Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
References
Chen, B., & Zhang, X. (2020). Scheduling coupled tasks with exact delays for minimum total job completion time. Journal of Scheduling. https://doi.org/10.1007/s10951-020-00668-1.
Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: A guide to the theory of NP-completeness. New York: W. H. Freeman.
Yu, W. (1996). The two-machine flow shop problem with delays and the one-machine total tardiness problem. PhD thesis, Eindhoven University of Technology.
Yu, W., Hoogeveen, J. A., & Lenstra, J. K. (2004). Minimizing makespan in a two-machine flow shop with delays and unit-time operations is NP-hard. Journal of Scheduling, 7, 333–348.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kubiak, W. A note on scheduling coupled tasks for minimum total completion time. Ann Oper Res 320, 541–544 (2023). https://doi.org/10.1007/s10479-022-04706-3
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-022-04706-3