# AMR-Assisted Order Picking: Models for Picker-to-Parts Systems in a Two-Blocks Warehouse
## 5 Numerical Experiments
### Experiments on the AMS Fleet Size and Speed  
This section analyzes the impact that increasing cart speed and fleet size have on total tardiness. Indeed, these are parameters that can be easily changed, with a related technological intervention, without the need to reorganize the entire picking system [21].  
Two different fleet sizes are considered, consisting of 2 and 3 carts, respectively; with larger fleet sizes, the tardiness goes consistently to zero for each instance considered, and thus the results are omitted. For AMR speed, expressed in km/h, we consider the following values: {2.4, 4.6, 4.8, 6.0, 7.2}.  
As anticipated in Section 4.1, the experiments are carried out for three instances of different sizes, consisting of 50 (SMALL), 150 (MEDIUM) and 300 items (LARGE), respectively. The impact of AMR speed on total tardiness can be observed for order instances of three different sizes. For each group of instances, SMALL, MEDIUM, and LARGE, respectively, and for each possible combination of the number of AMRs and speed, the corresponding tardiness values are shown respectively in Tables 1 and 2 (for the cases with separated and shared handover locations, respectively).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Small** & **Medium** & \multicolumn{2}{c}{**Large**} \\ \hline
**AMR Speed** & **Number of** & **Number of** & **Number of** & **Number of** & **Number of** \\
**(km/h)** & **AMR = 2** & **AMR = 2** & **AMR = 2** & **AMR = 2** & **AMR = 3** \\ \hline
2.4 & 2634 & 5645 & 4131 & 16,954 & 1870 \\
3.6 & 0 & 4863 & 2312 & 14,820 & 0 \\
4.8 & 0 & 3559 & 2241 & 13,173 & 0 \\
6.0 & 0 & 3513 & 2227 & 12,869 & 0 \\
7.2 & 0 & 2953 & 2112 & 11,314 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Values of tardiness as a function of the AMR speed—separated handover locations.  
As it can be seen from Tables 1 and 2, an increase in AMR speed, has a positive impact on tardiness. For example, a relatively small increase in the AMR speed from 2.4 km/h to 3.6 km/h for a medium-sized instance leads to remarkable decreases in tardiness. It can be seen, however, that in other cases, by increasing the speed, the decrease in tardiness is very marginal. This is due to the pickers' picking time, that becomes the bottlenecks of the system; although the cart takes less time to reach the handover location, it must wait for the picker, who has not yet finished picking.  
Given a constant AMR speed, increasing fleet size from 2 to 3 can have a significant impact on tardiness. An increase 2 to 3 of the number of AMR leads to a crucial decrease in tardiness for large instances. In general, the larger the number of orders, the greater the impact of increased fleet and speed on total tardiness. The presence of bottlenecks represented by human pickers can be observed also in these experiments.  
The experiments showed that an increase in these factors leads to an improvement in total tardiness, consistent with what was obtained in [21]. However, analysis of the results shows that the percentage improvement in tardiness after increasing fleet size is greater than the one obtained by the adoption of faster AMRs. This conclusion disagrees with what was stated in [21]. It can be argued that this result can be blamed on the size of the picking area, which is large compared to the number of aisles, and by the fact that the two-blocks layout creates different situations.  
Comparing the two implementations of the system, it appears that with shared handover location, the maximum percentage decrease in tardiness following an increase in fleet size. This configuration, moreover, turns out to be more efficient from the point of view of bottlenecks imputed to operators; the presence of a shared handover location, in fact, ensures greater coordination between operator and truck, limiting the latter's waiting time.  
In general, a possible solution to limit bottlenecks could be to employ two operators per aisle, consequently speeding up the overall picking process.