# Towards Productive and Ergonomic Order Picking: Multi-Objective Modeling Approach
## 5 Results
### Comparisons between Results of Minimization Functions with One Optimization Factor
The proposal is the worst in terms of employee productivity between one-objective solutions (time needed to complete the scenario is 657.84 s and energy consumption is 75.16 kcal). Figure 6: Storage assignment proposal based on minimization of the time-based objective function (scenario 3, short rack). The best solution for the order picker's physical health is the minimization of the health risk-based objective function, where we note that no box is placed in a storage space with a very-high health risk. Nine boxes are positioned in storage spaces with some health risk and others in spaces with negligible risk. On the other hand, this increases the time by 32.65% in comparison with time-objective optimization. A summary of the results for scenario 3 (short rack) and the other three scenarios described in the case study section is given in Table 6. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \begin{tabular}{c} **Scenario** \\ **(Rack Type)** \\ \end{tabular} & \multirow{2}{*}{**Observed Factor**} & \multicolumn{2}{c}{\begin{tabular}{c} **Time-Based** \\ **Optimization 4** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Energy-Based** \\ **Optimization 5** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **HR-Based** \\ **Optimization 6** \\ \end{tabular} } \\ \hline \multirow{3}{*}{\begin{tabular}{c} Scenario 1 \\ (Short rack) \\ \end{tabular} } & \(T\) 1 (s) & 478.71 & 488.39 & 642.2 \\ \cline{2-9}  & \(E\)2 (Kcal) & 55.09 & 54.83 & 72.93 \\ \cline{2-9}  & \(HR\)3 (value) & 64,321 & 154,416 & 2183 \\ \hline \multirow{3}{*}{\begin{tabular}{c} Scenario 2 \\ (Short rack) \\ \end{tabular} } & \(T\) (s) & 480.1 & 491.35 & 643.14 \\ \cline{2-9}  & \(E\) (Kcal) & 55.32 & 55.0 & 73.17 \\ \cline{2-9}  & \(HR\) (value) & 65,913 & 155,910 & 2183 \\ \hline \multirow{3}{*}{\begin{tabular}{c} Scenario 3 \\ (Short rack) \\ \end{tabular} } & \(T\) (s) & 495.95 & 505.93 & 657.84 \\ \cline{2-9}  & \(E\) (Kcal) & 57.43 & 57.11 & 75.16 \\ \cline{2-9}  & \(HR\) (value) & 67,107 & 126,508 & 1935 \\ \hline \multirow{3}{*}{\begin{tabular}{c} Scenario 4 \\ (Short rack) \\ \end{tabular} } & \(T\) (s) & 464.67 & 477.28 & 626.88 \\ \cline{2-9}  & \(E\) (Kcal) & 53.68 & 53.4 & 71.14 \\ \cline{2-9}  & \(HR\) (value) & 45,316 & 65,166 & 2532 \\ \hline \multirow{3}{*}{\begin{tabular}{c} Scenario 1 \\ (Long rack) \\ \end{tabular} } & \(T\) (s) & 970.68 & 973.42 & 1294.9 \\ \cline{2-9}  & \(E\) (Kcal) & 110.79 & 110.49 & 146.42 \\ \cline{2-9}  & \(HR\) (value) & 66,704 & 96,906 & 3718 \\ \hline \multirow{3}{*}{\begin{tabular}{c} Scenario 2 \\ (Long rack) \\ \end{tabular} } & \(T\) (s) & 973.07 & 976.32 & 1301.28 \\ \cline{2-9}  & \(E\) (Kcal) & 111.02 & 110.7 & 147.19 \\ \cline{2-9}  & \(HR\) (value) & 64,658 & 94,256 & 3224 \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Scenario 3 \\ (Long rack) \\ \end{tabular} } & \(T\) (s) & 988.92 & 991.49 & 1239.97 \\ \cline{2-9}  & \(E\) (Kcal) & 113.13 & 112.67 & 140.29 \\ \cline{2-9}  & \(HR\) (value) & 64,906 & 94,905 & 2924 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Scenario 4 \\ (Long rack) \\ \end{tabular} } & \(T\) (s) & 902.43 & 907.88 & 1234.55 \\ \cline{2-9}  & \(E\) (Kcal) & 103.15 & 102.93 & 139.51 \\ \cline{2-9}  & \(HR\) (value) & 65,653 & 65,803 & 2425 \\ \hline \hline \end{tabular}  
* \(T\)—time in seconds; 2 \(E\)—energy expenditure in Kcal; 3 \(HR\)—health risk; 4 time-based optimization is expressed in (s) for \(T\), in (Kcal) for \(E\), and (numerical value) for \(HR\); 5 energy-based optimization is expressed in (s) for \(T\), in (Kcal) for \(E\), and (numerical value) for \(HR\); 6 HR-based optimization is expressed in (s) for \(T\), in (Kcal) for \(E\), and (numerical value) for \(HR\).  
\end{table} 
Table 6: Comparison of results for different scenarios, rack type and single-objective function. Figure 8: Storage assignment proposal based on minimization of the health risk-based objective function (scenario 3, short rack).