Composing batches with yield uncertainty

This paper presents a class of job design problems arising from the fabrication process of printed circuit boards and integrated circuits. It considers a manufacturing process in which different types of jobs are processed in a batch processor, where the batch processor can process a batch (limited number) of jobs simultaneously. All jobs are tested in the batch processor and the defective jobs are discarded. Thus, for each type of job, the actual non-defective output from each batch is a random variable that depends on the number of jobs assigned to a batch. Given the yield rate of each type of job and the capacity of the batch processor, it is important to determine the batch composition; i.e., the number of each type of jobs in a batch, so that a certain system performance is achieved. This paper focuses on six performance measures that are appropriate for different manufacturing environments. For four of the performance measures, it develops procedures for determining optimal batch compositions. For the remaining performance measures, the paper constructs heuristics for finding near-optimal batch compositions and generate random problems to evaluate the effectiveness of the heuristics.