On scheduling multiple parallel two-stage flowshops with Johnson’s Rule

Guangwei Wu, Fu Zuo, Feng Shi () and Jianxin Wang
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Guangwei Wu: Central South University of Forestry and Technology
Fu Zuo: Central South University of Forestry and Technology
Feng Shi: Central South University
Jianxin Wang: Central South University

Journal of Combinatorial Optimization, 2024, vol. 47, issue 2, No 11, 20 pages

Abstract: Abstract It is well-known that the classical Johnson’s Rule leads to optimal schedules on a two-stage flowshop. However, it is still unclear how Johnson’s Rule would help in approximation algorithms for scheduling an arbitrary number of parallel two-stage flowshops with the objective of minimizing the makespan. Thus within the paper, we study the problem and propose a new efficient algorithm that incorporates Johnson’s Rule applied on each individual flowshop with a carefully designed job assignment process to flowshops. The algorithm is successfully shown to have a runtime $$O(n \log n)$$ O ( n log n ) and an approximation ratio 7/3, where n is the number of jobs. Compared with the recent PTAS result for the problem (Dong et al. in Eur J Oper Res 218(1):16–24, 2020), our algorithm has a larger approximation ratio, but it is more efficient in practice from the perspective of runtime.

Keywords: Scheduling; Two-stage flowshop; Approximation algorithm; Cloud computing (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10878-024-01107-z

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