## 4 Human-Machine-Logistics Collaborative Scheduling Method Considering Workers' LFE
### Adaptive Real-Time Scheduling Considering Workers' Learning and Forgetting Effects
#### 4.3.1 Adaptive Real-Time Allocation Considering Workers' Learning and Forgetting Effects
At time \(t\), for each service group in the service group set \(RT_{Z}\), the service time and service energy consumption are as follows:  
\[T_{f}^{t}=p_{nj}^{k}+p_{ni}^{k}+max\Big{(}sp_{ni}^{kt}-fp_{nj}^{kt},0\Big{)}+ max\Big{(}sp_{nj}^{kt}-fp_{nj}^{kt},0\Big{)} \tag{19}\]  
\[W_{f}^{t}=e_{i}^{act}p_{nj}^{k}+e_{i}^{act}p_{ni}^{kt}+e_{i}^{act}max\Big{(} sp_{ni}^{kt}-fp_{nj}^{kt},0\Big{)}+e_{j}^{sat}max\Big{(}mp_{ni}^{kt}- fp_{nj}^{kt},0\Big{)} \tag{20}\]  
where \(max\Big{(}sp_{ni}^{kt}-fp_{nj}^{kt},0\Big{)}\) represents the waiting time for the AGV \(a_{i}\) to pick up task \(O_{n}^{k}\), \(max\Big{(}sp_{nj}^{kt}-fp_{nj}^{kt},0\Big{)}\) represents the waiting time for task at the corresponding machine before being processed, and \(max\Big{(}mp_{ni}^{kt}-fp_{nj}^{kt},0\Big{)}\) represents the waiting time for AGV \(a_{i}\) to pick up task \(O_{n}^{k}\). Resource groups typically face a trade-off between completion time and energy consumption: high-power machines complete tasks in a shorter time but consume more energy, while low-power machines take longer to complete tasks but consume less energy. Therefore, it is difficult to achieve a combination of resources that is both low in energy consumption and short in time, and it is necessary to consider both the duration and energy consumption of service groups during scheduling. To select the optimal service group, this paper uses the actual task slack to allocate tasks from the task pool. The smaller the slack, the more biased the task allocation will be towards the combination of good machine-resource-worker groups, while larger slack will make the allocation lean towards combinations with relatively lower efficiency to improve the worker's learning effect. The following formulas are based on adding consideration of the worker's learning efficiency, considering the impact of learning and adaptation on the worker's processing time. Suppose at time \(t\), a task is issued, and the task's estimated average processing time is calculated as  
\[rp\left(O_{n}^{k}\right)=\sum_{n}^{r}\sum_{1}^{j}\frac{p_{n}^{k}\cdot E_{j}^{t}}{ T-n} \tag{21}\]  
where \(r\) is the total number of tasks, \(j\) is the selected machine sequence for a specific worker, and \(E_{j}^{t}\) represents the actual learning efficiency of worker \(h_{j}\) at time \(t\). The estimated transportation time is given by  
\[rl\left(O_{n}^{k}\right)=d_{n}^{k}/\overline{v} \tag{22}\]  
In this formula, \(d_{n}^{k}\) is the predicted average material handling distance for the remaining flow tasks, and \(\overline{v}\) is the movement speed of the material handling resources. Thus, the estimated remaining service time for the job is the sum of the remaining processing time and the remaining transportation time:  
\[rt\left(O_{n}^{k}\right)=rp\left(O_{n}^{k}\right)+rl\left(O_{n}^{k}\right) \tag{23}\]  
At time \(t\), the remaining time to complete job is  
\[\overline{A}^{t}=\left\{a_{i}^{t}\big{|}i=1,\ 2,\ \ldots,\ 1\right\} \tag{16}\]0  
The slackness of task \(O_{n}^{k}\) is the ratio of the estimated remaining service time to the remaining completion time. At time \(t\), the slackness of task is  
\[\overline{A}^{t}=\left\{a_{i}^{t}\big{|}i=1,\ 2,\ \ldots,\ 1\right\} \tag{16}\]1  
Task slackness is used to measure the difference between the actual completion time of a task and its theoretical completion time, reflecting whether the task is delayed. When the slackness is large, the task may have already been delayed or is about to be delayed, so the system should prioritize selecting resource combinations with shorter completion times to reduce delays. When the slackness is small, it indicates that the task has enough time to be completed, and the system can select resource combinations with lower energy consumption to reduce overall energy use. Based on this, this paper proposes an adaptive weighting evaluation function that uses task slackness as a weighting factor to dynamically adjust the resource allocation strategy.