## 4 Conclusions  
This paper proposes a discrete-event-simulation-based method for batch production of multiple satellite models based on a common manufacturing platform, which is a practical PFSP. We combine the advantages of discrete-event simulation modelling and  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Tie-Breaking** & \(\mathbf{PR_{O}}\) & \(\mathbf{PR_{IJPI}}\) & \(\mathbf{PR_{L}}\) \\ \hline TB\({}_{O}\) & 1555.15 & 1565.20 & 1577.75 \\ TB\({}_{FF}\) & 1615.86 & 1623.12 & 1635.08 \\ TB\({}_{IJPI}\) & 1562.80 & 1574.15 & 1575.48 \\ Mean & 1577.94 & 1587.49 & 1596.1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: ACT time of each heuristic on VRF benchmark.  
Figure 8: APRD vs. ACT of each algorithm on VRF benchmark.  
heuristic algorithms and propose a more practical method, including a flexible modelling methodology for the PFSP simulation meta-model and an improved NEH algorithm. The computational results demonstrate that the new heuristic outperforms the best NEH-based heuristics reported in the literature in terms of solution quality, and this is a 9.18% improvement over the initial NEH algorithm and a 1.40% improvement over the best current improved NEH algorithm. This means that a better and more practical approach is proposed for the problem of satellite batch production in the flowshop. Furthermore, this approach is generally applicable to similar flowshop problems in other fields.  
The main difference between our method and the traditional mathematical method lies in the innovative calculation approach of related objective functions. The reported literature on NEH-based algorithms uses a mathematical model to perform calculations, but this paper collects and processes data by running a simulation model. Secondly, the simulation model is simple to reconstruct, so it is ready to add or change various constraints according to an actual problem. Under these constraints, running the simulation model can easily obtain various production data, such as makespan and total flow time, which are difficult to achieve with traditional mathematical methods. In addition, the simulation model is straightforward to use and maintain because of the object-oriented nature of the simulation meta-model, so the ordinary worker can use software packages developed based on this method after simple training.  
Although this paper proposes a more pragmatic approach, we have not been able to provide a more robust case study due to the pace of batch production planning. The limitations of the algorithms and models in this paper also lie in the fact that the computation time is too long compared to mathematical methods. Therefore, this method is currently not applicable to optimisation scenarios with high real-time requirements. How to improve the speed of optimisation by combining simulations and algorithms is also one of the important problems that needs to be solved in the future.  
Material preparation, data collection, and analysis were performed by [PERSON] The entire research work was planned by [PERSON], and he completed the review and revision of the article before submission. All authors have read and agreed to the published version of the manuscript.  
This research received no formal funding.  
Not applicable.  
The raw data supporting the conclusions of this paper will be made available by the authors on reasonable request.  
We would like to thank the journal editors and reviewers, whose suggestions have greatly improved this paper.  
Authors [PERSON] and [PERSON] were employed by the company Chang Guang Satellite Technology Co., Ltd. Both authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.  
Three initials: [PERSON], [PERSON]; [PERSON]; and [PERSON].  
Permutation flowshop scheduling problem  
Average processing time  
Standard deviation  
Skewness  
KUR Kurtosis  
RPD Relative percentage deviation  
Average CPU time