# Towards Productive and Ergonomic Order Picking: Multi-Objective Modeling Approach
## 5 Results
### Comparisons between Results from Differently Weighted Multi-Objective Minimization Functions
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Scenario** \\ **(Rack Type)** \\ \end{tabular} & \multirow{2}{*}{**Observed Factor**} & \multicolumn{3}{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}{*}{\begin{tabular}{c} Scenario 3 \\ (Short rack) \\ \end{tabular} } & \(T\) (s) & 519.95 & 601.70 & 515.38 & 518.50 \\ \cline{2-6}  & \(E\) (Kcal) & 59.26 & 67.10 & 59.24 & 58.99 \\ \cline{2-6}  & \(HR\) (value) & 3328 & 1338 & 3925 & 65,515 \\ \hline \multirow{3}{*}{\begin{tabular}{c} Scenario 4 \\ (Short rack) \\ \end{tabular} } & \(T\) (s) & 486.81 & 566.03 & 483.87 & 486.79 \\ \cline{2-6}  & \(E\) (Kcal) & 54.94 & 62.64 & 55.23 & 55.26 \\ \cline{2-6}  & \(HR\) (value) & 3328 & 1338 & 3527 & 5517 \\ \hline \multirow{3}{*}{\begin{tabular}{c} Scenario 1 \\ (Long rack) \\ \end{tabular} } & \(T\) (s) & 1032.50 & 1211.3 & 1024.33 & 1023.95 \\ \cline{2-6}  & \(E\) (Kcal) & 116.75 & 136.45 & 116.45 & 116.04 \\ \cline{2-6}  & \(HR\) (value) & 3420 & 2624 & 3319 & 5116 \\ \hline \multirow{3}{*}{\begin{tabular}{c} Scenario 2 \\ (Long rack) \\ \end{tabular} } & \(T\) (s) & 1034.72 & 1213.52 & 1026.63 & 1026.44 \\ \cline{2-6}  & \(E\) (Kcal) & 117.00 & 136.7 & 116.66 & 116.25 \\ \cline{2-6}  & \(HR\) (value) & 3570 & 2624 & 3469 & 4317 \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Scenario 3 \\ (Long rack) \\ \end{tabular} } & \(T\) (s) & 1033.04 & 1212.89 & 1024.9 & 1044.67 \\ \cline{2-6}  & \(E\) (Kcal) & 117.21 & 137.07 & 116.92 & 114.45 \\ \cline{2-6}  & \(HR\) (value) & 3120 & 2474 & 3769 & 3916 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Scenario 4 \\ (Long rack) \\ \end{tabular} } & \(T\) (s) & 1019.24 & 1198 & 1011.32 & 1012.96 \\ \cline{2-6}  & \(E\) (Kcal) & 115.24 & 134.85 & 114.83 & 114.72 \\ \cline{2-6}  & \(HR\) (value) & 3968 & 3622 & 3766 & 4919 \\ \hline \hline \end{tabular}  
* t time, e: energy and o: health risk value (due the fact that HR is calculated with the OWAS).  
\end{table} 
Table 8: _Cont._ \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Observed Factor**} & \multirow{2}{*}{**Rack Type**} & \multicolumn{2}{c}{**Time-Based**} & \multicolumn{3}{c}{**Weighted Multi-Objective Minimization Function**} \\ \cline{3-6}  & & **Optimization** & **t + e + o** & **0.1t + 0.1e + 0.8o** & **0.8t + 0.1e + 0.1o** & **0.1t + 0.8e + 0.1o** \\ \hline \multirow{3}{*}{Time (s)} & Short rack & 100\% & +4.55\% & +21.45\% & +3.83\% & +3.20\% \\ \cline{2-6}  & Long rack & 100\% & +7.42\% & +26.09\% & +6.57\% & +7.12\% \\ \hline \multirow{3}{*}{Energy (Kcal)} & Short rack & 100\% & +2.67\% & +16.80\% & +2.83\% & +1.62\% \\ \cline{2-6}  & Long rack & 100\% & +6.42\% & +24.42\% & +6.11\% & +5.33\% \\ \hline \multirow{3}{*}{HR (value)} & Short rack & 100\% & \(-94.51\%\) & \(-97.79\%\) & \(-93.94\%\) & \(-41.62\%\) \\ \cline{2-6}  & Long rack & 100\% & \(-94.69\%\) & \(-95.72\%\) & \(-94.59\%\) & \(-93.03\%\) \\ \hline \hline \end{tabular}  
* t: time, e: energy and o: health risk value (due the fact that HR is calculated with the OWAS).  
\end{table} 
Table 9: Comparisons of the average results from a perspective of time-based objective minimization function. but more than 50% less than with other multi-objective minimization functions. Scenarios S2 (all types of boxes are equally represented) and S3 (heavy boxes predominate) each contain one situation with very-high risk.