Sequencing a hybrid two-stage flowshop with dedicated machines

The paper deals with a two-stage hybrid flowshop problem with one machine in the first stage and two different machines in parallel in the second one. The objective of scheduling such a problem is to minimize the makespan. We demonstrate that the problem is NP-complete. We formulate a dynamic program, which is beyond our grasp for problems of more than 15 jobs. We have conducted experimentation to evaluate the time performance the dynamic programming procedure for "small size" problems.We treat the n-job, two-stage hybrid flowshop problem with one machine in the first stage and two different machines in parallel in the second stage. The objective is to minimize the makespan. We demonstrate that the problem is NP-complete. We formulate a dynamic program, which is beyond our grasp for problems of more than 15 jobs. Our search for heuristic approaches led to the adoption of the Johnson sequence, which motivated two of the three approaches: dynamic programming and sequence-and-merge. The third approach, the greedy heuristic, was included as example of an elementary heuristic