# Slotting Optimization Model for a Warehouse with Divisible First-Level Accommodation Locations
## 3 Warehouse Description and Methodology  
The mathematical model is built and evaluated based on real data from a distribution center (DC) of a beverage company that supplies Chile and neighboring countries, provided with around 1200 SKUs on inventory in its dependencies. The DC picking area is modeled to develop the SLAP-VH, where the SKUs are represented as loaded pallets of homogeneous dimensions. As can be seen in Figure 3, the warehouse is composed of columns of racks with equal height and the same number of slots. The width and depth of the storage positions of racks are the same for the entire warehouse with dimensions 1 \(\times\) 1.2 m\({}^{2}\). The height varies between 0.7 m to 1.2 m according to the division of the location and SKU format dimensions. Thus, there are three operations (\(o\)) where only one of them can be applied for each location, that is: the location cannot be divided, can be divided into two parts, or can be divided into three parts. Warehouse aisles correspond to the space between each rack, which are listed from left to right. The design of the warehouse is represented as a rectangular section, where the entrance of the cranes to the locations are on both sides of the aisle, except for the first and last side. Additionally, the warehouse has four exits to the consolidation and dispatch area. Into the warehouse, only trilateral cranes are considered with one operator onboard and an average speed of 5 km/h, where minimizing the distance of crane movements allows determining the number of trips during an 8-h shift, concluding in this way the number of operators needed to satisfy the requirements. This fact, however, can be addressed with greater depth in future researches. In the warehouse under study, there are three storage considerations: (a) locations should be assigned to the pallets according to affinity; (b) The pallets with the highest demand should ideally be assigned in locations without division, and; (c) two columns of locations, which do not include racks, cannot be divided. These columns are called \"Perchas\". These are worked separately, treating as a fourth subproblem for SLAP-VH. Perchas are locations stacking pallets that are stored on the floor at the top, arranged in stacks. This area is managed according to the dedicated storage strategy, since, as shown in Figure 4, each location has capacity for twelve pallets, that is, five pallets can be assigned in base and depth, and then start to be stacked while maintaining ergonomics and operator protection. It is important to store only one type of SKU for each Percha location, since a great storage depth generates inconveniences such as, for example, not finding a pallet of SKU \"A\" since it is under a stack of SKU pallets \"B\". In other cases, this situation can cause  
Figure 3: Layout of the study distribution center. The lighter slots represent Perchas, while the darker slots are racks. the operator may forget that they stored a pallet under other SKUs, passing the expiration date. Regarding time, stacking pallets of different SKU types demands the operator to spend more time searching and moving the necessary pallets until reaching the desired one. The decision to divide locations is based on the demand for the products: for example, if an SKU is less requested in a period, this will be assigned to locations of smaller capacity and further from the warehouse. The opposite happens with a highly demanded SKU, which will be assigned to a high capacity location and close to the exit. Finally, the Perchas are locations defined by the company for a certain type of SKU where the decision consists of positioning the pallet according to its proximity to the exit point since these locations are not divisible. SLAP-VH only considers the first-level stacking locations, that is, the first location from the floor of each rack. Storage is governed by order priority rules, specifically by EDD (Earliest Due Date), except for the picking slots, corresponding to the first level of accommodation.