# Non-Traditional Layout Design for Robotic Mobile Fulfillment System with Multiple Workstations
## 5 Numerical Experiments
### Comparison of Traditional and Flying-V Layouts
#### 5.5.2 Space Use  
As additional cross aisles are inserted in a flying-V warehouse, space use is sacrificed. Therefore, how to tradeoff between the benefit of travel saving and the disadvantage of space waste is a practical problem. To address this, we integrate in Table 14 experimental results of the two aspects together. When the warehouse is relatively small, as much as 18.75% travel distance can be saved but the space use rate decreases 6.94%. However, as the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(K\)} & \multirow{2}{*}{\(L\)} & \multirow{2}{*}{\(\frac{L}{W}\)*} & **Travel Distance** & \multirow{2}{*}{Flying-V} & \multirow{2}{*}{Reduction} & \multirow{2}{*}{Diff.(\%)} \\  & & & **Traditional** & & & \\ \hline \multirow{4}{*}{1} & 24 & 1.33 & 62.640.00 & 53,426.30 & 9213.70 & 14.71 \\  & 32 & 1.0 & 91,200.00 & 75,871.32 & 15,328.68 & 16.81 \\  & 40 & 0.8 & 123,600.00 & 101,495.84 & 22,104.16 & 17.88 \\ \hline \multirow{4}{*}{2} & 24 & 1.33 & 41,040.00 & 36,177.13 & 4862.87 & 11.85 \\  & 32 & 1.0 & 62,400.00 & 54,731.05 & 7668.95 & 12.29 \\  & 40 & 0.8 & 87,312.00 & 77,246.66 & 10,065.34 & 11.53 \\ \hline \multirow{4}{*}{3} & 24 & 1.33 & 36,160.00 & 32,093.01 & 4066.99 & 11.25 \\  & 32 & 1.0 & 53,346.00 & 47,627.74 & 5718.26 & 10.72 \\  & 40 & 0.8 & 72,656.00 & 65,730.83 & 6925.17 & 9.53 \\ \hline \multirow{4}{*}{4} & 24 & 1.33 & 32,400.00 & 29,481.72 & 2918.28 & 9.01 \\  & 32 & 1.0 & 47,040.00 & 42,905.27 & 4134.73 & 8.79 \\  & 40 & 0.8 & 63,584.00 & 58,440.49 & 5143.51 & 8.09 \\ \hline \multirow{4}{*}{5} & 32 & 1.0 & 44,240.00 & 38,656.56 & 5583.44 & 12.62 \\  & 40 & 0.8 & 59,036.00 & 52,780.39 & 6255.61 & 10.60 \\ \hline \multirow{4}{*}{6} & 32 & 1.0 & 42,024.00 & 37,070.60 & 4953.40 & 11.79 \\  & 40 & 0.8 & 55,644.00 & 49,890.49 & 5753.51 & 10.34 \\ \hline \multirow{4}{*}{7} & 32 & 1.0 & 40,604.00 & 35,672.87 & 4931.13 & 12.14 \\  & 40 & 0.8 & 53,532.00 & 47,000.59 & 6531.41 & 12.20 \\ \hline \multirow{4}{*}{8} & 32 & 1.0 & 39,360.00 & 34,275.14 & 5084.86 & 12.92 \\  & 40 & 0.8 & 51,750.00 & 44,912.53 & 6837.47 & 13.21 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Total distance comparison (\(L=60\)).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(K\)} & \multirow{2}{*}{\(L\)} & \multirow{2}{*}{\(\frac{L}{W}\)*} & **Travel Distance** & \multirow{2}{*}{Flying-V} & \multirow{2}{*}{Reduction} & \multirow{2}{*}{Diff.(\%)} \\  & & & **Traditional** & & & \\ \hline \multirow{4}{*}{1} & 20 & 0.6 & 8600.00 & 6321.85 & 2278.15 & 26.49 \\  & 40 & 1.1 & 25,200.00 & 20,778.70 & 4421.30 & 17.54 \\  & 60 & 1.6 & 49,800.00 & 43,235.56 & 6564.44 & 13.18 \\ \hline \multirow{4}{*}{2} & 20 & 0.6 & 6312.00 & 5175.76 & 1136.24 & 18.00 \\  & 40 & 1.1 & 17,200.00 & 14,724.78 & 2475.22 & 14.39 \\  & 60 & 1.6 & 31,800.00 & 28,253.21 & 3546.79 & 11.15 \\ \hline \multirow{4}{*}{3} & 20 & 0.6 & 5224.00 & 4201.00 & 1023.00 & 19.58 \\  & 40 & 1.1 & 14,864.00 & 12,887.36 & 1976.64 & 13.30 \\  & 60 & 1.6 & 28,504.00 & 25,455.79 & 3048.21 & 10.69 \\ \hline \multirow{4}{*}{4} & 20 & 0.6 & 4600.00 & 3700.90 & 899.10 & 19.55 \\  & 40 & 1.1 & 13,260.00 & 11,732.31 & 1527.69 & 11.52 \\ \cline{1-1}  & 60 & 1.6 & 25,920.00 & 23,562.41 & 2357.59 & 9.10 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Total distance comparison (\(N=20\)).  
warehouse size increases, a roughly 10% travel saving can be obtained for just 2% or 3% space loss. This suggests that flying-V is applicable if space is not a bottleneck resource, or if the warehouse is of a medium or large size, for example, over 5000 m\({}^{2}\) (this is equivalent to \(N=24,L=60\)).