Multi-depot periodic vehicle routing with variable visit patterns

In Periodic Vehicle Routing Problems (PVRPs), customers require multiple deliveries over a given time horizon. This paper investigates a generalization of the PVRP which was introduced to us by a logistics company specialized in the transportation of valuable goods where two different customer types are considered. The first type has a set of fixed visit patterns from which one must be selected. The second type of customer defines a maximum number of days between visits that must be respected, resulting in variable visiting patterns which enable greater flexibility when scheduling visits across the time horizon. Including this second type of customer considerably increases the size of the search space while also providing additional opportunities to improve solutions. We propose a heuristic for the problem and assess its quality by comparing its results against those achieved by state-of-the-art methods for a closely related problem from the literature. The results indicate that our heuristic is not only competitive, but also produces many new best-known solutions for benchmark instances. Finally, we introduce new instances based on real-world data and conduct an empirical analysis concerning the impact of the two customer types on solution quality, resource utilization and possible trade-offs when solving the problem.