivery tours in a grid-cell format

This paper presents a methodology to be used in the design of multi-delivery tours associated with the servicing of a heterogeneous region, where the density of visiting points and the amount of cargo vary over the served area. Both vehicle cycle time and vehicle load are treated probabilistically. The region under analysis is partitioned into a number of sectors, rings, and districts, with the polar coordinates centered at the depot. We assume a rectangular grid structure for the representation of the spatial variables. This division is intended to attain a quasi-homogeneous distribution effort (approximate equal number of vehicles) in each partition. The optimization model seeks the best fleet of vehicles that minimizes total daily transport costs. As an example, the model is applied to a parcel delivery problem in the city of São Paulo, Brazil.