A Multi-Depot Green Vehicle Routing Problem (MDGVRP) is considered in this paper. In MDGVRP, Alternative Fuel-powered Vehicles (AFVs) start from different depots, serve customers, and, at the end, return to the original depots. The limited fuel tank capacity of AFVs forces them to visit Alternative Fuel Stations (AFS) for refueling. The objective is to minimize the total carbon emissions. A Two-stage Ant Colony System (TSACS) is proposed to find a feasible and acceptable solution for this NP-hard (Non-deterministic polynomial-time) optimization problem. The distinct characteristic of the proposed TSACS is the use of two distinct types of ants for two different purposes. The first type of ant is used to assign customers to depots, while the second type of ant is used to find the routes. The solution for the MDGVRP is useful and beneficial for companies that employ AFVs to deal with the various inconveniences brought by the limited number of AFSs. The numerical experiments confirm the effectiveness of the proposed algorithms in this research.

To the best of our knowledge, there is only one approach for solving neutrosophic cost minimization transportation problems. Since neutrosophic transportation problems are a new area of research, other researchers may be attracted to extend this approach for solving other types of neutrosophic transportation problems like neutrosophic solid transportation problems, neutrosophic time minimization transportation problems, neutrosophic transshipment problems, and so on. However, after a deep study of the existing approach, it is noticed that a mathematical incorrect assumption has been used in these existing approaches; therefore there is a need to modify these existing approaches. Keeping the same in mind, in this paper, the existing approach is modified. Furthermore, the exact results of some existing transportation problems are obtained by the modified approach.