# Simulation-Based Analysis on Operational Control of Batch Processors in Wafer Fabrication
## 2 Literature Review on BP Control Rules
With information on product arrivals and the state of the manufacturing system, the batch processors may be more efficiently controlled. For example, if we have information about future product arrivals at the time that a machine becomes idle, and there are wafer lots in the queue smaller than the batch capacity, we may use the information to determine whether to start the process right away or wait for future job arrivals to form a batch with more jobs. A dynamic batching heuristic, called DBH, is presented in Reference [13] for a BP station with a single BP and a single job family where information about upcoming job arrivals is considered. In DBH, the planning horizon is the BP processing time \(T\) and the number of forecasted arrivals, \(L\), is smaller than or equal to \(C-1\) where \(C\) is the batch capacity. DBH is activated when a batch processor becomes idle, and \(q\geq 1\) wafer lots are waiting in the queue. At the time epoch \(t_{0}\) (current decision time), DBH first examines \(q\) against the capacity of the batch processor. If \(q\geq C\), \(C\) lots are loaded and processed immediately. If \(q<C\), DBH makes a batching decision to minimize the total delay time, given the forecasted job arrivals. The amount of additional delay time for products currently waiting in the queue is compared to the amount of saved delay time for the future arrivals by waiting until the arrivals occur. Figure 2 shows a waiting time change when the BP station waits for one incoming lot and load \(q+1\) lots at time epoch \(t_{1}\) where \(t_{i}\) represents the arriving time epoch of the next \(i\)th lot after \(t_{0}\). The saved wait time can be calculated as \(\text{Area}_{2}(t_{1})-\text{Area}_{1}(t_{1})\), compared to the wait time in the immediate loading case. From Figure 2, \(\text{Area}_{1}(t_{1})=q(t_{1}-t_{0})\) and \(\text{Area}_{2}(t_{1})=T-(t_{1}-t_{0})\). The saved wait time is calculated for all the time epochs of \(L\), and the one with the largest positive value is selected for the loading time. If all the saved wait times are negative (this means that the delayed loading leads to more waiting time), the machine starts processing jobs with the partial batch immediately. A BP control heuristic named the NACH (Next Arrival Control Heuristic) is presented in Reference [14] for both a single product family and multiple product families. The heuristic only considers the next job arrival and determines if it is more efficient to start the batch process immediately or at the next arrival time. When the loading is postponed until the next arrival time, the decision process is repeated at the next arrival time. It is shown that their heuristic is robust in the sense that it performs well even with prediction errors. The NACHM (NACH with multiple processors) is an extended version of NACH for a BP station with parallel batch processors [5]. Extensive review work on BP control problems with real-time job arrival data is carried out in References [15; 16]. Even though BP control decisions with real-time shop-floor information mostly provide better performance than  
Figure 2: Changes in waiting time when the lots are loaded at time \(t_{1}\). The saved wait time is \(\text{Area}_{2}(t_{1})\) – \(\text{Area}_{1}(t_{1})\). threshold policies, most real-world wafer fabs use MBS-based policies for batching decisions [17]. This is because threshold policies are easy to implement and the future information used in look-ahead control policies is often incorrect, due to unpredictable problems, such as equipment malfunctions, product quality problems, urgent orders, etc. Most research studies on BP control problems have considered stand-alone BP stations. A few pieces of research handle discrete processors in the downstream, upstream, and both upstream/downstream together with batch processors. A loading decision procedure is proposed in Reference [18] for a \(\beta\)\(\rightarrow\)\(\delta\) network to minimize the production lead time.