In this paper we solve the Vehicle Routing Problem with Lunch Break (VRPLB)
which arises when drivers must take pauses during their shift, for example,
for lunch breaks. Driver breaks have already been considered in long haul
transportation when drivers must rest during their travel, but the underlying
optimization problem remains difficult and few contributions can be found for
less than truckload and last mile distribution contexts. This problem, which
appears in the furniture delivery industry, includes rich features such as time
windows and heterogeneous vehicles. In this paper we evaluate the performance
of a new mathematical formulation for the VRPLB and of a fast and high
performing heuristic. The mixed integer linear programming formulation has
the disadvantage of roughly doubling the number of nodes, and thus significantly
increasing the size of the distance matrix and the number of variables. Consequently,
standard branch-and-bound algorithms are only capable of solving small-sized
instances. In order to tackle large instances provided by an industrial partner,
we propose a fast multi-start randomized local search heuristic tailored for the
VRPLB, which is shown to be very efficient. Through a series of computational
experiments, we show that solving the VRPLB without explicitly considering the
pauses during the optimization process can lead to a number of infeasibilities.
These results demonstrate the importance of integrating drivers pauses in the
resolution process
