Makespan minimization in a no-wait flow shop problem with two batching machines

This paper deals with the problem of task scheduling in a no-wait flowshop with two batching machines. Each task has to be processed by both machines. All tasks visit the machines in the same order. Batching machines can process several tasks per batch so that all tasks of the same batch start and complete together. The batch processing time for the first machine is equal to the maximal processing time of the tasks in this batch, and for the second machine is equal to the sum of the processing times of the tasks in this batch. We assume that the capacity of any batch on the first machine is bounded, and that when a batch is completed on the first machine it is immediately transferred to the second machine. The aim is to make batching and sequencing decisions that allow the makespan to be minimized.