A green vehicle routing problem with multi-depot, multi-tour, heterogeneous fleet and split deliveries: a mathematical model and heuristic approach

Vehicle Routing Problem (VRP) is one of the most studied combinatorial optimization problems with many variants and extensions. This study introduces a novel VRP variant: Green Vehicle Routing Problem with Multi-Depot, Multi-Tour, Heterogeneous Fleet and Split Deliveries. In this problem, different vehicle types (heterogeneous fleet) with limited fleet sizes are allowed and the vehicles can be assigned to different depots (multi-depot). A vehicle can be used multiple times (multi-tour) and multiple vehicles can be assigned to a route (split delivery). The problem is formulated as a Mixed Integer Linear Programming (MILP) model to minimize the total carbon emissions. A Genetic Algorithm (GA), employing a MILP model and using niching and constraint handling techniques, is also developed to solve the problem effectively. The proposed algorithm has been tested on four hypothetical but realistic distribution networks. The results demonstrate the robustness and effectiveness of the proposed GA method on practical distribution scenarios.