## 5 Conclusions  
This study proposes a two-echelon vehicle routing problem with a drop box facility (2 EVRP-DF) which is modeled as an integer linear programming problem. The 2 EVRP-DF demonstrates the utilization of drop box facilities to carry out reverse logistics activities in urban areas. This study also considers environmental aspects by considering the amount of carbon emissions released by vehicles, and compares the results of 2 EVRP-DF with a common practice model where, in reverse logistics activities, customers go directly to the depot rather than intermediate facilities. Numerical examples are carried out to show the effectiveness of using the drop box facility compared to common practice. The use of drop boxes in the 2 EVRP-DF model allows an average reduction in total costs (transportation and emissions) of 72.02%. In addition, it is also seen that there is a drastic increase in the number of emissions released by vehicles in common practice, where this does not occur in the 2 EVRP-DF model.  
Furthermore, the experiment using SA to solve the 2 EVRP-DF problem model presents less significant results compared to GUROBI. The average difference in solutions between GUROBI and SA is only 0.51%, but in terms of time SA can provide a more acceptable computation time compared to GUROBI which reaches 6.5 h. However, the computational results still need to be tested on more complex characteristics of problems that might occur in practice or real life. In the comparison between SA and GA in solving 2 EVRP-DF, SA also outperforms GA in finding a minimum objective solution by an average difference of 0.21%.  
For further research, it is recommended to explore various metaheuristic algorithms to solve 2 EVRP-DF problems, because there are growing number of developments regarding metaheuristic algorithms available in the literature. It will also be more interesting if a combination of algorithms such as a hybrid algorithm between SA and GA can solve the problem. In term of problem characteristics, it is interesting to consider uncertainty factors such as travel time, demand, and locker availability in the model.  
Conceptualization, M.R., A.A.N.P.R., A.S., R.N., R.LL, Y.T.P.; methodology, M.R., A.A.N.P.R.; software, M.R., A.A.N.P.R., M.R.W.; validation, M.R., A.A.N.P.R., M.R.W.; formal analysis, M.R., A.A.N.P.R.; investigation, M.R., A.A.N.P.R.; resources, M.R., A.A.N.P.R., Y.T.P.; data curation, M.R., A.A.N.P.R., D.F.P., A.W.W.; writing--original draft preparation, M.R., A.A.N.P.R., D.F.P., A.W.W.; writing--review and editing, M.R., A.A.N.P.R., R.I.L., S.S.; visualization, M.R., A.A.N.P.R., D.F.P., A.W.W.; supervision, R.N., Y.T.P., A.A.N.P.R.; project administration, R.I.L., Y.T.P., S.S., A.A.N.P.R.; funding acquisition, A.S., R.N., Y.T.P., A.A.N.P.R. All authors have read and agreed to the published version of the manuscript.  
Figure 6: Correlation between total carbon emission and customers.  
This research received no external funding.  
Data Availability StatementData available on request from the authors.  
The authors gratefully acknowledge financial and non-financial support from Bina Nusantara University, Institut Teknologi Sepuluh Nopember, Universitas Petramina, Mapua University, Universitas Pendidikan Nasional, Universitas Gadjah Mada for this work.  
The authors declare no conflict of interest.