Flowshop scheduling problem with a batching machine and task compatibilities

This paper deals with the problem of task scheduling in a flowshop with two (discrete and batching) machines. Each task has to be processed by both machines. All tasks visit the machines in the same order. The first machine is a discrete machine that can process no more than one task at a time, and the second machine is a batching machine that can process several tasks per batch with the additional feature that the tasks of the same batch have to be compatible. A compatibility relation is defined between each pair of tasks, so that an undirected compatibility graph is obtained which turns out to be an interval graph. The batch processing time is equal to the maximal processing time of the tasks in this batch and all tasks of the same batch start and finish together. The aim is to make batching and sequencing decisions and minimize the makespan.