Improved approximation algorithms for two-stage flowshops scheduling problem

• Published in: Theoretical computer science Vol. 806; pp. 509 - 515
• Main Authors: Wu, Guangwei, Chen, Jianer, Wang, Jianxin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 02.02.2020
• Subjects: Approximation algorithm; Flowshops; makespan; Scheduling; Flowshops; makespan; Scheduling; Approximation algorithm
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2019.08.028

•This relationship between the multiple two-stage flowshops problem and the classical MAKESPAN problem is studied.•If the MAKESPAN problem has an α-approximation algorithm, then the problem has a 2α-approximation algorithm.•Two restricted cases of the problem, which are of practical importance, have an (α+1/2)-approximation algorithm.•The approximation ratios 2.6 for the problem and 11/6 for two restricted cases are improved to 2+ϵ and 1.5+ϵ respectively. This paper considers the problem of scheduling n two-stage jobs on m two-stage flowshops so as to minimize the makespan. By studying the relationship between the problem and the classical makespan problem, we prove that if there is an α-approximation algorithm for the makespan problem, then for the general case of the problem, we can construct a 2α-approximation algorithm, and for two restricted cases which are of practical importance, we can construct an (α+1/2)-approximation algorithm. As a result, by employing the polynomial-time approximation scheme for the makespan problem, we get a (2+ϵ)-approximation algorithm for the general case and a (1.5+ϵ)-approximation algorithm for the two restricted cases, which significantly improve the previous approximation ratios 2.6 and 11/6 respectively.