# AMR-Assisted Order Picking: Models for Picker-to-Parts Systems in a Two-Blocks Warehouse
## 2 Literature Review
In fact, while the investment costs for a manual warehouse are low, on the other hand the operator spends a considerable part of his working time moving from one shelving to another, and this is not efficient [23]. A possible solution to reduce this non-value-added fraction of time is to equip a human operator with an automated guided vehicle, typically an AGV (Automated Guided Vehicle) [24] or an AMR (Automated Mobile Robot) cart [25]. The main difference between these two types of automated vehicles lies in the fact that an AGV follows predefined routes, while an AMR, on the contrary, has some intelligence and can recalculate the route in case of obstacles or congestions. AMR-assisted Order Picking has many advantages, including reduced walking time for the operator, increased performance, easy implementation, paired with higher reliability and flexibility. On the other hand, employing automated vehicles requires higher investments, both in terms of startup costs and periodical maintenance [21]. Studies on optimized AMR-assisted Picker-to-Parts systems have started appearing in the literature only recently (see [26]). The authors of [21] studied an AMR-assisted Picker-to-Parts system, with the aim of minimizing the total tardiness of orders with respect to the due date. In their study, a standard single block rectangular warehouse, consisting of parallel aisles and with items stored on both sides, is analyzed. The corridors can be accessed through perpendicular main corridor placed frontally, as depicted in Figure 1. The study relies on a clear subdivision in zones of the warehouse: each aisle represents a distinct zone with a single picker assigned to it. The picker collects the items in the aisle of competence and transports them to the respective handover location, located at the crossing of the aisle with the main corridor. The handover locations are visited by AMRs, that are loaded with the picked articles and then transport the items from the picking areas to a designed depot, where items are further processed toward packing and delivering. Once the items are unloaded from the AMR, the batch is considered completed from the picking-optimization viewpoint, the AMR is equipped with new containers to collect items and can start processing a new batch. Regarding the picking activity, a synchronized Zone Picking strategy [3] is considered, according to which the items of the same batch are collected simultaneously by different pickers in different zones. If the items of a batch are stored in different  
Figure 1: Warehouse with standard layout. several operators are involved in retrieving of them. The quality of the final solution is measured in relation to the minimization of the total delay. The research contributions of the study developed in [21] include the formulation of Mixed Integer Programming (MIP) for the layout depicted in Figure 1. Note that using MIPs to model and solve layout problems is a common practice (see, for example, [27]). The models discussed in the remainder of the paper are modifications to such a model aiming at accommodating a two-blocks layout configuration and some other peculiarities emerging from the real application we consider.