# Dominance rule and opposition-based particle swarm optimization for two-stage assembly scheduling with time cumulated learning effect

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## Abstract

This paper introduces a two-stage assembly flowshop scheduling model with time cumulated learning effect, which exists in many realistic scheduling settings. By the time cumulated learning effect, we mean that the actual job processing time of a job depends on its scheduled position as well as the processing times of the jobs already processed. The first stage consists of two independently working machines where each machine produces its own component. The second stage consists of a single assembly machine. The objective is to identify a schedule that minimizes the total completion time of all jobs. With analysis on the discussed problem, some dominance rules are developed to optimize the solving procedure. Incorporating with the developed dominance rules, a dominance rule and opposition-based particle swarm optimization algorithm (DR-OPSO) and branch-and-bound are devised. Computational experiments have been conducted to compare the performances of the proposed DR-OPSO and branch-and-bound through comparing with the standard O-PSO and PSO. The results fully demonstrate the efficiency and effectiveness of the proposed DR-OPSO algorithm, providing references to the relevant decision-makers in practice.

## Keywords

Two-stage assembly Flowshop scheduling Time cumulated learning function Dominance rule Particle swarm optimization## Notes

### Funding

This paper was funded in part by the National Natural Science Foundation of China (Nos. 71501024, 71871148), by Taiwan’s Ministry of Science and Technology (No. MOST105-2221-E-035-053-MY3), by China Postdoctoral Science Foundation (Nos. 2018T110631, 2017M612099), and by Sichuan University (No. 2018hhs-47).

### Compliance with ethical standards

### Conflict of interest

All of the authors declare that they have no conflict of interest.

### Human participants or animals

This paper does not contain any studies with human participants or animals performed by any of the authors.

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