Vehicle Routing Problem with Synchronization and Scheduling Constraints of support vehicles

Many transportation planning processes in real-world applications are complex and require strong cooperationamong various vehicles. When using expensive vehicles, their utilization plays a decisive role in an efficient supply chain. In mining production or civil construction processes, such as mining unloading or road building, the machines are typically mobile, and synchronization between different types of vehicles ensures better use of vehicle fleets, reduces traveled distances, non-productive times, and logistics costs. In this paper, we consider two types of vehicles, called primary and support vehicles. Primary vehicles perform operations and are assisted by at least one support vehicle, with support vehicles scheduled according to a First-Come, First-Served (FCFS) policy. We refer to this practical problem as the vehicle routing problem with synchronization and scheduling constraints of support vehicles. To tackle this problem, we introduce three mixed-integer linear programming models. The first approach involves vehicle routing with synchronization only, breaking each task into several subtasks by duplicating nodes in the graph representation, which produces an equivalent network flow problem. The second model addresses subtasks by adding constraints that determine the assignment of each subtask to a specific primary and support vehicles. The third model incorporates an additional FCFS scheduling constraint for support vehicles. Computational results on 100 real-world instances show that the second model reduces the first model’s computational time by 30%. In contrast, the results of the third model indicate that the FCFS constraint for support vehicles has little impact on solution quality and slightly increases computation time, demonstrating the robustness and practical applicability of the scheduling approach.