## 4 A General Solving Methodology
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Deterministic Scenario**} & \multicolumn{3}{c}{**Stochastic Scenario**} & \multicolumn{3}{c}{**Fuzzy Scenario**} \\ \cline{2-7}
**Instance** & **BKS** & **OBD** & **GAP (\%)** & **Det** & **Stochastic** & **Stoch-Fuzzy** & **Fuzzy** \\  & **(1)** & **Sol. (2)** & **(1)–(2)** & **Sol. (3)** & **Sol. (4)** & **Sol. (5)** & **Sol. (6)** \\ \hline A-n32-k5 & 787.1 & 787.2 & 0.01\% & 1117.0 & 797.5 & 1119.0 & 1245.4 \\ A-n33-k5 & 662.1 & 662.1 & 0.00\% & 895.4 & 667.8 & 811.6 & 988.8 \\ A-n33-k6 & 742.7 & 742.7 & 0.00\% & 860.6 & 755.0 & 868.6 & 990.8 \\ A-n37-k5 & 672.5 & 674.2 & 0.26\% & 974.8 & 682.4 & 926.8 & 1044.3 \\ A-n38-k5 & 733.9 & 739.7 & 0.79\% & 768.4 & 761.5 & 945.0 & 1118.5 \\ A-n39-k6 & 833.2 & 835.2 & 0.24\% & 835.7 & 835.3 & 1118.1 & 1236.4 \\ A-n45-k6 & 952.2 & 957.1 & 0.51\% & 1074.2 & 1030.0 & 1264.9 & 1510.4 \\ A-n45-k7 & 1147.4 & 1156.4 & 0.79\% & 1251.6 & 1161.2 & 1438.8 & 1754.7 \\ A-n55-k9 & 1074.5 & 1085.9 & 1.06\% & 1128.6 & 1126.9 & 1292.8 & 1584.8 \\ A-n60-k9 & 1360.6 & 1365.8 & 0.38\% & 1380.4 & 1371.5 & 1791.1 & 2135.4 \\ A-n61-k9 & 1040.3 & 1049.0 & 0.83\% & 1128.4 & 1118.6 & 1361.2 & 1622.5 \\ A-n63-k9 & 1633.7 & 1641.0 & 0.45\% & 1720.9 & 1689.4 & 2248.6 & 2847.1 \\ A-n65-k9 & 1184.7 & 1195.2 & 0.89\% & 1332.2 & 1271.5 & 1594.6 & 1936.4 \\ A-n80-k10 & 1776.2 & 1792.7 & 0.93\% & 2013.0 & 1838.5 & 2761.4 & 3334.5 \\ B-n31-k5 & 676.1 & 676.5 & 0.06\% & 697.5 & 677.3 & 693.2 & 1068.4 \\ B-n35-k5 & 958.9 & 959.4 & 0.05\% & 1053.4 & 1033.2 & 1215.4 & 1588.0 \\ B-n39-k5 & 553.2 & 553.7 & 0.08\% & 585.6 & 584.6 & 855.3 & 1037.3 \\ B-n41-k6 & 835.8 & 840.8 & 0.60\% & 924.9 & 862.8 & 1152.2 & 1344.5 \\ B-n45-k5 & 754.0 & 754.7 & 0.10\% & 776.4 & 768.3 & 1085.0 & 1202.7 \\ B-n50-k7 & 744.2 & 744.2 & 0.00\% & 789.4 & 778.1 & 991.7 & 1235.8 \\ B-n52-k7 & 754.5 & 756.8 & 0.31\% & 852.1 & 763.8 & 1084.5 & 1355.6 \\ B-n56-k7 & 716.4 & 719.4 & 0.42\% & 802.6 & 735.5 & 1023.0 & 1340.3 \\ B-n57-k9 & 1602.3 & 1603.8 & 0.09\% & 1915.8 & 1700.0 & 2047.6 & 2723.9 \\ B-n68-k9 & 1300.2 & 1306.5 & 0.48\% & 1491.7 & 1359.1 & 1776.7 & 2348.9 \\ B-n78-k10 & 1250.6 & 1256.6 & 0.48\% & 1413.0 & 1383.9 & 1759.8 & 2146.6 \\ E-n22-k4 & 375.3 & 375.3 & 0.00\% & 375.3 & 375.3 & 376.4 & 502.3 \\ E-n30-k3 & 505.0 & 505.0 & 0.00\% & 505.0 & 507.9 & 742.4 & 838.0 \\ E-n33-k4 & 837.7 & 839.4 & 0.21\% & 839.7 & 839.7 & 1183.0 & 1506.9 \\ E-n76-k10 & 841.3 & 852.0 & 1.27\% & 926.0 & 902.9 & 1194.6 & 1336.8 \\ \hline
**Average** & **941.6** & **945.8** & **0.39\%** & **1049.3** & **978.6** & **1266.3** & **1549.2** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of results, in terms of traveled distance, for the different VRP scenarios. depicts the configuration of the deterministic solution and its associated cost (1797.05). This cost can be seen as a lower-bound reference value in a scenario with perfect information. Figures 11-13 show a representation of the obtained solution considering different levels of uncertainty. As the level of uncertainty increases, the total cost also increases, i.e., the highest cost (1860.94) is reached in the completely fuzzy scenario, where the solution cost has increased up to 3.43% with respect to the deterministic solution. This extra cost is mainly caused by the rise in failure costs, since a greater number of detours and round-trips are expected when the uncertainty in the demand at each node is higher. Note also that the solutions have different configurations in each scenario, since the optimization algorithm attempts to generate routes that reduce the risk of failure.