## 3 A Collaborative Scheduling Framework for Human-Machine-Logistics Considering Workers' LFE
### A Real-Time Human-Machine-Logistics Collaborative Scheduling Framework Considering Workers' LFE  
The real-time reactive scheduling framework, illustrated in Figure 1, integrates three key components: (1) a real-time state model of the human-machine-material resources that accounts for workers' learning and forgetting effects, (2) dynamic self-organization of human-machine-material resources based on real-time worker states and task demands, and (3) an adaptive scheduling method leveraging real-time self-organization, while also considering learning and forgetting effects. Each module operates as follows:  
In intelligent workshops, technologies such as RFID, sensors, and processors enable manufacturing resources to communicate and execute tasks intelligently. These modules facilitate the monitoring of resource state changes, thereby improving the coordination of workshop operations. However, worker efficiency remains challenging to assess directly due to the influence of numerous factors. To address this, a mathematical model incorporating learning and forgetting dynamics is employed to estimate workers' real-time efficiency, allowing for continuous adjustment of resource states in the workshop.  
The random arrival of tasks and constantly changing resource availability in intelligent workshops necessitate a highly flexible approach to multi-resource collaboration. To meet these requirements, we propose a dynamic self-organization strategy for human-machine-material resources, which reflects the real-time nature of tasks. This strategy effectively meets the workshop's task demands by dynamically matching and integrating available service resources based on their real-time capabilities, thereby achieving optimal resource organization in response to task requirements.  
An adaptive allocation method based on task slackness is then implemented to optimize task assignment. Task slackness serves as a metric for evaluating the suitability of a service group for a specific task, ensuring that the most appropriate resources are allocated to balance completion time, energy consumption, and delay. Additionally, a conflict resolution mechanism for Automated Guided Vehicles (AGVs) is integrated, prioritizing urgent tasks and minimizing delays caused by resource conflicts. This ensures that critical tasks are handled efficiently, maintaining the overall productivity of the workshop.  
\begin{table}
\begin{tabular}{c c} \hline
**Notations** & **Description** \\ \hline \(O_{n}^{k}\) & The \(n\_\)th operation of the \(job^{k}\) \\ \(E_{v}^{l}\) & Total energy consumption of \(a_{i}\) \\ \(E_{m}^{l}\) & Total energy consumption of \(m_{j}\) \\ \(L^{k}\) & Delay time of the \(job^{k}\) \\ \(C^{k}\) & Completion time of the \(job^{k}\) \\ \(D^{k}\) & Due date of the \(job^{k}\) \\ \(g_{l}\) & Human–machine collaborative production group \\ \(g_{j}^{l}\) & Real-time state of \(g_{j}\) at time \(t\) \\ \(h_{j}^{t}\) & Real-time state of worker resource \(h_{j}\) at time \(t\) \\ \(m_{j}^{t}\) & Real-time state of machine resource \(m_{j}\) at time \(t\) \\ \(a_{i}^{l}\) & Real-time state of logistics resource \(a_{i}\) at time \(t\) \\ \(sp_{ni}^{kl}\) & Time at which logistics task \(a_{i}\) starts processing operation \(O_{n}^{k}\) \\ \(fp_{nj}^{kl}\) & Time at which machine completes operation \(O_{n-1}^{k}\) \\ \(sp_{nj}^{kl}\) & Time at which machine \(m_{j}\) starts processing operation \(O_{n}^{k}\) \\ \(fp_{nj}^{kl}\) & Time at which machine completes operation \(O_{n}^{k}\) \\ \(mp_{ni}^{kl}\) & Time at which logistics task arrives at the location of operation \(O_{n}^{k}\) \\ \(fp_{nj}^{kl}\) & The completion time of the last operation before processing by the machine \(m_{j}\) \\ \hline \end{tabular}
\end{table}
Table 1: _Cont._