# AMR-Assisted Order Picking: Models for Picker-to-Parts Systems in a Two-Blocks Warehouse
## 6 Conclusions  
The present study analyzes a warehouse with a two-block layout and proposes optimization models for two possible implementations of an AMR-assisted hybrid order picking system. The first solution is standard, with separated handover locations for each sub-aisle, while the second allows the pickers operating on pairs of sub-aisles facing each other to share the handover location. This increases the complexity of the optimization but potentially leads to more efficient solutions in terms of total tardiness. The optimization is carried out by attacking two novel mathematical programming models we propose via black-box solvers.  
The study is conducted on real-world data originating from a German brick-and-mortar grocery retailer and the experimental simulations carried out suggest that a layout consisting of two blocks and separated handover locations is more efficient for a limited number of items; as the size of the instance increases, however, the layout consisting of two blocks and shared handover location is more optimal. This happens because, for small order instances, the high cart loading times in the second layout mentioned are associated with sub-corridors with very low quantities of items to be picked. As instance size increases, on the other hand, the higher loading times in that configuration are offset by lower cart waiting times in each sub-corridor, due to the greater flexibility of the layout, and higher quantities of items to be picked in each sub-corridor.  
It is possible to conclude, therefore, that for a company handling many items, the most efficient implementation for an AMR system in a two-block warehouse is the one making use of shared handover location; this configuration, compared to the other one, also allows for the greatest percentage improvement in tardiness following the increase in fleet size. Increasing the number of AMRs turns out to be the most strategically cost-effective intervention.  
In addition, experiments conducted on fleet size and cart speed showed that an increase in these factors leads to an improvement in total tardiness, consistent with what observed in the previous literature. However, the analysis of the results shows that the percentage improvement in tardiness after increasing fleet size is greater than the one obtained by increasing speed of AMRs. The conclusion disagrees with some of the results previously published. This happens because of the two-blocks layout configuration and because the size of the picking area is large compared to the number of aisles in the real warehouse considered and, therefore, the work of the human pickers plays an important role in determining the total tardiness.  
Conceptualization, G.P. and R.M.; methodology, G.P. and R.M.; software, G.P. and X.C.; validation, G.P.; formal analysis, G.P. and R.M.; investigation, G.P. and X.C.; resources, D.L. and M.K.; data curation, G.P., D.L. and M.K.; writing--original draft preparation, G.P. and R.M.; writing--review and editing, G.P., X.C., D.L., M.K. and R.M.; visualization, G.P.; supervision, R.M.; project administration, R.M. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to their confidential nature.  
The authors declare no conflict of interest.