# Non-Traditional Layout Design for Robotic Mobile Fulfillment System with Multiple Workstations
## 6 Conclusions  
This work addresses the warehouse layout design problem in the context of a RMFS, which is an emerging approach that is attracting a lot of attention in the e-commerce industries. Although there exist extensive research in this field, most studies focus on warehouses with a traditional layout. To the best of our knowledge, this might be the first attempt to consider a non-traditional warehouse layout for a RMFS. To improve the efficiency of the system at a high level, this paper optimizes the location of workstations from a strategic design perspective. Aisle configuration is also taken into consideration to investigate the effects on expected travel distance. We first deduce the expression of travel distance from any storage location to any candidate workstation; then, we propose an integer programming model to determine the picking station location, which is a typical facility location problem. Based on this methodology, we design and conduct a variety of numerical experiments on both traditional and flying-V layouts, through which we find two rules of thumb that can replace the complex computation process: \(2n\) rule and \(n+1\) rule. By using theoretical and experimental studies, we draw the following conclusions:  
1. The flying-V layout can save 8\(\sim\)26% of robot travel distance compared with a traditional layout, and the distance saving is related to the number of workstations and warehouse size. When the warehouse of a medium or large size, saving 10% in distance may only necessitate sacrificing about 2\(\sim\)3% of space use. 2. For a warehouse with a traditional layout, we can simply use the \(2n\) rule to locate workstations; likewise, for the flying-V layout, the \(n+1\) rule can be used to approximately locate the workstations. The travel distance gap for the two cases would be less than roughly 1.5% and 5%, respectively. 3. The \"optimal\" cross-aisle angle can be set as large as possible as long as the angled cross-aisle intersects the left or right edge of the warehouse. There exist several limitations in this study. First, this work is based on an assumption of random storage policy. However, as in some other existing RMFS related research, more storage policies, especially the class-based policy, are worthy of further investigation. Second, the proposed IP model is solved by solver rather than well-designed efficient algorithms. Therefore, developing advanced solution methodologies for this problem and compare their performance with existing facility location related algorithms maybe a future research direction. Moreover, the optimum number of workstations is not determined in this work. We conduct the sensitivity analysis over different number of workstations, whereas the tradeoff between distance saving and construction cost is not covered. Another  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\(N\)} & \multirow{2}{*}{\(L\)} & \multicolumn{2}{c}{**Travel Distance**} & \multirow{2}{*}{**Diff. (\%)**} & \multicolumn{2}{c}{**Space Use (\%)**} & \multirow{2}{*}{**Diff. (\%)**} \\ \cline{3-3} \cline{5-8}  & & \multicolumn{2}{c}{**Traditional**} & & & \multicolumn{2}{c}{**Traditional**} & & \multicolumn{1}{c}{**Flying-V**} \\ \hline \multirow{6}{*}{24 (\(K=4\))} & 20 & 5920.00 & 4810.00 & 18.75 & 41.67\% & 34.72\% & 6.94 \\  & 30 & 10,800.00 & 9411.01 & 12.86 & 44.12 & 38.85 & 5.27 \\  & 40 & 16,800.00 & 14,894.50 & 11.34  
limitation is due to the efficiency evaluated criteria. Rather than travel distance, future studies can consider travel time or the makespan. In addition, more non-traditional warehouse layout designs can be explored in the future, such as fishbone or chevron ones. Finally, to make this work more realistic, the impact of batching decisions on layout design can also be taken into consideration in the future research, and extensive sensitivity analysis over different batching time strategies can be explored as well. Conceptualization, X.L. and L.F.; methodology, X.L. and L.F.; software, X.Y. and J.Z. ; formal analysis, X.Y. and M.Q.