A column‐generation‐based approach to fleet design problems mixing owned and hired vehicles

Abstract

AbstractWe look at the problem of choosing a fleet of vehicles to carry out delivery tasks across a long time horizon. The delivery quantities may vary significantly from day to day, and from season to season, and the underlying routing problem may have rich constraints, for example, time windows, multiple compartments, multiple commodities, and compatibility constraints. We consider the option of hiring extra vehicles from external carriers in order to efficiently carry out the day‐to‐day operations while containing the costs of owning the fleet. The goal is to design a fleet so as to minimize the sum of costs of routing the fleet every day of the horizon, the acquisition costs, the maintenance costs, and the costs of hiring external vehicles. In the literature, there is no previous work on fleet design for a long time horizon, which also considers the hiring options. We propose to tackle the problem using column generation and develop three different heuristics. The methods proposed are tested and compared on a set of real‐world problems. It is also shown how introducing the possibility of hiring helps reducing the overall cost and the number of idle vehicles over the planning horizon.