On the complexity of coupled-task scheduling

A coupled-task is a job consisting of two distinct operations. These operations require processing in a predetermined order and at a specified interval apart. This paper considers the problem of sequencing n coupled-task jobs on a single machine with the objective of minimizing the makespan. By making assumptions about processing times, we obtain many special cases and explore the complexity of each case. NP-hardness proofs, or polynomial algorithms, are given to all except one of these special cases. The practical scenario from which this problem originated is also discussed.