## 7 Conclusions  
This paper presented a heuristic approach for simultaneously solving transfer line balancing and buffer allocation problems considering the market demand uncertainty. We proposed to solve the overall problem using a combination of heuristic-based algorithm and NSGA-II. The new heuristic decoding principles enabled the industrial needs of the demand uncertainty to be met, which fulfilled the feasibility and improved the quality of each solution, thus achieving a better performance of the algorithm. During the decoding, the heuristic principles also provided each solution with a penalty mechanism to support the elimination of worse solutions. Based on this, we also proposed a pre-screening strategy to eliminate obviously worse solutions from each generation, thus greatly reducing the waste in computational time. Finally, we introduced and tested a simulation strategy to enhance the stability of the estimation of the throughput.  
An industrial case study in a multi-unit manufacturing system producing four engine blocks was illustrated to both validate this approach and compare the novel approach with the original one. The comparison of the results showed that the novel approach provided significantly better results in Case A and Case C (with set coverage of 78.71% and 83.27%) and better performance in Case B and Case D (with set coverage of 59.06% and 62.94%), thus validating both the efficiency and effectiveness of this approach.  
There are several aspects that might be further researched in the future. 1 From the problem point of view, future studies could consider an increased problem complexity to be closer to a real industrial situation, which would mean taking some other neighboring problems or more detailed information of the machining parameters or the machine tools into consideration. 2 From the solution point of view, the concept of multi-fidelity to evaluate BAP or other sub-problems might also be another relevant area for future research studies, which may enhance the efficiency of the methods.  
Moreover, there are some suggestions that may help the potential industrial application in a similar situation. Simulations can provide much more information than the production rate used in this paper; thus, more relevant indicators such as the idle time of machine tools or the energy efficiency of the overall multi-unit manufacturing system could be introduced as objectives to evaluate the final performance of the manufacturing system according to the requirements of the decision makers.  
Conceptualization, H.S. and G.M.; Data curation, H.S., G.M., A.L. and L.X.; Formal analysis, H.S. and G.M.; Funding acquisition, A.L. and L.X.; Investigation, H.S. and L.X.; Methodology, H.S. and G.M.; Project administration, G.M. and L.X.; Resources, G.M., A.L. and L.X.; Software, H.S.; Supervision, H.S., G.M., A.L. and L.X.; Validation, H.S., G.M., A.L. and L.X.; Writing--original draft, H.S.; Writing--and editing, G.M., A.L. and L.X. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China [Grant No. 2011 ZX04015-022], and National Natural Science Foundation of China [51975417].  
Not applicable.  
The data supporting the findings of this study are available within the article.  
We thank the Recruitment Program of High-end Foreign Experts of the Chinese State Administration of Foreign Experts Affairs.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
This appendix provides the detailed simulation results considered in Section 4.4. Figure 11 includes summary reports for the percentage range of the three levels of the