A two-machine multi-family flowshop scheduling problem with batch processing

We consider a two-machine multi-family flowshop scheduling problem with non-identical capacity requirements or sizes on a batch processing machine. A batch processing machine is the one which can process a number of jobs simultaneously as a batch. Once the process begins, no job can be released from the batch machine until the entire batch is completely processed. The objective is to find a sequence of families and sequence of jobs in each family such that the makespan is minimized. We show that the optimal sequence of batches can be determined by a full batch grouping policy. A polynomial time algorithm is proposed for solving this problem. An Illustrated example is also provided.