## 4 Results and Analysis
### Time Horizon Impact on Operations  
Table 3 illustrates how handling activities vary across different planning horizons (1 week, 2 weeks, and 3 weeks) for the 50-part group. The results show that the optimization model maintains consistent performance regardless of the length of the planning period. For direct picking, the percentage remains stable across all planning horizons, with only a slight decrease from 13.83% in the 1-week and 2-week horizons to 13.73% in the 3-week horizon. This stability suggests that the optimization model is effective in consistently managing direct picking activities, regardless of the planning period. Replenishment activities also show minimal variation, staying nearly identical across the different horizons, with a minor increase to 33.97% in the 3-week horizon. This indicates that the model can reliably manage replenishment needs over extended periods without significant changes in the handling activity percentage. Buffer area usage and forward-to-buffer area transfers exhibit \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Part Group** & **Scenario** & \begin{tabular}{c} **Direct Picking** \\ **(Sum/Mean)** \\ \end{tabular} & \begin{tabular}{c} **Replenishment** \\ **(Sum/Mean)** \\ \end{tabular} & \
\begin{tabular}{c} **Buffer Usage** \\ **(Sum/Mean)** \\ \end{tabular} &
\begin{tabular}{c} **Forward-to-Buffer** \\ **Transfer (Sum/Mean)** \\ \end{tabular} \\ \hline \multirow{4}{*}{50 Parts} & Simulation PD & 18,822/15.69 \(\pm\) 0.9 & 405/0.34 \(\pm\) 0.03 & 3067/2.55 \(\pm\) 0.21 & 3231/2.69 \(\pm\) 0.24 \\ \cline{2-6}  & (s,S) Policy & 26,520/22.1 \(\pm\) 1.2 & 361/0.3 \(\pm\) 0.04 & 57,720/48.1 \(\pm\) 4.5 & 4944/4.12 \(\pm\) 0.38 \\ \cline{2-6}  & Business as Usual & 42,633/35.49 \(\pm\) 1.5 & 390/0.32 \(\pm\) 0.03 & 131,074/109.13 \(\pm\) 5.1 & 23,479/19.54 \(\pm\) 1.7 \\ \cline{2-6}  & Simulation KD & 9711/8.09 & 434/0.36 & 15,658/13.04 & 3750/3.13 \\ \hline \multirow{4}{*}{200 Parts} & Simulation PD & 32,381/6.74 \(\pm\) 0.5 & 857/0.17 \(\pm\) 0.02 & 4623/0.96 \(\pm\) 0.1 & 5142/1.07 \(\pm\) 0.11 \\ \cline{2-6}  & (s,S) Policy & 47,040/9.8 \(\pm\) 0.7 & 768/0.16 \(\pm\) 0.02 & 7200/1.5 \(\pm\) 0.18 & 6969/1.45 \(\pm\) 0.15 \\ \cline{2-6}  & Business as Usual & 66,492/13.84 \(\pm\) 0.9 & 836/0.17 \(\pm\) 0.02 & 478,690/99.70 \(\pm\) 8.2 & 55,486/11.55 \(\pm\) 1.0 \\ \cline{2-6}  & Simulation KD & 26,842/5.59 & 896/0.19 & 234/0.05 & 9296/1.94 \\ \hline \multirow{4}{*}{300 Parts} & Simulation PD & 33,124/4.60 \(\pm\) 0.4 & 1044/0.15 \(\pm\) 0.02 & 5592/0.78 \(\pm\) 0.09 & 5879/0.81 \(\pm\) 0.08 \\ \cline{2-6}  & (s,S) Policy & 48,600/8.1 \(\pm\) 0.6 & 936/0.13 \(\pm\) 0.02 & 8280/1.15 \(\pm\) 0.14 & 7560/1.05 \(\pm\) 0.12 \\ \cline{2-6}  & Business as Usual & 66,611/9.25 \(\pm\) 0.7 & 1026/0.14 \(\pm\) 0.02 & 302,231/41.97 \(\pm\) 4.5 & 46,077/6.39 \(\pm\) 0.6 \\ \cline{2-6}  & Simulation KD & 27,302/3.79 & 1032/0.14 & 237/0.03 & 10,641/1.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Sum and mean of handling activities for different part groups (50, 200, 300 parts). a similarly stable pattern, with only slight variations as the planning horizon increases. For instance, buffer area usage increases marginally from 18.91% in the 1-week and 2-week horizons to 19.067% in the 3-week horizon. This consistency across metrics underscores the robustness of the optimization model in handling inventory activities effectively, even as the planning horizon extends. Overall, Table 3 demonstrates that the optimization model's performance remains steady over different planning periods, ensuring reliable and efficient handling activities regardless of the planning horizon. Table 4 presents the sum and mean values of handling activities across different planning horizons (1 week, 2 weeks, and 3 weeks) for the 50-part group. The key takeaway is that both the total handling activities and average efficiency remain consistent, regardless of the planning period.