# Slotting Optimization Model for a Warehouse with Divisible First-Level Accommodation Locations
## 10 Discussion  
Considering those authors who propose different ways of approaching the Slotting optimization problem, the vast majority of these focus on solving it through metaheuristics based on search and accommodation placement. However, this study is carried out under a decomposition of the problem that determines each key decision. While decomposition is one of the optimal methods for tackling problems with broad key decisions, separating the problem allows greater handling of data manipulation and a dedicated focus on each decision to be resolved. The computational results reveal the impact on the flow time of the executions for each subproblem and at the same time for each scenario, where each model provides the necessary data to address the problem in a sequential method and additional information that allows generating an effective analysis of each subproblem which helps to create a faster and better result in the SLAP-VH solution procedure. Ref. [1] analyzed the efficiency between solving the assignment problem metaheuristically and mathematically, where the latter does not turn out to be very fast in terms of the average execution time (\(26,640\) s, while the heuristic algorithm took \(155\) s). However, it provides a solution that is very close to optimal, where the mean gap of the solutions is \(4.3\%\) after excluding an outlier.  
This study groups each factor of the Slotting design to improve the Picking operation, such as distance, cost of operation, crane movements, use of human resources, and storage strategies based on implementation alternatives. Although the studies carried out by other authors evaluate the application of the methodology, the results obtained before the application are similar when using both decomposition and a metaheuristic. Comparing the result obtained by [14] which obtains a \(4\%\) reduction in the cost of human resources considering the departure of a specific batch of accommodation, the same percentage was obtained in the reduction of costs for accommodation in first level locations corresponding to the SLAP-VH problem. In addition, Slotting has been applied in the same way as in each of the compared investigations, where the methodology used is the same, but the impact depends completely on the storage space since it is not the same case to apply a Slotting optimization in a maritime terminal [11] versus a beverage distribution center. As for the infrastructure, the handling of the type of material, and, most importantly, the specific objective of performing the Slotting. For example, the results obtained by [12] are related to the objective of programming and assigning cranes, according to their specifications, to carry out operations in the locations where they can work. While for this study, the results obtained are related to improving the picking process and reducing the distance of cranes.  
Finally, the solution to the problem will depend on four major factors: the storage location type, the storage strategy, the number of SKUs to be stored, and the warehouse's size. All these factors are strongly related when it comes to minimizing travel time, operational cost, and storage usage. The model used in this research connects these factors considering divisible locations in racks and \"Percha\" locations, the two storage strategies evaluated in the different scenarios, families, subfamilies and SKUs, and the warehouse entry/exit distance. Comparing the different scenarios, \(E_{1}\) exceeded \(E_{2}\) in terms of the quality of the solution and the computational time optimally, significantly improving the distance traveled by the cranes and, simultaneously, the warehouse space usage as well as the operating cost.