## 5 Case Study
### Effectiveness Analysis of the Proposed Method  
Due to fluctuations in the number of workshop orders, which vary with peak and off-peak seasons, three different order quantities were selected for this case study: small, medium, and large. This section presents the results of experiments conducted under three order quantity scenarios, considering five different worker learning and forgetting speeds. In each scenario, the order arrival rate follows a normal distribution. By conducting multiple simulations, the experimental results for each scheduling method under different worker learning and forgetting speeds were collected and compared. The proposed method was evaluated against five scheduling rules from [PERSON] et al. [52] and [PERSON] [53], including First-Come-First-Served (FCFS), Shortest Processing Time + Shortest Transportation Time (SPT + STT), Longest Processing Time + Longest Transportation Time (LPT + LTT), Shortest Remaining Processing and Transportation Time (SRPTT), and Longest Remaining Processing and Transportation Time (LRPTT). The comparison also includes an order insertion rule (OC) [35] from the previous literature. The proposed human-machine-logistics collaborative scheduling method (HMLCS) was tested both with and without considering the learning and forgetting effects of workers. The following Table 6 shows a comparison of the results between considering (NNW) and not considering worker learning and forgetting effects (NLF): \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{6}{c}{**Without Learning and Forgetting Effects (NLF)**} & \multicolumn{6}{c}{**Considering Learning and Forgetting Effects (NNW)**} \\ \hline \multirow{2}{*}{**Algorithm**} & **Order** & **Makespan** & **Energy** & **Transitions** & **Algorithm** & **Order** & **Makespan (s)** & **Energy** & **Consumption** & **Tardiness** (s)** \\  & **Size** & **(s)** & **Consumption** & **(K)** & **(s)** & **(K)** & **(K)** & **(K)** & **(s)** \\ \hline \multirow{2}{*}{HCML} & 20 & 3558 & 573,172 & 40 & \multirow{2}{*}{HCML} & 20 & 3464 & 535,336 & 21 \\  & 40 & 6464 & 1,109,272 & 111 & & 40 & 5944 & 989,220 & 47 \\ \multirow{2}{*}{CS} & 60 & 9087 & 1,635,784 & 499 & & 60 & 8121 & 1,407,748 & 102 \\  & 20 & 3967 & 590,400 & 99 & & 20 & 3553 & 538,448 & 37 \\ \multirow{2}{*}{OC} & 40 & 7299 & 1,146,788 & 472 & \multirow{2}{*}{OC} & 40 & 6065 & 1,004,932 & 108 \\  & 60 & 10,071 & 1,674,104 & 1043 & & 60 & 8257 & 1,443,756 & 388 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of results with and without Worker LFE (NNW vs NLF). When considering the learning and forgetting effects (NNW), the HCMLCS algorithm demonstrates significant performance improvements in completion time, energy consumption, and delay time compared to all scheduling methods under the no-learning-and-forgetting (NLF) scenario. Specifically, for an order size of 20, the completion time, energy consumption, and delay time were reduced by an average of 10.65%, 8.52%, and 73.04%, respectively. For an order size of 40, the three indicators decreased by 17.63%, 12.76%, and 86.26% on average, respectively. For an order size of 60, the improvements were even more significant, with reductions of 20.79%, 16.43%, and 88.35%, respectively. Particularly in terms of delay time, as the order size increases, the optimization effect of HCMLCS with learning and forgetting effects becomes more pronounced, indicating its strong advantage in large-scale order scenarios. To comprehensively evaluate the performance of HCMLCS under different conditions, the following section compares its performance with and without considering the learning and forgetting effects (NLF vs NNW) and explores its optimization effects across various order sizes. Even without considering the learning and forgetting effects, the HCMLCS algorithm still exhibits significant advantages in completion time and delay control. For order sizes of 20, 40, and 60, completion time was reduced by 9.63%, 10.31%, and 12.4%, respectively.