A variable neighborhood search for the green vehicle routing problem with two-dimensional loading constraints and split delivery

We address the Green Vehicle Routing Problem with Two-Dimensional Loading Constraints and Split Delivery (G2L-SDVRP), which extends the split delivery vehicle routing problem to include customer demands represented by two-dimensional, rectangular items. We aim to minimize carbon dioxide (CO2) emissions instead of travel distance, a critical issue in contemporary logistics activities. The CO2 emission rate is proportional to fuel consumption and measured in terms of the vehicle’s total weight and traveled distance. We propose the first metaheuristic for the G2L-SDVRP, based on a variable neighborhood search approach that designs effective routes and guarantees the feasibility of loading constraints using various strategies, such as lower bound procedures, the open space heuristic, and a constraint programming model. We evaluate the performance of our approach through computational experiments using benchmark and newly created instances. The results indicate that the proposed approach is effective. It achieves improved solutions for 21 out of 60 instances in relatively short computing times when compared to existing methods for the G2L-SDVRP. Furthermore, our approach is competitive on benchmark instances of a related variant, namely the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints, improving the best-known solutions for 50 out of 180 instances.