A general and scalable matheuristic for fleet design

We look at the problem of choosing a fleet of vehicles to carry out delivery tasks across a very long time horizon -- up to one year. The delivery quantities may vary markedly day to day and season to season, and the the underlying routing problem may have rich constraints -- e.g., time windows, compatibility constraints, and compartments. While many approaches to solve the fleet size and mix (FSM) problem in various contexts have been described, they usually only consider a "representative day" of demand. We present a method that allows any such single-day FSM solver to be used to find efficient fleets for a long time horizon. We propose a heuristic based on column generation. The method chooses a fleet of vehicles to minimise a combination of acquisition and running costs over the whole time horizon. This leads to fleet choices with much greater fleet utilisation than methods that consider only a subset of the available demand data. Issues with using a heuristic sub-problem solver within the context of column generation are discussed. The method is compared to two alternative methods on real-world data, and has shown to be very effective.