An efficient polynomial-time approximation scheme for parallel multi-stage open shops

• Published in: Discrete Applied Mathematics Vol. 377; pp. 390 - 401
• Main Authors: Dong, Jianming, Jin, Ruyan, Lin, Guohui, Su, Bing, Tong, Weitian, Xu, Yao
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 31.12.2025
• Subjects: Efficient polynomial-time approximation scheme; Linear programming; Makespan; Parallel multi-stage open shops; Scheduling; Linear programming; Scheduling; Makespan; Efficient polynomial-time approximation scheme; Parallel multi-stage open shops
• ISSN: 0166-218X
• DOI: 10.1016/j.dam.2025.08.004

Various new scheduling problems have been arising from real-world applications and spawning new research areas in the scheduling field. We study the parallel multi-stage open shops problem, which generalizes the classic open shop scheduling and parallel machine scheduling problems. Given m identical k-stage open shops and a set of n jobs, we aim to process all jobs on these open shops with the minimum makespan, i.e., the completion time of the last job, under the constraint that job preemption is not allowed. We present an efficient polynomial-time approximation scheme (EPTAS) for the case when both m and k are constant. The main idea for our EPTAS is the combination of several categorization, scaling, and linear programming rounding techniques. Jobs and/or operations are first scaled and then categorized carefully into multiple types so that different types of jobs and/or operations are scheduled appropriately without increasing the makespan too much. •Proposed first EPTAS for parallel multi-stage open shops scheduling.•Combined categorization, scaling, and linear programming rounding methods.•Demonstrated effective gap-filling strategy for small job scheduling.•Achieved near-optimal makespan within polynomial runtime complexity.