## 2 Literature Review  
In this section, we review some studies that have developed dispatching rules for wafer fabrication in terms of 300 mm and 450 mm wafer sizes.  
For 300 mm wafer fabrication, [PERSON] and [PERSON] [14] proposed a dispatching rule, termed Modified Nearest Job First (MNJF), for an OHT with single loop. The dispatching rule aims to improve the throughput of lots while minimizing the delivery times. They found the dispatching rule was effective. [PERSON] et al. [15] adopt Petri nets to model the coupling dynamics among transport jobs and OHT vehicles in an intrabay loop of a 300 mm wafer fab. In addition, they proposed a heuristic algorithm to adjust the dual solution to a feasible schedule. Numerical results demonstrated that their solution methodology could generate good schedules within a reasonable amount of computation time for realistic problems. Compared to a popular vehicle dispatching rule, their approach can achieve 25.6% improvements on the average delivery time in our realistic test cases. [PERSON] et al. [16] proposed an adaptive dispatching rule (ADR), whose parameters are determined dynamically by real-time information relevant to scheduling, for semiconductor fabs. A real fab simulation model was used to investigate the effectiveness of the ARD. Their simulation results showed that ADR with constant weighting parameters outperforms the conventional dispatching rule on average. [PERSON] et al. [17] proposed a hybrid push/pull (PP) dispatching rule for an AMHS. In addition, they had conducted simulation experiments to investigate the effectiveness of the dispatching rule. Their simulation results showed that the PP could reduce WIPs as well as delivery time of lots significantly. [PERSON] and [PERSON] [18] proposed a differentiated preemptive dispatching policy (DPD) to prioritize lots in a 300 mm fab, with hot lots being served first. Finally, they suggested that an OHT transporter should keep distance from the front OHT transporter to prevent blocking situations. In another study, [PERSON] [19] proposed a Heuristic Preemptive Dispatching Method (HPD) to reduce the waiting times and eventually the delivery times of lots in an OHT of a 300 m wafer fab. Their simulation results showed that the HPD was effective. However, as these aforementioned dispatching rules were dedicated to the OHTs used in a 300 mm wafer fab, they may not be suitable for the conveyor-based AMHS to be used for 450 mm wafer fabrication. Thus, effective dispatching methods suitable for the conveyor-based AMHSs to be used in a 450 mm fabrication environment are still required.  
There are some studies dedicated to developing dispatching rules for 450 mm wafer fabrication and they are reviewed as follows. [PERSON] [20] proposed a Heuristic Preemptive Dispatching Method (HPD) for a conveyor-based AMHS in a simulated 450 mm wafer fab. Their experiments showed that the HPD was effective due to promising delivery times for both hot and normal lots. Further, [PERSON] et al. [12] proposed a novel dispatching method, termed Heuristic Preemptive Dispatching Method using Activated Roller Belt (HPDB), a novel method with effective dispatching rules based on a kind of advanced belt, the ARB. The HPDB nearly improved the problems found in the HPD [18] and R-HPD [13]. However, while the HPDB only allows a lot to directly transfer from Intra-Line 1 to Intra-Line 2 so as to access the empty machines on Intra-Line 2, it cannot best utilize the empty machines on Intra-Line 1. This has prompted us to improve the HPDB by proposing a new dispatching method, termed a-HPDB. The a-HPDB allows a lot to change between Intra-Line 1 and Intra-Line 2 freely so as to access available machines on both sides. We detail the a-HPDB in the next section.