Solving the vehicle routing problem with lunch break arising in the furniture delivery industry

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.