Time-dependent fleet size and mix multi-depot vehicle routing problem

This paper considers an extension of classical distribution problems and introduces the time-dependent fleet size and mix multi-depot vehicle routing problem. This important class of problems finds applications in urban logistics and service design. The solution to this problem impacts the performance of distribution companies and can help design policies to improve traffic and congestion issues. We propose a mathematical model for this challenging problem, along with several generic and problem-specific valid inequalities. A powerful matheuristic is proposed to solve large instances of the problem generated from real traffic data. Our matheuristic is also assessed on a set of instances from the literature. The computational results demonstrate that our two approaches can select the appropriate vehicle type to reduce the fixed costs while designing the routes of each vehicle from each selected depot, taking into account the departure time to avoid traffic congestion and minimize the total distribution costs. The results also show that our matheuristic is more effective than the exact method in terms of solution quality and computational time. Finally, we demonstrate the importance of considering congestion information in the design of the algorithm, showing that a constant travel time solution underestimates the costs by 15% and, more importantly, that an algorithm that takes traffic data into account produces solutions about 5% better than the former.