# Towards Productive and Ergonomic Order Picking: Multi-Objective Modeling Approach
## 4 Methodology for the Experiment
### Calculation of Total Energy Consumption, Used for the Minimization Function  
Total energy consumption, used for the minimization function, was calculated with the Formula (15):  
\[E_{total}=E_{walking}+E_{picking} \tag{15}\]  
where \(E_{picking}\) represents the average energy consumption [37] calculated based on the Formula (16):  
\[E_{job}=\frac{\sum\limits_{i=1}^{n_{l}}E_{post}\cdot t_{i}+\sum\limits_{i=1}^ {n}\triangle E_{task_{i}}}{T} \tag{16}\]  
where [37]:  
* \(E_{job}\) = average energy expenditure rate of the job (Kcal/min),
* \(E_{post}\) = metabolic energy expenditure rate due to the maintenance of the \(i^{th}\) posture (Kcal/min),
* \(t_{i}\) = time duration of \(i^{th}\) posture (min),
* \(n_{l}\) = total number of body postures employed in the job,
* \(\triangle E_{task}\) = net metabolic energy expenditure of the \(i^{th}\) task in a steady-state (Kcal). * \(E_{walking_{i}}\) is calculated by the Formula (17):  
\[E_{walking_{i}}=T_{walking_{i}}\cdot BMR \tag{17}\] \begin{table}
\begin{tabular}{l c} \hline \hline \multicolumn{1}{c}{**Type of Situation**} & **Objective Function** \\ \hline All three decision factors are equally important & \(\min(\sum\limits_{i=1}^{9}\sum\limits_{j=1}^{45}(t_{ij}\cdot x_{ij}),\sum \limits_{i=1}^{9}\sum\limits_{j=1}^{45}(e_{ij}\cdot x_{ij}),\sum\limits_{i=1}^ {9}\sum\limits_{j=1}^{45}(o_{ij}\cdot x_{ij}))\) \\ \hline The health risk is the most important decision factor & \(\min(\sum\limits_{i=1}^{9}\sum\limits_{j=1}^{45}0.1\cdot(t_{ij}\cdot x_{ij}), \sum\limits_{i=1}^{9}\sum\limits_{j=1}^{45}0.1\cdot(e_{ij}\cdot x_{ij}),\sum \limits_{i=1}^{9}\sum\limits_{j=1}^{45}0.8\cdot(o_{ij}\cdot x_{ij}))\) \\ \hline Time is the most important decision factor & \(\min(\sum\limits_{i=1}^{9}\sum\limits_{j=1}^{45}0.8\cdot(t_{ij}\cdot x_{ij}), \sum\limits_{i=1}^{9}\sum\limits_{j=1}^{45}0.1\cdot(e_{ij}\cdot x_{ij}),\sum \limits_{i=1}^{9}\sum\limits_{j=1}^{45}0.1\cdot(o_{ij}\cdot x_{ij}))\) \\ \hline Energy is the most important decision factor & \(\min(\sum\limits_{i=1}^{9}\sum\limits_{j=1}^{45}0.1\cdot(t_{ij}\cdot x_{ij}), \sum\limits_{i=1}^{9}\sum\limits_{j=1}^{45}0.8\cdot(e_{ij}\cdot x_{ij}),\sum \limits_{i=1}^{9}\sum\limits_{j=1}^{45}0.1\cdot(o_{ij}\cdot x_{ij}))\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Differently weighted scenarios. where for BMR the value of \(3.39\frac{\text{Kcal}}{\text{min}}\) was used, which coincides with the velocity of walking \(v_{walking}=0.83\frac{\text{m}}{8}\)[37]. Calculation of the Overall Level of Health Risk Based on OWAS Coding, Used for the Minimization Function  
To use the OWAS method in the minimization function, we needed to determine numerical values that will unequivocally communicate health risks for specific boxes on specific storage spaces because the OWAS codes did not prove useful. In the first step, which followed the standard OWAS procedure, work postures during order picking in the case study warehouse rack [63] were observed and recorded (Figure 5). The observation was followed by codifying. We assigned a 4-digit code to each posture that appeared in the order picking process. The resulting codes depend on the classification for different parts of the body. The first numeric value in the 4-digit code refers to the back (4 postures), the second to arms (3 postures), the third to legs (7 postures), and the fourth to the mass of the load handled (3 categories). Codes were a prerequisite for calculating the overall level of health risk for a specific box at a specific storage space, taking into account the box's frequency in the entire scenario. In a particular case study (1 storage rack and four different scenarios), 405 calculations were needed (9 different boxes with their frequencies, five different heights above the ground). For each numerical value in the 4-digit code, a reasonably thought-out numerical value was assigned to indicate the health risk level for a specific group of postures/categories (back, arms, legs, mass).