No-Wait Flow Shop Problem with Two Batch Processing Machines

Abstract In this paper, no-wait flow shop problems on two batch processing machines are studied. Batch processing machines are executing groups or batches of tasks together. One considers so-called max-batch machines and sum-batch machines. In the first case, a batch of tasks is processed simultaneously and the processing time of a batch is given by the longest processing time of the tasks in the batch. In the second case, the batch processing time is given by the sum of processing times of the tasks assigned to it. In both situations, all tasks in a batch start and are completed and available at the same time. The aim is to make batching and sequencing decisions so that the makespan is minimized. Limited and unlimited batch sizes are analyzed in a no-wait scheduling environment and new algorithms as well as complexity results are presented.