A note on “scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan”

In a recent paper, Chen J.S. Chen, Scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan, European Journal of Operational Research 190 (2008) 90–102] proposes a heuristic algorithm to deal with the problem Scheduling of Nonresumable Jobs and Flexible Maintenance Activities on A Single Machine to Minimize Makespan  . Chen also provides computational results to demonstrate its effectiveness. In this note, we first show that the worst-case performance bound of this heuristic algorithm is 2. Then we show that there is no polynomial time approximation algorithm with a worst-case performance bound less than 2 unless P=NP$P=\mathit{NP}$, which implies that Chen’s heuristic algorithm is the best possible polynomial time approximation algorithm for the considered scheduling problem.