## 5 VRPs with Synchronization Issues  
Modern transportation systems are not only of a large scale, but are also characterized by a high level of dynamism--i.e., unexpected events may occur at any time, thus requiring a change in the schedule or routing--and synchronization--i.e., the observable and quantifiable phenomenon resulting from direct or indirect interactions between system elements or processes [52]. Exact approaches, as well as classic heuristics and meta-heuristics, are not usually designed for such dynamic scenarios. On the other hand, discrete-event heuristics (DEH) combine a fast heuristic algorithm with a discrete-event simulation [53]. As represented in Figure 5, while the heuristic is responsible for making decisions, the simulation  
Figure 4: Flowchart of a learnheuristic for the VRP. updates the state of the system event by event in order to evaluate how the decisions made by the heuristic affect the overall system with all of its parallelisms, dynamism, and synchronization. In this way, every decision can be made by considering the exact state of the system at that time. A DEH is also more flexible and relatively easy to maintain, since a change in the system can usually be tackled with a slight change in the simulation component without affecting the heuristic. Furthermore, the simulation and heuristic components shown in Figure 5 might be intended as two distinct elements, which would allow us to implement them in two different workstations or endpoints. In this way, the same simulation may be used by different heuristics. A typical set of problems in which DEHs might be beneficial are multi-tier vehicle routing problems and multi-vehicle routing problems, where different types of vehicles contribute to shipments. Belonging to this category are all multimodal supply chain scenarios [54], where a shipment might involve different transportation modes, such as planes, trains, ships, cargo ships, trucks, and vans. [PERSON] and [PERSON] [55] might be considered some of the pioneers, since they first highlighted the need for combining  
Figure 5: Flowchart of a discrete-event heuristic for the VRP. heuristics with simulations. In greater detail, they approached the VRP with time windows and synchronized visits (VRPTWSyn) when applied to home healthcare services for elders. In their model, it might be necessary for more than one staff member to be present simultaneously or in a given order. They emphasized the importance of temporal synchronization and precedence constraints by suggesting a mixed integer programming formulation of the problem and employing a heuristic approach. However, in the concluding remarks, they mentioned the need for a more efficient model for larger instances. Years later, [PERSON] et al. [56] proposed a new approach based on simulated annealing with dedicated local searches for solving the VRPTWSyn. They tested it on instances from [PERSON] and [PERSON] [55], showing that, in some cases, their solution was able to improve the best-known solutions. Two further applications that might benefit from these solutions that are capable of dealing with high dynamism and synchronization are car-sharing and ride-sharing operations [57, 58]. Car-sharing and ride-sharing are rapidly spreading, especially in big cities, and they are becoming part of our everyday life. Nowadays, customers require increasingly efficient service with fewer waits and delays. Both problems are marked by a rigid time dependency, the necessity of synchronizing the involved agents, and unexpected occurrences that arrive once the solution has already been computed--e.g., a driver that receives an unexpected request for a ride when they are already on their way. A solution that is able to consider all of these aspects was recently proposed by [PERSON] et al. [59], whose algorithm dealt with dynamic routing and scheduling scenarios and used combined trip sharing and walking. A recently born and futuristic scenario is also that considered, for instance, by [PERSON] et al. [60], [PERSON] et al.