# Wave Planning for Cart Picking in a Randomized Storage Warehouse
## 1 Introduction
### The Importance of Order Picking for a Warehouse and the Type of Order Picking
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Types** & **Advantages** & \multicolumn{2}{l}{**Disadvantages**} & \multicolumn{2}{l}{**Applications**} \\ \hline  & \(\bullet\) & Pickers gain deep & \(\bullet\) & Multi-part orders & \(\bullet\) & Warehouses that deal \\ Zone picking (Pick and & & & & \(\bullet\) & Less interaction & \(\bullet\) & with a high number \\ pass) [2; 5; 7; 14; 15] & \(\bullet\) & & & \(\bullet\) & Inconsistent & \(\bullet\) & of SKUs \\  & & & & & & demand per zone & \\ \hline  & & & & & \(\bullet\) & More complicate & \\  & & & & & planning and & \\  & & & & & computing & \\  & & & & & are required & \\  & & & & & & \\  & \(\bullet\) & Maximize shipping & \(\bullet\) & Difficult to process & & \\  & & & & & more than one & \\  & & & & & wave simultaneously & \\  & & & & & \(\bullet\) & Idle time while & \\  & & & & & some workers wait & \\  & & & & & for others & \\  & & & & & \(\bullet\) & Not easy to add & \\  & & & & & similar work or & \\  & & & & & additional tasks to a & \\  & & & & & wave that is already & \\  & & & & & in progress & \\ \hline  & & & & \(\bullet\) & Select the shipping & \(\bullet\) & Bulk pick and/or \\  & & & & & carton prior to the & & case pick \\  & & & & order & \(\bullet\) & Distribution-to-store \\ Put to store [4; 5; 8; 18; 19] & & & formal & & picking process & & order carton \\  & & & packing operation & \(\bullet\) & Difficult to get this & \(\bullet\) & Convey complete \\  & & & & type of logic to & & cartons to shipping and \\  & & & & work effectively & & start a new carton \\ \hline  & & & & & \(\bullet\) & Leave a lot of room & \\  & & & & & for human error & \\ Cart picking [5; 6; 8; 18; 19; 20] & & & many customer & \(\bullet\) & Slower & \(\bullet\) & E-commerce companies \\  & & & & & picking speeds & & \\ \hline  & & & & & \(\bullet\) & Slightly more & \\  & & & & expensive than a & & \\  & & & & magnetic strip & & \\  & & & & & \(\bullet\) & Tags must be placed & \(\bullet\) & Case pick \\  & & & & in hangtags at & \(\bullet\) & Pallet load \\ Radio frequency (RF) & \(\bullet\) & Increasing & & the source & \(\bullet\) & Put away \\ picking [5; 8; 21] & & & accuracy level & \(\bullet\) & Labor must be & \(\bullet\) & Order \\  & & & & expended to & & checking operation \\  & & & & tag items & & \\  & & & & \(\bullet\) & Tags sometimes & \\  & & & cannot be read & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._Upon order picking equipment, picking orders (also called picking lists) are finally generated. Normally, order picking equipment (or systems) are classified as part-to-picker, picker-to-part, or put systems [14]. The important attributes in picking orders are what SKU, how many quantities, and where stored (illustrated as (I Q S) in Figure 1). Picker-to-parts systems are commonly the order picker walks or drives along the aisles to pick items [8]. In parts-to-picker system, an automatic device brings unit loads from the storage area to the picking stations (sometimes also called picking bays), where the pickers select the required amount of each item. Cart picking systems are particularly popular in case for e-commerce companies, which deal with many customer order lines, must be picked in a short time window. For small items, a well-managed cart picking system can result in around 500 picks on average per order picker hour. Wave picking is used if orders by splitting and/or batching for a common destination or common truck loading time are released simultaneously for picking in multiple warehouse areas. It is a picking system that considers customer orders handling, storage locations, and/or picking equipment concurrently. Algorithms for generating picking orders are: [PERSON] and [PERSON] [22] proposed a linear programming approach to assign the inventory to the orders to maximize the order fill rate, [PERSON] et al.