A note on scheduling coupled tasks for minimum total completion time

A recent Journal of Scheduling paper by Chen and Zhang (J Sched, 2020. https://doi.org/10.1007/s10951-020-00668-1 ) proves that the problem of scheduling coupled tasks to minimize total completion time is NP-hard in the strong sense even for the case with all tasks having the same, though not necessarily unit, processing times. This note shows a simpler proof of that result, and strengthens it by proving that the problem is NP-hard in the strong sense even if all tasks are unit-time.