# Multi-AGV Scheduling under Limited Buffer Capacity and Battery Charging Using Simulation Techniques
## 3 Multi-AGV Scheduling Rules for Practical Shopf floors  
### Practical Manufacturing Shopffloor with Limited Buffer Capacity and Charging Policy  
Figure 1 depicts the transportation procedure of AGVs considered in this paper, where AGVs are used to transport a batch of finished goods from the production line to the delivery point. The finished goods are produced in the production line and forwarded to the pickup location. The transportation batches waiting at the pickup location constitute the output buffer of the production line, and they have to wait at the pickup location until an AGV comes and picks them up. Initially, AGVs stay in charging stations, and one of them is requested to perform the transportation procedure whenever a transportation batch appears at the pickup location. Then, the AGV visits the pickup location to load the batch to transport, travels to the drop-off location, and unloads the batch. After the transportation batch is unloaded, we have to check the start-charge condition, and the AGV returns to a charging station if and only if this condition is met. Otherwise, the AGV continues to perform the transportation procedure for the next transportation batches. In this paper, the start-charge condition is defined by two sub-conditions. Sub-condition 1 for start-charge: every pickup location in the entire shopfloor is empty. Sub-condition 2 for start-charge: the battery level of the AGV is lower than the pre-defined threshold, \(T_{charging}\). The start-charge condition is met if one of those two sub-conditions is satisfied. Typically, multi-AGV systems contain multiple charging stations. In this paper, a charging station for an AGV satisfying the start-charge condition is chosen by applying the charging station selection rules listed in Table 1.  
For the transportation procedure in Figure 1, this paper considers two practical issues: limited buffer capacity and battery charging. First, limited buffer capacity indicates that the capacity of the pickup location is limited. Let \(L_{i}\) denote the \(i\)th production line in a given shopfloor, \(W(L_{i})\) the number of transportation batches in the pickup location for \(L_{i}\), and \(W_{max}(L_{i})\) the buffer capacity of \(L_{i}\). \(L_{i}\) can forward finished goods to the pickup location only if \(W(L_{i})<W_{max}(L_{i})\). In contrast, the manufacturing process of \(L_{i}\) is temporarily halted when \(W(L_{i})=W_{max}(L_{i})\), and \(L_{i}\) can resume its process when \(W(L_{i})<W_{max}(L_{i})\). This constraint reflects the limited space for storing products or items, and it can help mitigate the excessive work-in-process (WIP). Second, battery charging is also an important issue in practical multi-AGV systems, and the performance of any AGV scheduling approach will be overestimated if battery charging is ignored. The transportation procedure in Figure 1 contains two conditions related to battery charging: start-charge and stop-charge. While the former is explained \begin{table}
\begin{tabular}{c c} \hline \hline
**Rule** & **Charging Station to Choose** \\ \hline Dedicated charging station (DCS) & Charging station where the AGV stays at time \(t=0\) \\ \hline Random charging station (RCS) & A random empty charging station \\ \hline Furthest charging station (FCS) & The furthest empty charging station \\ \hline Nearest charging station (NCS) & The nearest empty charging station \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Charging station selection rules. Figure 1: Transportation procedure of AGVs. above, the latter is used to determine if an AGV at a charging station can receive the transportation request. In other words, an AGV can start the transportation procedure for a transportation batch if and only if it satisfies the stop-charge condition, which is characterized by two sub-conditions as follows:  
Sub-condition 1 for stop-charge: there are one or more production lines that have a non-empty output buffer.