Table 2 List of symbols.
From: Digital twin-based multi-level task rescheduling for robotic assembly line
Symbol | Description | Symbol | Description |
|---|---|---|---|
m | Total workstations | \(t_{m}\) | Moving time between assembly points |
n | Total number of parts of product | \(t_{b}\) | Basic assembly time of \(task_{i}\) |
N | Total number of products | \(n_{i}\) | Total number of tasks assigned to \(S_{i}\) |
\(S_{i}\) | Number of workstations, \(i = 1,2,...,m\) | \(T_{i}\) | Working time of \(S_{i}\) |
\(R_{i}\) | Number of robots, \(i = 1,2,...,m\) | \(Tool_{r}\) | Assembly tools available for \(R_{r}\) |
\(P_{i}\) | Number of parts, \(i = 1,2,...,n\) | \(tool_{ir}\) | Tool \(R_{r}\) used to complete \(task_{i}\) |
\(task_{i}\) | Task corresponding to \(P_{i}\), \(i = 1,2,...,n\) | \(T_{s}\) | Total working time |
\(t_{ir}\) | Total assembly time \(R_{r}\) takes to complete \(task_{i}\) | \(L\) | Load balancing |
\(t_{i}\) | Completion time of \(task_{i}\) | \(T_{s}^{\prime }\) | Total working time after disturbance |
DL | Delivery time | \(L^{\prime}\) | Load balancing after disturbance |
\(T_{c}\) | Cycle time of RAL | \(\Delta L_{0}\) | Initial threshold of load balancing |
\(\Delta T_{s0}\) | Initial threshold of total working time | \(L_{DT}\) | Virtual load balancing |
\(T_{sDT}\) | Virtual total working time | \(\Delta L\) | Threshold of load balancing |
\(\Delta T_{s}\) | Threshold of total working time | \(f_{1}\) | Objective function of total working time |
\(t_{t}\) | Tool switching time | \(f_{2}\) | Objective function of load balancing |
