## 4 Human-Machine-Logistics Collaborative Scheduling Method Considering Workers' LFE
### Real-Time Status Model of Human-Machine-Logistics Resources  
In the Industrial Internet-of-Things (IIoT) environment, the real-time status of critical resources in an intelligent workshop forms the foundation for the human-machine-object collaborative scheduling system. The capability status of manufacturing resources includes both resource attributes and real-time states. Resource attributes cover operational capabilities, energy consumption, and service quality, while real-time states encompass anomaly detection, dynamic queues, workload, and service processes. To accurately depict the real-time status of human-machine-object resources, this study constructs state models for workers, processing equipment, and handling equipment. The concept of \"operation ratio\" is introduced as a key indicator of worker real-time efficiency, reflecting human factors in a more comprehensive manner.  
**Definition 1.--Worker's Real-time Efficiency**. _The slackness of a real-time task is a key factor that influences the matching between tasks and service groups, and predicting the remaining processing time of a real-time task is essential for calculating slackness. In the human-machine-logistics collaborative work environment, the learning and forgetting characteristics of workers affect the processing duration, and the operational efficiency of production resource groups exhibits dynamic characteristics, making it difficult to estimate the actual time accurately. Therefore, this paper defines the ratio between the actual task processing time and the theoretical task processing time at a given moment as the task time ratio, and the product of the task time ratio and the theoretical remaining time is used as the estimate for the remaining processing time of the task \(O_{n}^{k}\)._  
In the production process, processing equipment and workers work in combination, so a production resource group model consists of one piece of production equipment and one worker operating the equipment.  
\[g_{j}=\left(h_{j},m_{j}\right) \tag{10}\]  
At time \(t\), the real-time state model of production resources is composed of the real-time states of workers and processing equipment and can be expressed as follows:  
\[g_{j}^{t}=\left(h_{j}^{t},m_{j}^{t}\right) \tag{11}\]  
\[h_{j}^{t}=\left(h_{j},a_{j}^{L},b_{j}^{F1},T_{j}^{cum},T_{j}^{down},\theta_{j },E_{nj}^{k}\right) \tag{12}\]  
\[m_{j}^{t}=\left(m_{j},S_{j}^{t},L_{j}^{pos},p_{nj}^{k},e_{j}^{sta},e_{j}^{act },sq_{j}\right) \tag{13}\]  
where \(a_{j}^{L}\) represents the worker's learning ability, \(b_{j}^{F1}\) represents the forgetting speed, \(T_{j}^{cum}\) represents the total working time, \(T_{j}^{down}\) represents the idle time, \(\theta_{j}\) represents the worker's maximum learning efficiency, and \(E_{nj}^{k}\) represents the worker's processing efficiency at time \(t\) when handling the current task. \(S_{j}^{t}\) represents the types of services that can be provided, \(L_{j}^{pos}\) represents the location information, \(p_{nj}^{k}\) represents the service time for the current task, \(e_{j}^{sta}\) represents the idle power, \(e_{j}^{act}\) represents the operating power, and \(sq_{j}\) represents the service queue.  
The real-time state model of logistics equipment includes eight characteristic values, such as service options \(S_{i}^{t}\), resource location \(L_{i}^{pos}\), transport time \(p_{ni}^{k}\), standby energy \(e_{i}^{sta}\), transport energy \(e_{i}^{act}\), transport speed \(\overline{v}\), and service queue \(sq_{i}\).  
\[a_{i}^{t}=\left(a_{i},S_{i}^{t},L_{i}^{pos},p_{ni}^{k},e_{i}^{sta},e_{i}^{act}, \overline{v},sq_{j}\right) \tag{14}\]