# Slotting Optimization Model for a Warehouse with Divisible First-Level Accommodation Locations
## 3 Warehouse Description and Methodology
For this reason, this research focuses exclusively on the assignment of these locations, which can be divided into three positions, in two, or they can be maintained without performing any division. In this sense, three, two, or one pallet can be stored respectively. Each first-level storage slot has capacity for two pallets of maximum height (Figure 5(a.1,a.2)), while a divided slot (Figure 5(b.1,b.2)) has capacity for four medium height pallets, or six pallets of minimum height (Figure 5(c.1,c.2)). Therefore, the term \"location\" will be used to denote the storage space of a rack with a capacity of one pallet of maximum height, while the storage space of a divided slot of less height will be called \"position\". Within the warehouse, SKUs are classified based on the Pareto principle according to the class or product family to which they belong, where 80% of the total quantity demanded corresponds to type \"A\" SKUs, 15% to the \"B\" and 5% to the \"C\". The ABC classification is essential to know the need for accommodation of each SKU based on its demand. Each of the families has a different number of SKUs and each family has a regrouping called a subfamily, which is based on the weight of the products. In this way, the grouping by families only allows determining the product category, while the regrouping by subfamilies allows classifying with more information about each SKU based on the size of the product. This creates a greater connection between stackability priority and affinity between the products. In this sense, it is necessary to clarify that grouping by product families and subfamilies is a strategy defined by the company, which is enhanced by the ABC classification by periods. Initially, there were 12 families, however, in order to group those with a smaller quantity without affecting stackability, 7 families were finally obtained. As [3] indicates, the general assignment problem is classified as an NP-hard complexity problem. From this statement, SLAP-VH can also be considered as an NP-hard problem, since it applies a stricter constraint set for the general storage assignment problem. The case study considered 726 SKUs that must be distributed in 1170 locations, a value that may increase considering the division of locations. Therefore, evaluating all the possible combinations becomes an impractical strategy given the order compilation time \(O(n! )\) for exact algorithms. However, based on the assumptions used and presented in Table 3, the underlying complexity tends to decrease, reducing the number of decisions and the combination of cases that arise when trying to model reality. In this way, the presented model results in a mixed-integer linear programming problem (MILP). Figure 4: Representation of Perchas locations with a two-sided view, where each rectangle represents an SKU pallet. Bold arrows indicate pallet entry. * The Warehouse Starts Empty to Accommodate SKUs Packing
* All accommodation operations are performed by homogeneous cranes
* Stored pallets are homogeneous and loaded by a single SKU
* All SKUs must be stored in at least one location or position
* All locations used in the problem corresponds to the first accommodation level
* All locations can be divided, except for _Perchas_
* The distance is measured with respect to the warehouse exits and the end of the aisle in a linear way
* The distance is equal for both divided and without division locations
* A not divided location is assigned when an SKU demands at least one pallet bin
* A two-position location is assigned when an SKU demands between 0.5 and 1 pallet bin
* A three-position location is assigned when an SKU demands less than half of a pallet bin  
Figure 5: Representation of the first accommodation level locations with simple, double, and triple division, where (**a.1**), (**b.1**), and (**c.1**) correspond to the front view of a storage location in a rack, while (**a.2**), (**b.2**), and (**c.2**) correspond to the side view. Bold arrows indicate pallet entry.