## 3 Methodology
### The a-HPDB Method
#### 3.2.1 The Dispatching Rules  
* _The unprocessed hot lot (uH) first (Rule 1)_. As shown in Figure 5, if there is an uH following an unprocessed normal lot (uN) in a row moving toward the nearest machine within the distance D1 then the uH has the priority to reserve that machine. As a result, other uN keep moving in the Intra-bay.
* _First come first serve for uNs (Rule 2)_. Figure 6 shows that if there are uNs within the distance D1 moving toward the nearest empty machine then the first uN has the priority to reserve that machine. As a result, the other uNs will keep in the Intra-Line. As the loading and unloading happening in the L&UL of a machine, it will not block other lots in the Intra-Line.
* _Directly move a processed lot (pL) to Intra-Line 2 (Rule 3)_. As shown in Figure 7, unload a pL (either processed hot lot (pH) or processed normal lot (pN)) first from a machine to the L&UL line. Then, based on the position of the processing machine, either move the pL directly to Intra-Line 2 if the machine is on Intra-Line 2 side (as shown in Figure 7a) or first move the pL to Intra-Line 1 and then to Intra-Line 2 if the machine in on Intra-Line 1 side (as shown in Figure 7b). This rule expedites the exit of a pL from an Intra-bay.
* _Directly move an uH from Intra-Line 1 to Intra-Line 2 (Rule 4)_. As shown in Figure 8, when there is an uH moving in the Intra-Line 1, meanwhile an empty machine in the \"Quick area\" (a set of machines locates within the distance between the current position of the uH and the exit of this Intra-bay) is available, immediately transfer the uH to Intra-Line 2 to directly access that empty machine.
* _Directly move an uL to Intra-Line 1 from Intra-Line 2 (Rule 5)_. As shown in Figure 9, when an uL (an unprocessed hot lot or normal lot) is moving in Intra-Line 2 there is meanwhile an empty machine in Intra-Line 1, then the AMHS controller directly moves the uL to Intra-Line 1 to access that empty machine.
* _Reserve the nearest machine to the Intra-bay for hot lots (Rule 6)_. Figure 10 shows the 6 th dispatching rule in which the nearest machine to Inter-Line is reserved for hot lot. This can enhance the chance for the nearest machine to serve hot lots. As a result, the hot lots can enjoy a higher service priority and leave an Intra-bay more quickly. When an Intra-bay has far less hot lots than normal lots, it ensures hot lots to be mostly served by this reserved machine to result in a desired system performance.
* _Skip occupied machine (Rule 7)_. As shown in Figure 11, this rule aims to shorten the travel distance for a hot lot. If some specific machines are not available then an unprocessed lot (uL) such as the L1 can skip these machines and directly change from Intra-Line 1 to Intra-Line 2 to skip unnecessary traveling.  
Figure 5: The unprocessed hot lot (uH) first (Rule 1).  
Figure 8: Directly move an uH to Intra-Line 1 from Intra-Line 2 (Rule 4).  
Figure 6: First come first serve for uNs (Rule 2).  
Figure 7: (a) Directly move a pL to Intra-Line 2 (b) first move a pL to Intra-Line 1 and then to Intra-Line 2 (Rule 3).  
Figure 11: Skip occupied machine.  
Figure 10: Reserve the nearest machine to the Intra-bay for hot lots.  
Figure 9: Directly move an uL to Intra-Line 1 from Intra-Line 2 (Rule 5).