# Towards Productive and Ergonomic Order Picking: Multi-Objective Modeling Approach
## 5 Results
### Comparisons between Results from Differently Weighted Multi-Objective Minimization Functions  
A comparative analysis on four different scenarios in two different warehouses, differing in length of storage spaces, was made based on three differently weighted multi-objective functions. In the first, time, energy expenditure and health risk are equally weighted. In the second, the health-risk is the most weighted and in the third, time-risk is the most weighted. Results are presented in Table 8. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Observed Factor**} & \multirow{2}{*}{**Rack Type**} & \multicolumn{2}{c}{**Time-Based Optimization**} & \multicolumn{2}{c}{**Energy-Based Optimization**} & \multicolumn{2}{c}{**HR-Based Optimization**} \\ \hline \multirow{3}{*}{Average time (s)} & Short rack & 100\% & +2.32\% & +33.97\% \\ \cline{2-5}  & Long rack & 100\% & +0.37\% & +32.2\% \\ \hline \multirow{3}{*}{Average energy (Kcal)} & Short rack & 100\% & \(-\)0.53\% & +32.0\% \\ \cline{2-5}  & Long rack & 100\% & \(-\)0.3\% & +30.89\% \\ \hline \multirow{3}{*}{Average HR (value)} & Short rack & 100\% & +106.88\% & \(-\)96.34\% \\ \cline{2-5}  & Long rack & 100\% & +34.34\% & \(-\)95.31\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparisons of the average results from the perspective of time-based optimization. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Scenario** \\ **(Rack Type)** \\ \end{tabular} } & \multirow{2}{*}{**Observed Factor**} & \multicolumn{2}{c}{**Weighted Multi-Objective Minimization Function**} \\ \cline{3-6}  & & **t + e + o** & **0.1t + 0.1e + 0.8o** & **0.8t + 0.1e + 0.1o** & **0.1t + 0.8e + 0.1o** \\ \hline \multirow{3}{*}{Scenario 1 (Short rack)} & \(T\) (s) & 498.36 & 579.85 & 495.74 & 475.24 \\ \cline{2-6}  & \(E\) (Kcal) & 56.45 & 64.33 & 56.55 & 54.07 \\ \cline{2-6}  & \(HR\) (value) & 3328 & 1338 & 3527 & 5314 \\ \hline \multirow{3}{*}{Scenario 2 (Short rack)} & \(T\) (s) & 501.57 & 583.47 & 498.04 & 500.27 \\ \cline{2-6}  & \(E\) (Kcal) & 56.78 & 64.67 & 56.77 & 56.79 \\ \cline{1-1} \cline{2-6}  & \(HR\) (value) & 3328 & 1338 & 3726 & 65,316 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of results for different scenarios, rack type, and minimization based on differently weighted multi-objective functions. The average results of the differently weighted multi-objective minimization functions are compared according to the type of rack (short, long) from the perspective of time-based optimization in Table 9.  
As presented in Table 9, it is important to emphasize that the order picker is never exposed to very-high health risk in the first three analyzed situations (t + e + o, 0.1t + 0.1e + 0.8o, 0.8t + 0.1e + 0.1o), even in a situation where time is the most crucial decision factor. In the equal importance of all factors, the order picker is exposed 19 times to some risk and 58 times when the time is the most important factor. The order picker is exposed to some risk only 12 times when health risk is the most weighted factor. Different behavior was found only in the multi-objective emphasizing energy minimization function (0.1t + 0.8e + 0.1o) for the short rack. There, the HR value also decreases,