# Slotting Optimization Model for a Warehouse with Divisible First-Level Accommodation Locations
## 2 Previous Literature
Reducing costs has a strong impact on the entire order picking process since all activities are connected. Ref. [15] state that the optimization of positioning not only reduces costs and energy in the operation but also improves the efficiency of the storage of goods. Therefore, optimizing the Slotting process helps to complete orders at a faster pace, benefiting the consolidation work (i.e., a process that groups the demand for orders from different areas, into complete orders), and the service level delivered to end consumers. Managers want to reduce the time spent on movements within the warehouse, not only to decrease labor cost and production downtime but also to shorten customer response time. Ref. [16] developed a study of the time of the activities carried out in the preparation of orders in Maines Paper and Food Services (Inc in Conklin, NY), concluding that 40% of the time is spent on travel. Therefore, reducing this percentage could significantly save a warehouse operating expense. Reducing travel time implies reducing the distance of cargo transfer and therefore the number of operators required to place an order. Ref. [17] state that the distance largely depends on the design of the warehouse. It is logical, in the case of slotted storage, to place the merchandise that has a high turnover in privileged locations close to the dispatch point. In contrast, when placing an order where items need to be selected in a single tour, it makes more sense to assign SKUs to locations that minimize travel time for routes. Figure 2: Definition of periods for SLAP-VH based on the monthly demand of each SKU grouped by families. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reference** & **Characteristic of the Model** & **Storage Strategy** & **Function to Optimize** & **Solution Method** \\ \hline
[16] & Warehouse with Crossover-Aisles with one direction of movement. & Weight order. & Minimize total distance traveled. & \begin{tabular}{c} Mathematical model \\ programming language C. \\ Simulation Microsoft Visual \\ Basic 6.0. \\ \end{tabular}  \\ \hline
[13] & Linear movement of objects. & Single storage. & \ \begin{tabular}{c} Minimize the number \\ of obstructive objects. \\ \end{tabular}  & \begin{tabular}{c} Mathematical programming \\ model.Genetic algorithm (GA). \\ \end{tabular}  \\ \hline
[15] & \begin{tabular}{c} Based on the principle of \\ lower energy and \\ shorter time. \\ \end{tabular}  & Random. & \ \begin{tabular}{c} Minimize total energy \\ consumption. \\ Minimize storage time. \\ \end{tabular}  & \begin{tabular}{c} Discrete particle swarm \\ optimization (PSO). \\ \end{tabular}  \\ \hline
[11] & \begin{tabular}{c} Storage of containers in a \\ maritime terminal. \\ \end{tabular}  & Category of containers. & \ \begin{tabular}{c} Minimize travel \\ distance and time \\ required load transfer. \\ \end{tabular}  & \begin{tabular}{c} Mixed-integer \\ programming model. \\ Hybrid stacking algorithm \\ sequence procedure. \\ \end{tabular}  \\ \hline
[18] & \begin{tabular}{c} Travel distance considering \\ three axes. \\ \end{tabular}  & Symmetric storage. & \ \begin{tabular}{c} Minimize total travel \\ distance. \\ \end{tabular}  & \begin{tabular}{c} Mathematical model evaluated \\ in LINGO Software. \\ \end{tabular}  \\ \hline
[19] & \begin{tabular}{c} Stored cycle travel times and \\ double-depth retrieval. \\ \end{tabular}  & \ \begin{tabular}{c} Random. \\ Always positioned first \\ to the second lane. \\ \end{tabular}  & Minimize travel time. & \begin{tabular}{c} Analytical model. \\ Simulation. \\ \end{tabular}  \\ \hline
[20] & \begin{tabular}{c} Warehouse symmetrical \\ storage locations for a \\ single product. \\ \end{tabular}  & Symmetric storage. & \ \begin{tabular}{c} Minimize total travel \\ distance. \\ \end{tabular}  & \begin{tabular}{c} Mixed-integer \\ programming model. \\ Metaheuristics: Differential \\ evolution (DE), Global \\ optimization of the local and \\ near neighbor particle swarm \\ (GLNPSO). \\ \end{tabular}  \\ \hline
[21] &