An exact approach for the green vehicle routing problem with two-dimensional loading constraints and split delivery

This paper presents a study about the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints (2L-CVRP) and its three variants: allowing split delivery (2L-SDVRP), with green requirements (G2L-CVRP), and integrating split delivery with green requirements (G2L-SDVRP). When considering split delivery, a customer can be served by more than one vehicle. The green variant takes into consideration the CO2 emission. Our objective is to analyze the cost benefits obtained with the aggregation of split delivery and the reduction of CO2 emission. Mathematical models are presented for each variant, and instances are solved with a branch-andcut approach. We develop a tailored procedure to address the packing subproblem, including the computation of lower bounds, a constructive-based heuristic, and a constraint programming formulation. Computational experiments performed on literature instances and newly created ones show that the proposed approach can outperform previous results. Besides that, the green variant has solutions with low emissions of CO2. The variant with split delivery has solutions with lower cost but at the expense of higher computing time.