# Towards Productive and Ergonomic Order Picking: Multi-Objective Modeling Approach
## 3 Case Study  
For a simple validation of our models, we analyzed a warehouse that consists of a single storage rack with five vertical and nine horizontal storage levels (Figure 3B). On that storage rack, boxes are stocked in 45 storage spaces (Figure 3A). Storage spaces have fixed and equal dimensions. The box is positioned in the middle of the front width of the storage space. The order pickers can pick items from each of them one at a time. Two different lengths of storage rack are analyzed--the first one with 1.06 m spacing between rack holders and the other with 3.18 m spacing. The box is always stocked in the middle of two rack holders. Distances between the depot (I/O) and the end of a specific position from P1 to P9 are also shown in (Figure 3A). The order picker handles nine types of cardboard boxes without handles in the above-described warehouse (Table 2). Boxes appear in three sizes: Large (31 cm \(\times\) 37 cm \(\times\) 45 cm), Medium (20 cm \(\times\) 30 cm \(\times\) 40 cm), and Small (7 cm \(\times\) 11 cm \(\times\) 18 cm). Each box size is represented in three different masses: Large (0.1 kg, 5 kg, 10 kg), Medium (0.1 kg, 5 kg, 10 kg), and Small (0.1 kg, 1 kg, 5 kg). In the described working laboratory environment (Figure 3A), which is an excellent approximation to the actual storage environment of smaller dimensions, it was necessary to obtain data on the picking time for each box type/mass at all five possible shelf heights. Nine men with a mean age of 42 (SD 17.8) years, the height of 179 (SD 5.2) cm, weight of 86 (SD 9.4) kg, and eight women with a mean age of 40 (SD 15.2) years, the height of 163 (7.4) cm, the weight of 62 (12.4) kg participated in the experiment. The participants were of different professions. Five men and four women are physical workers, two male and three female are students, and the rest are office workers. None of them have ever worked as an order picker in a warehouse. They all signed a consent form approved by the Senate of the Faculty of logistics at the University of Maribor. The participants picked cardboard boxes without handles in three different volumes and with four different loadings from shelves on five different heights in the steel warehouse rack. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Box Type/Mass** & **Label** & **Box Type/Mass** & **Label** & **Box Type/Mass** & **Label** \\ \hline Large/0.1 kg & L & Medium/0.1 kg & M & Small/0.1 kg & S \\ \hline Large/5 kg & L & Medium/5 kg & M & Small/5 kg & S \\ \hline Large/10 kg & L & Medium/10 kg & M & Small/1 kg & S \\ \hline \end{tabular}
\end{table} 
Table 2: Types and masses for the boxes. Figure 3: The case study’s storage rack: (**A**)—technical data; (**B**)—placement in the laboratory. During the experiment, each participant picked the ordered box from a rack and lowered or lifted the box on a surface for disposal, using a grip of the box's side surfaces between the palms (Figure 4). A sequence of boxes on the picking list was determined randomly and was the same for all participants. The participants did not know how heavy the box they should pick is. After unloading the box on the surface for disposal, the assistant immediately read the new number of the box for picking and removed the box from improvised surface for disposal. A video camera with a rate of 60 frames per second recorded the participants while they were performing the tasks. Later a time study was conducted by measuring picking times directly from the video recordings (Table 3). The laboratory-derived average times from Table 3 were later used as input data for model validation and for use in simulated scenarios.