# Slotting Optimization Model for a Warehouse with Divisible First-Level Accommodation Locations
## 2 Previous Literature
\begin{tabular}{c} Placing of accommodation \\ lots with a fleet of k \\ homogeneous teams. \\ \end{tabular}  & \begin{tabular}{c} Priority rule FCFS (First \\ Come First Served). \\ \end{tabular}  & \ \begin{tabular}{c} Minimize the total time \\ of lot formation. \\ \end{tabular}  & \begin{tabular}{c} Statistical design of \\ divided parcels. \\ Metaheuristic of intelligent \\ neighborhood search (INS). \\ \end{tabular}  \\ \hline
[1] & \begin{tabular}{c} Bi-objective. \\ Storage of blocks of pallets \\ with storage locations for a \\ single product. \\ \end{tabular}  & Random. & \ \begin{tabular}{c} Minimization of the \\ total travel distance. \\ Maximization of the \\ average use of storage. \\ \end{tabular}  & \begin{tabular}{c} Mathematical model and a \\ constructive heuristic \\ algorithm. \\ \end{tabular}  \\ \hline
[12] & \begin{tabular}{c} Storage and recovery. \\ Storage location for a \\ single product. \\ \end{tabular}  & Random. & \ \begin{tabular}{c} Minimize travel time. \\ Secondary function: \\ maximize storage use. \\ \end{tabular}  & \begin{tabular}{c} Decomposition of \\ 3 subproblems. \\ Metaheuristic methods: \\ Random, priority rule, and \\ Genetic Algorithm. \\ \end{tabular}  \\ \hline
[14] & \ \begin{tabular}{c} Storage of homogeneous \\ characteristics and WMS \\ integration. \\ \end{tabular}  & FIFO rule (First In First \\ Out). & Minimize total costs. & \begin{tabular}{c} Optimization model. \\ Tabo search metaheuristic. \\ Empirical rule. \\ \end{tabular}  \\ \hline
[22] & \begin{tabular}{c} Application of new storage \\ strategy. \\ \end{tabular}  & \begin{tabular}{c} The selection area is \\ divided into two \\ sections called free \\ seats and start \\ locations. \\ \end{tabular}  & \ \begin{tabular}{c} Minimize the time \\ required for order \\ preparation. \\ \end{tabular}  & \begin{tabular}{c} Simulation (FlexSim). \\ Matlab. \\ \end{tabular}  \\ \hline
[23] & \begin{tabular}{c} The model is based on \\ correlated data products \\ parameters, clients’ orders \\ and warehouse layout. \\ \end{tabular}  & Correlated data from the analysis of the ABC, \ \begin{tabular}{c} Ensure the shortest \\ time to access products \\ of the highest \\ frequency from the \\ gates \\ \end{tabular}  & \begin{tabular}{c} software Pickup Simulo \\ codified in PHP language and \\ MySQL relational databases. \\ Application of artificial neural \\ networks \\ \end{tabular}  \\ \hline  
On the other hand, travel time depends entirely on the location of the SKUs in the warehouse and, in turn, on the storage strategy. The latter is an important factor in warehouse performance, since optimizing the slotting process consists of optimizing storage locations based on the characteristics of the racks and also the requirements of the processes within the warehouse. Given the above, this work proposes an optimization model for the Slotting process (SLAP-VH), where its distinctive feature is the consideration of a warehouse whose locations corresponding to the first accommodation level are divisible. To the best of our knowledge, this feature has not been previously considered within SLAP literature. This work is divided into two stages: determining the optimal location for each SKU in a planning horizon with four defined periods, and determine the best of two allocation scenarios to reduce travel distance and costs. SLAP-VH is solved through a mixed-integer linear programming model (MILP), considering a representative sale day belonging to the most critical period (highest number of orders). The choice of the solution method addressed for SLAP-VH was determined from a comparative table between three metaheuristics and an optimization method (namely: PSO, GA, Tabu Search, and optimization), where the high execution times of the metaheuristics motivated the construction of these evaluation scenarios, solving them from a MILP optimization model with the Gurobi solver through an exact procedure.