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

• Published in: European journal of operational research Vol. 197; no. 2; pp. 825 - 827
• Main Authors: Xu, Dehua, Yin, Yunqiang, Li, Hongxing
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-09-2009; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Algorithms; Applied sciences; Approximation; Effectiveness; Exact sciences and technology; Heuristic; Heuristic algorithm; Inventory control, production control. Distribution; Maintenance; Operational research and scientific management; Operational research. Management science; Production scheduling; Scheduling; Scheduling Single machine Maintenance Heuristic algorithm Worst-case analysis; Scheduling, sequencing; Single machine; Studies; Worst-case analysis; Worst-case analysis; Scheduling; Maintenance; Heuristic algorithm; Single machine; Performance evaluation; Polynomial approximation; Worst case method; Task scheduling; Makespan; Polynomial method; Approximation algorithm; Workload; Polynomial time; Case study; Heuristic method; Best approximation
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2008.07.021

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
, which implies that Chen’s heuristic algorithm is the best possible polynomial time approximation algorithm for the considered scheduling problem.