## 6 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multicolumn{6}{c}{**Best Nonflexible Hybrid Solution**} & \multicolumn{6}{c}{**Best Flexible Hybrid Solution**} & \multirow{2}{*}{**Gap**} \\ \cline{2-2} \cline{5-12}  & **OC** & **RC** & **FC** & **TC** & **SS** & **OC** & **RC** & **FC** & **TC** & **SS** & **TC** \\ \hline \hline \multicolumn{12}{c}{**Low variability**} \\ \hline Cr30x5a-1 & 200.00 & 619.51 & 3.45 & 822.96 & 1\% & 200.00 & 575.14 & 3.31 & 778.45 & 2\% & –5.41\% \\ Cr30x5a-2 & 200.00 & 626.01 & 0.04 & 826.05 & 1\% & 200.00 & 607.28 & 0.12 & 807.40 & 3\% & –2.26\% \\ Cr30x5a-3 & 200.00 & 507.99 & 17.56 & 725.55 & 2\% & 187.50 & 509.25 & 17.48 & 714.22 & 3\% & –1.56\% \\ Cr30x5b-1 & 200.00 & 682.97 & 0.32 & 883.29 & 2\% & 225.00 & 623.22 & 14.59 & 862.81 & 0\% & –2.32\% \\ Cr30x5b-2 & 200.00 & 625.32 & 0.00 & 825.32 & 2\% & 187.50 & 625.32 & 0.00 & 812.82 & 2\% & –1.51\% \\ Cr30x5b-3 & 200.00 & 684.58 & 5.95 & 890.53 & 1\% & 187.50 & 684.58 & 6.35 & 878.43 & 1\% & –1.36\% \\ Cr40x5a-1 & 200.00 & 733.47 & 3.22 & 936.70 & 0\% & 162.50 & 731.84 & 0.07 & 894.41 & 1\% & –4.51\% \\ Cr40x5a-2 & 200.00 & 691.47 & 11.15 & 902.63 & 1\% & 225.00 & 639.02 & 0.81 & 864.83 & 1\% & –4.19\% \\ Cr40x5a-3 & 200.00 & 748.64 & 9.88 & 958.52 & 1\% & 162.50 & 752.88 & 3.26 & 918.64 & 0\% & –4.16\% \\ Cr40x5b-1 & 200.00 & 858.58 & 1.94 & 1060.53 & 2\% & 162.50 & 852.04 & 12.24 & 1026.78 & 1\% & –3.18\% \\ Cr40x5b-2 & 300.00 & 690.57 & 0.65 & 991.22 & 2\% & 225.00 & 690.57 & 0.62 & 916.18 & 1\% & –7.57\% \\ Cr40x5b-3 & 200.00 & 780.62 & 0.07 & 980.69 & 2\% & 175.00 & 772.87 & 0.29 & 948.16 & 2\% & –3.32\% \\ \hline \hline \multicolumn{12}{c}{**Average**} & 208.33 & 687.48 & 4.52 & 900.33 & 1.42\% & 191.67 & 672.00 & 4.93 & 868.59 & 1.42\% & –3.45\% \\ \hline \hline \multicolumn{12}{c}{**Medium variability**} \\ \hline Cr30x5a-1 & 200.00 & 619.51 & 9.17 & 828.68 & 0\% & 200.00 & 575.14 & 9.67 & 784.81 & 2\% & –5.29\% \\ Cr30x5a-2 & 200.00 & 626.01 & 0.60 & 826.61 & 2\% & 200.00 & 607.28 & 1.94 & 809.22 & 3\% & –2.10\% \\ Cr30x5a-3 & 200.00 & 507.99 & 24.30 & 732.29 & 2\% & 187.50 & 509.25 & 24.10 & 720.85 & 3\% & –1.56\% \\ Cr30x5b-1 & 200.00 & 681.50 & 14.31 & 895.80 & 1\% & 225.00 & 623.22 & 18.32 & 866.53 & 3\% & –3.27\% \\ Cr30x5b-2 & 200.00 & 625.32 & 0.01 & 825.33 & 2\% & 187.50 & 625.32 & 0.00 & 812.82 & 2\% & –1.52\% \\ Cr30x5b-3 & 200.00 &Some instances show an opposite behavior, i.e., opening costs either increase or remain the same while routing costs decrease. For example, the nonflexible solution of the instance _Cr30x5a-1_ opens two depots of size 1000 each. Alternatively, the flexible solution opens one depot of size 1500 and one depot of size 500, i.e., the total capacity is equal and, given our defined costs structure, also the opening costs. However, this slight change drives a redesign of routes that decreases RC. An additional example is given by the instance _Cr40x5a-2_. Figure 7 depicts the best solution found by both the nonflexible approach (a) and our flexible approach (b). The solution in Figure 6(a) locates two depots of size 1750 each, and the solution in Figure 6(b) locates three depots of size 875 each. The latter case has a total capacity that is smaller than the former's; however, opening costs are higher since the fixed cost is clearly greater when 3 facilities are open instead of 2. This new configuration decreases considerably routing costs (Table 4), which shows that considering facility sizing decisions not only reduces total costs by decreasing depots capacity but also by increasing it, since shorter routes can be designed.