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

Truck queuing analysis at landfill sites in a waste collection vehicle routing problem

This paper presents an analysis of a truck queuing problem at landfill sites due to a static rest time of truck drivers in a waste collection vehicle routing problem. The analysis is based on a solution of two datasets from a benchmark waste collection problem using the nearest greedy heuristic algorithm.In this problem, all drivers need to have a one-hour rest break during their collection.The rest break can start from 11.00 a.m. to 12.00 p.m. However, based on the solution from a previous study, all drivers have their rest break almost at the same time. Consequently, all drivers travelled to landfill sites to unload waste approximately at the same time.Based on the truck queuing analysis presented in this paper, there is a long queue at landfill site 3 (ten trucks arrived between 2.52 p.m. to 2.53 p.m.) for dataset 1; whereas for dataset 2, 13 trucks arrived at landfill site 1 between 4.10 p.m. to 4.55 p.m. Thus, it may be concluded that the static rest time period of truck drivers can cause truck queuing at landfill sites. Long queues at landfill sites will increase the service time at landfill sites as well as affect the drivers’ arrival time at customers. This paper suggests that future works need to consider a dynamic rest time period in solution techniques to overcome the truck queuing problem at landfill sites for solving the waste collection vehicle routing problem