## 5 Conclusions and Future Work  
This study addressed the biobjective Cumulative Capacitated Vehicle Routing Problem. This problem mainly arises in commercial contexts such as the delivery of perishable goods, in which there are differentiated based on priority indexes. In the case of a pooled transportation service, it might help to estimate the trade-off between delivering the orders in the same sequence as customers board the vehicle and the minimum arrival time of the system. For this problem, a mixed-integer programming formulation and two metaheuristic algorithms were developed. A commercial optimization software was able to solve the model for small size instances, whereas the algorithms showed their effectiveness by providing feasible results in a reasonable amount of computational time. The algorithms showed their efficiency by providing good quality fronts for the small size instances. Additionally, for larger instances, both algorithms provided good values for the multiobjective metrics evaluated. Although none of the algorithms outperformed each other, the MA-RK v2 obtained fronts with a higher quantity of points, more density, and more coverage of the sets. However, the MA-RK v1 was slightly faster. One intuition is that MA-RK v1 is more intensive in the local search, stagnating in local optima, while MA-RK v2 maintains the diversity, allowing to escape from local optima and populating the Pareto-fronts. However, more computational experiments are needed to clarify this effect. In summary, all procedures provided a positive contribution to a more sustainable balance between economic and customer service objectives. Our results provide useful insights for business applications in terms of considering customer satisfaction and gaining a valuable sustainable advantage given that the reduction in the traveled time translates into a reduction of CO\({}_{2}\) emissions. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Instance** \\ **Name** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **X\({}^{\prime}\)/X\({}^{\prime\prime}\)** \\ \end{tabular} } & \multicolumn{2}{c}{**Exact**} \\ \cline{3-4}  & & **MA-RK** & **MA-RK** \\  & & **v1** & **v2** \\ \hline \multirow{2}{*}{**FNO3**} & MA-RK v1 & 0 & 0 \\ \cline{2-4}  & MA-RK v2 & 0.875 & 0 \\ \hline \multirow{2}{*}{**FNO4**} & MA-RK v1 & 0 & 0.333 \\ \cline{2-4}  & MA-RK v2 & 0.500 & 0 \\ \hline \multirow{2}{*}{**FNO5**} & MA-RK v1 & 0 & 0 \\ \cline{2-4}  & MA-RK v1 & 0 & 0 \\ \hline \multirow{2}{*}{**FNO6**} & MA-RK v1 & 0 & 0 \\ \cline{2-4}  & MA-RK v2 & 0.800 & 0 \\ \hline \multirow{2}{*}{**FNO7**} & MA-RK v1 & 0 & 0 \\ \cline{2-4}  & MA-RK v1 & 0 & 0 \\ \hline \multirow{2}{*}{**FNO8**} & MA-RK v1 & 0 & 0 \\ \cline{2-4}  & MA-RK v2 & 1 & 0 \\ \hline \multirow{2}{*}{**FNO9**} & MA-RK v1 & 0 & 0 \\ \cline{2-4}  & MA-RK v2 & 1 & 0 \\ \hline \multirow{2}{*}{**FNO10**} & MA-RK v1 & 0 & 0 \\ \cline{2-4}  & MA-RK v2 & 1 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Coverage of two sets value for the rest of the instances. Future research lines include the design of routes using congested environments with travel speed variation. This fact can be addressed either by modifying the objective function to include the variability in the travel time during the day or using a risk aversion approach, by adding a profit to each node associated with the order of visit. In addition, considerations involving time windows as priority metrics, and demand uncertainty can be worth consideration, as well as factors such as labor costs or balance of the total traveled distance among routes, which seem to dominate the overall cost. Conceptualization, S.N.-G. and E.O.-B. ; methodology, S.N.-G. and D.F.-D.; software, S.N.-G. and D.F.-D.; validation, S.N.-G., D.F.-D., and E.O.-B. ; formal analysis, S.N.-G., D.F.-D., and E.O.-B. ; investigation, S.N.-G. and D.F.-D.; resources, S.N.-G. and E.O.-B. ; data curation, S.N.-G. and D.F.-D.; writing--original draft preparation, S.N.-G.; writing--review and editing, E.O.-B.