Unlike classic vehicle routing problems, real-time vehicle routing problems (RTVRPs) are real-world dynamic vehicle routing problems (DVRPs) in which customer requests are identified over the time horizon of operations without previous knowledge. In this problem, received requests are answered as quickly as possible and then dispatched to a service vehicle. Considering the RTVRP’s timing constraints, a solution must provide the best trade-off between the computation time required to find the solution and the proposed solution’s costs. A feeder vehicle routing problem (FVRP) consists of a heterogeneous fleet of vehicles, including trucks and motorcycles. In this problem, motorcycles pass easily in crowded areas, and the traffic of urban logistics is distributed easily. The feeder approach also lowers the number of times the vehicle returns to the central depot for loading, resulting in cost and time savings. The present article proposes a real-time feeder vehicle routing problem (RTFVRP) in a situation where every truck and every motorcycle can join during the freight delivery process. After modeling the RTFVRP through mixed-integer linear programming, a dynamic inertia weight particle swarm optimization (DIWPSO) algorithm is offered to solve the problem. The results of the static version of the FVRP in the small and the last time slices show that the GAMS outputs outperform those of the DIWPSO and differential evolution (DE), both indicating a similar performance. The results of running these algorithms for 21 DVRP test instances revealed that the PSO outperforms the DE in quality and solution runtime in both static and dynamic versions. Overall, the PSO and DE algorithms generated 34.33% and 30.37% cost savings in implementing RTFVRP, respectively, compared to the case that all requests were available at the beginning of the working day.
