# Simulation-Based Analysis on Operational Control of Batch Processors in Wafer Fabrication
## 2 Literature Review on BP Control Rules  
The BP control rules involve an event-based decision procedure for loading a batch of wafer lots on batch processors in real-time. When a batch processor completes the processing service of a batch and there exist products waiting in the queue, decisions should be made whether to start loading a batch of wafer lots right away or wait for wafer lots to arrive, and which job type to be loaded. One possible loading alternative is to load jobs immediately regardless of how many jobs exist in the waiting queue. In this case, only a single wafer lot might be loaded and processed on the batch processor. Another possible control rule is that the processing cycle is initiated only when the batch size reaches the batch capacity. In this case, the jobs which have arrived earlier should wait for upcoming jobs to form a full batch load. An in-between strategy is a threshold strategy. A commonly used threshold strategy is MBS (minimum batch size) [8]. The MBS loading strategy works as follows: Let \(q\) be the number of wafer lots waiting in the queue at a BP station, \(B\) be the predetermined MBS value (or threshold value), and \(C\) be the batch capacity. When a batch processor becomes idle, a BP control decision is initiated. If \(q<B\), the BP waits until there are \(B\) jobs present at the queue--at which point, it starts serving them together. If \(B\leq q\leq C\), all the \(q\) jobs are immediately loaded as a batch for having a BP process service. If \(q>C\), only \(C\) wafer lots are loaded immediately for processing, and the others must wait. The determination of the optimal MBS is a main research topic in the MBS-based control strategy. A stochastic dynamic program is provided in Reference [9] to determine the optimal MBS value for a BP station. It is proved that the MBS control policy is optimal for minimizing mean waiting time when the jobs arrive with a Poisson process, and the processing times are independent and identically distributed. An MBS-based BP control problem is examined in Reference [10] for a reentrant two-stage \(\delta\)\(\rightarrow\)\(\theta\) system where the first stage is a DP station with multiple discrete processors and the second is a BP station with only one batch processor. (In this paper, notations \(\delta\) and \(\beta\) will be used for discrete and batch processes, respectively.) The discrete processors are subject to failure, which implies that the arrivals of jobs to the BP station are uncertain. Since the system is reentrant, the jobs leaving the BP station visit the DP station again. It is claimed that the control decision at the BP station affects the availability of material at the downstream station, which is especially important when the downstream DP station is a bottleneck resource. An MBS-based control algorithm is introduced in Reference [11] to determine the optimal threshold value with the objective of minimizing the number of customers in the system. It is found that at high BP traffic intensities, the system performance is relatively insensitive to the threshold value because there are always enough customers in the queue at a service completion, while at low BP traffic intensities, it is better to set the MBS value low because the time spent waiting for jobs to arrive is long. A theory-based queueing model is presented in Reference [12] to determine the threshold value for a BP station with multiple machines where multiple types of products are processed. A closed-form formula is presented to approximate the steady-state performance measures, including lead time and WIP levels. A genetic algorithm (GA) based batching decision is proposed to find the near-optimal batch sizes for different product families. The MBS-based strategies discussed above only consider WIPs in the queue for BP loading decisions. In modern wafer fabs with advanced shop-floor information systems, real-time manufacturing data can be collected with which smart operational controls become possible.