## System Specification
### Transformation of SACOP  
Considering the strong coupling relationship between various devices in the SACOP environment, it is extremely difficult to simultaneously schedule stackers, AGVs, and picking stations to operate without conflicts and achieve energy consumption and operation efficiency optimization goals. Furthermore, even if there is a set of optimized collaborative solutions, they have almost no anti-interference ability in the face of various uncertain factors in actual operations. Based on the above understanding and inspired by TPPM, this paper proposes an approach to find a key device to dominate the entire scheduling process and ensure that it can be transformed into a collaborative scheduling solution. Due to the ability of AGVs to connect upstream and downstream units in the system, their scheduling schemes have the potential to drive stackers and picking stations to operate. Therefore, this paper chooses them as key devices, thereby transforming the original SACOP problem into a modified multi-AGV scheduling task problem (MMATSP), as shown in Figure 5.  
Figure 4: Picker-led TPPM main process. The modifications of the MMATSP mainly include two aspects, which correspond to the interaction strategy of stacker, AGV, and the interaction strategy of picking station, AGV: one is that the stacker subsystem will perform pickup waiting correction on the original solution, and the other is that the picking station subsystem will perform waiting correction caused by capacity limit. Interaction strategy of stacker, AGV: Due to the maximum driving speed and the ideal driving speed with the lowest energy consumption of the stacker, there is a \"minimum time\", represented by \(t_{min}\), and an \"ideal time\", represented by \(t_{best}\), for the extraction process of each container. We refer to the time between the moment when the previous AGV leaves the aisle and the moment when the next AGV arrives at the aisle as the \"demand time\" for this container, represented by \(t_{demand}\). The stacker subsystem adopts the following operating strategy: for \(t_{demand}>t_{best}\), operate at the ideal driving speed; for \(t_{best}>t_{demand}>t_{min}\), operate at the specified speed to ensure synchronized container handover with the AGV; and for \(t_{demand}<t_{min}\), operate at the rated maximum speed to reduce the waiting time of the AGV. Interaction strategy of picking station, AGV: Waiting correction caused by capacity limit refers to the need for the AGV delivery to consider the capacity limit of the picking station. When an AGV arrives at the picking station, if the pallet containing this order is open or if the picking station capacity does not reach the upper limit, then the delivery is completed; if the order does not belong to any pallet being operated and the picking station capacity reaches the upper limit, then wait for the picking station capacity to be released. Due to the possibility of system deadlock caused by AGVs on standby waiting, standby waiting is modified to set up a temporary store buffer to wait for the capacity release in this paper, which is called buffer waiting. An example of a system deadlock is shown in Figure 6. When using the buffer waiting strategy, orders that need to wait are directly sent to the buffer, while the AGV continues to perform subsequent tasks. When the picking station capacity is released, the original AGV picks up the order from the buffer and sends the container to the picking station. Compared to standby waiting, the buffer waiting strategy increases the construction cost of the buffer and incurs additional energy consumption for AGV's round-trip to and from the buffer. However, on the one hand, it can enable AGVs to quickly carry out subsequent order tasks, thereby improving overall efficiency. On the other hand, it converts standby waiting time into AGV's round-trip time, which is equivalent  
Figure 5: Transforming the complex coupling SACOP problem into AGV-led MMATSP. to exchanging energy consumption for efficiency considering the first advantage.