ACO-based Multi-objective Scheduling of Identical Parallel Batch Processing Machines in Semiconductor Manufacturing

The batch processing machines (BPMs) have the ability to process more than one job together (called a batch). So the scheduling problem of the BPMs concerns not only the priorities of the jobs obtaining the processing service of a BPM, but the number of the jobs processed together on them. According to diverse classified criteria (such as the number of the BPMs and the job families), the scheduling problem of the BPMs can be further divided into several styles, e.g., a single BPM scheduling problem (SBPM), identical parallel BPMs scheduling problem (PBPM) , non-identical PBPM, the BPMs scheduling problemwith compatible job families and the BPMs scheduling problem with incompatible job families. In this paper, we address the BPMs scheduling problem in a semiconductor wafer fabrication facility (fab), in where there are many BPMs, such as diffusion machines, oxidation machines and dry strip machines. The jobs processed on those machines cannot be batched together unless they use the same recipe of those BPMs. As a result, the scheduling problem of those BPMs is abstracted as identical PBPM with incompatible job families. In a fab, because most of upstream and downstream machines of the BPMs are non-BPMs, jobs must be batched or split regularly during their fabrication processes. Therefore, a good scheduling solution of those BPMs is essential to efficiently utilize their capacity and satisfy the requirements of their downstream machines to balance the fab-wide workload and achieve better fab-wide operational performance. In recent years, there have been many studies of the BPMs scheduling problem. Mathirajan and Sivakumar (Mathirajan & Sivakumar, 2006) have reviewed 98 articles published between 1986 and 2004 on this topic, and the research has considerably evolved since 2004. For example, to minimize the makespan or average flow time of the jobs, Chien and Chen (Chien & Chen, 2007) developed a genetic algorithm (GA) for batch sequencing combined with a novel timetabling algorithm to handle waiting time constraints, frequency-based setups, limited machine availability and a rolling horizon-based scheduling mechanism for scheduling of furnaces for semiconductor fabrication. Chou et al. (Chou et al., 2006) presented a hybrid GA for SBPMwith arbitrary job release times. Tomeet due date requirements from customers, Gupta and Sivakumar (Gupta & Sivakumar, 2007) presented a dynamic scheduling method for SBPM with a look-ahead batching strategy to control the delivery performance between earliness and tardiness measures. Erramilli and Mason (Erramilli & Mason, 2006) proposed a 8