# Towards Productive and Ergonomic Order Picking: Multi-Objective Modeling Approach
## 5 Results
### Comparisons between Results of Minimization Functions with One Optimization Factor  
As described, we used all three single-objective minimization functions on four different scenarios in two different warehouses, differing in length of storage spaces. Below we present the results for the short rack and scenario 3 in which heavy boxes predominate. When optimization considers just time, we can see (Figure 6) that heavier boxes (10 kg, colored orange) are placed close to the depot (I/O) and in a golden zone, where picking times are shorter. Walking time has an impact but only in a limited way due to the short distances between storage spaces in a rack. As the number of boxes for storing is smaller than the number of available storage spaces, empty storage spaces expectedly appear on the rack's remote part (according to the depot I/O). The best solution in a time-based manner encompasses two cases with a very-high health risk, which makes the proposal unsuitable from the point of view of safety (the \(HR\) value is 67,107). On the other hand, the proposal is excellent in terms of employee productivity (calculated time is 495.95 s and energy consumption is 57.43 Kcal). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Health Risk Level (HRL)**} & \multicolumn{3}{c}{**(HRL) Occurrence Frequency for Specific Rack Type**} \\ \hline \hline
**Type** & **Number of Cases** & **Short Rack** & **Long Rack** \\ \hline \multirow{3}{*}{Very-high risk} & 9 & 1 & 0.25\% & 0 & 0\% \\ \cline{2-6}  & 2 & 12 & 2.96\% & 8 & 1.98\% \\ \cline{2-6}  & 1 & 4 & 0.99\% & 5 & 1.23\% \\ \hline \multirow{3}{*}{Some risk} & 4 & 7 & 1.73\% & 0 & 0\% \\ \cline{2-6}  & 3 & 13 & 3.21\% & 13 & 3.21\% \\ \cline{2-6}  & 2 & 71 & 17.53\% & 37 & 9.14\% \\ \cline{2-6}  & 1 & 122 & 30.12\% & 133 & 32.84\% \\ \hline Negligible risk & one to several & 175 & 43.21\% & 209 & 51.60\% \\ \hline Sum & 405 & 100\% & 405 & 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Frequency of occurrence of a specific health risk level. When optimization considers just nearby, we can see (Figure 7) that heavier boxes (10 kg, colored orange) are placed in a golden zone, and below it, in storage spaces where picking energy expenditures are small. Walking time has an impact but only in a limited way due to the short distances between storage spaces in a rack. As the number of boxes for storing is smaller than the number of available storage spaces, empty storage spaces expectedly appear in the last remote column (according to the depot (I/O) and on the lowest and highest shelves due to significant picking energy expenditures. The best solution in an energy-based manner encompasses four cases with a very-high health risk, which makes the proposal even more unsuitable from the point of view of safety than the time-based proposal (\(HR\) value is 126,508). The proposal is also worse in terms of employee productivity (calculated time is 505.93 s and energy consumption is 57.11 kcal). When optimization considers just health risk, we can see (Figure 8) that heavier boxes (10 kg, colored orange) are placed in a golden zone and below and above it, in storage spaces far from the depot (I/O). Unlike in the previous two storage assignment proposals, empty storage spaces are now located closer to the depot (I/O). Placing boxes on the end of the rack corridor reduces the share of time spent performing a certain posture in the total time spent for picking boxes out of the shelves, thus reducing the health risk. As the number of boxes for storing is smaller than the number of available storage spaces, empty storage spaces appear closer to the depot (I/O), above and below the golden zone due to some or very-high health risks. The result matches expectations before the use of the health-risk minimization function. The best solution in the health risk-based manner encompasses no cases with a very-high health risk, making the proposal excellent from the point of view of safety (\(HR\) value is 1935).