# Slotting Optimization Model for a Warehouse with Divisible First-Level Accommodation Locations
## 2 Previous Literature  
Slotting optimization research can be divided into two areas. The first is the modeling of the slotting process to improve efficiency in order preparation, load movement, handling of heavy over lightweight items, among others. And the second area is related to model resolution, using for example, exact, heuristic, and/or metaheuristic algorithms, among others [9]. Several researchers have developed both mathematical and heuristic models to address Slotting related to the Storage Location Assignment Problem (SLAP). Some of these studies can be consulted in Table 1, where the models developed tend to be very complex due to the SLAP NP-Hard complexity. In this sense, ref. [10] affirm that most of the storage and recovery problems fall into this category, which motivates the use of heuristics for their resolution. Besides, certain investigations propose decompositions of the problem, where initially the number of locations is addressed and the assignment is considered afterward. Using this strategy, ref. [11] addressed the SLAP for outbound containers in a maritime terminal, which was divided into two stages. They first determined the number of locations from a mixed-integer linear programming model and then defined the exact storage location based on a hybrid sequence stacking algorithm. This experimental study demonstrated effectiveness in comparing and analyzing performance in total travel distance between the yard and the bunk, the imbalance of the workload between different blocks of containers, and the percentage of repetitions in loading operations. In this way, the hybrid sequence stacking algorithm reduces the unnecessary movement of containers in cargo operations to 18%, compared to 30% of the average rehandle percentage in the case study analyzed. It is interesting to note that the vast majority of the studies carried out consider as an objective function the minimization of time, cost, or distance. However, authors such as [12] developed a mathematical model that minimizes storage time by incorporating a two-objective optimization approach: maximization of space availability and minimization of production due date measurements. Ref. [1] developed a mathematical model that considers two simultaneous goals: minimize travel distance and maximize average storage usage. The SLAP-VH also incorporates this feature, considering the minimization of cranes route as the main objective function, and the maximization of storage use as a secondary function. One of the main parameters of the SLAP modeling is the planning horizon. Research in the field reveals that evaluation periods adjusted to the problem achieve greater effectiveness in the correct arrangement of SKUs. For example, in [13] was defined the time horizon in periods of discrete units (days) to consider the real situation of the research, where the storage warehouse releases outgoing objects and stores incoming objects in each unit period. For the case of SLAP-VH, the period (\(t\)) is based on the normal distribution of the demand for each SKU (see Figure 2), this allows the Slotting to be defined as active since the correct accommodation adapts to the temporality of the products according to the defined periods. The models proposed by the researchers are commonly solved by heuristics or metaheuristics, considering the complexity of the SLAP. However, these heuristic and metaheuristic algorithms are not able to guarantee the optimality of the solutions, although, in some cases, they offer nearly optimal solutions depending on the execution times and the parameter setting. Researchers have evaluated the effectiveness of different algorithms for the SLAP. For example, ref. [14] made a comparison between an optimization method, a Tabu Search metaheuristic, and an empirical rule. The authors concluded that the size of the accommodate list has a significant effect on its structure and the optimality of the results. Additionally, the optimization method reduced labor costs compared to the solutions provided by metaheuristics.