A continuous approximation model for the fleet composition problem

This paper presents a continuous approximation model to determine the long-term vehicle fleet composition needed to perform distribution activities. The problem is a realistic variant of the vehicle routing problem, in which the fleet size and mix are also decision variables. The types of vehicles differ in terms of their capacities, fixed costs and variable costs. The objective is to minimize the total cost, subject to capacity and route duration constraints. We assume customers are distributed over a circular service region partitioned into zones, each of which is serviced by a single vehicle. The routing costs are assessed through a continuous approximation model. We present a mixed integer non-linear formulation for the problem, followed by computationally efficient upper and lower bounding procedures. The performance of the model and of its bounds is assessed on several test instances.