## 2 Literature Review  
Table 1 shows a summary of the methods for creating family groupings that predominate in the literature of DC operation management. These methods include frequency-based methods, quantity-based methods and data mining-based methods. Frequency-based methods [5; 6] determine groupings by the number of orders containing two items at the same time. Quantity-based methods [7; 8; 9] determine the groupings by the quantity of items in  
an order. Data mining methods used algorithms, such as ARM, to estimate the correlation between items based on levels of support, lift and confidence [10; 11; 12]. Most of the methods summarized in this table evaluate the relationship between a pair of items (itemset size = 2); thus, every possible combination of two items is evaluated. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Method** & **Metric** & & **Remarks** \\ \hline \multirow{6}{*}{[PERSON] and [PERSON] [5]} & & \(\bullet\) & Frequency-based method. \\  & & \(\bullet\) & Itemset size = 2. \\  & The proportion of orders which contains a pair of items in the same order. & \(\bullet\) & Evaluate every possible combination of two items. \\  & & \(\bullet\) & Require large data to get statistically significant results. \\ \hline \multirow{6}{*}{[PERSON] [7]} & & Similarity between pairs of items based on order-item-quantity rule. & \(\bullet\) & Quantity-based method. \\  & Similarity between any pair of customers based on the customer-order-item-quantity rule. & \(\bullet\) & Itemset size = 2. \\  & & \(\bullet\) & User's a mathematical program to determine optimal grouping of items and customers. \\  & & \(\bullet\) & Conducts a WITNESS simulation study to test the layout solutions. \\ \hline \multirow{6}{*}{[PERSON] [8], [PERSON] [9]} & & \(\bullet\) & Quantity-based method. \\  & & \(\bullet\) & Itemset size = 2. \\  & & \(\bullet\) & Formulate a Quadratic Generalized Assignment Model to determine optimal location of SKUs in storage slots. \\  & & \(\bullet\) & Use heuristics to find solutions to the storage assignment model since mathematical program is NP-hard. The heuristics has three phases: clustering, ranking and interchanging phases. \\  & & \(\bullet\) & Conduct a simulation study to evaluate storage location solutions. Conduct additional simulation studies to evaluate the order’s weight constraints; see [PERSON] [12]. \\ \hline \multirow{6}{*}{[PERSON] et al. [6]} & & Similarity coefficient proportional to the probability that a pair of items will be ordered together and the probability that these two items will be ordered. & \(\bullet\) & Frequency-based method. \\  & & \(\bullet\) & Itemset size = 2. \\  & & \(\bullet\) & Formulate and solves the problem as a two-stage Clustering Assignment Model. \\  & & \(\bullet\) & Present a small case study using a dataset from industry. \\ \hline \multirow{6}{*}{[PERSON] et al. [10], [PERSON] et al. [11]} & & \(\bullet\) & Data Mining-based method. \\  & & \(\bullet\) & Itemset size = 2. \\  & & \(\bullet\) & Evaluate support and lift between a pair of items (the similarity metric integrates support and lift with turnover rate and distance). \\  & & \(\bullet\) & Formulate and solves the problem as a Generalized Assignment Model. \\  & & \(\bullet\) & Present a real case study using a dataset from industry. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Methods for the creating of family groupings. [PERSON] and [PERSON] [5] propose storing together correlated SKUs consisting of the items ordered together to a distribution center. The authors show that this approach reduces the order picking time when compared to the random assignment policy. The authors note that this approach requires a large dataset of SKUs to obtain statistically significant results. [PERSON] [7] uses cluster analysis to create groups of correlated items based on metrics that measure the demand relationship between two items that appear on the same order together and the demand relationship between customers.