## 5 Conclusions  
In MTO companies, optimal order scheduling is the golden key to corporate profits. Due to dynamic and uncertain customer demand and constraint resources, it is hard to schedule the customer orders. Therefore, order scheduling and multi-item scheduling problem considering capacity constrained resources (CCR) are investigated in the current research. The novel problem of order scheduling and multi-item scheduling is presented by considering uncertain dynamic demand of products, capacity constrained resource, and a drum buffer rope (DBR) mechanism. A heuristic based on the DBR method is proposed for  
Figure 8: NP value for different categories of problems after and before using the optimal buffer size. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Problem** & \multicolumn{2}{c}{**Before Buffer Size Tuning**} & \multicolumn{2}{c}{**After Buffer Size Tuning**} \\ \cline{2-5}
**Category** & **Mean NP** & **Median NP** & **Mean NP** & **Median NP** \\ \hline TS & 54,231.66 & 54,115.5 & 65,591.09 & 63,926.4 \\ TM & 212,368.9 & 214,561 & 260,831.2 & 261,927 \\ TL & 340,871 & 339,523 & 352,721.7 & 352,416.5 \\ LS & 172,125.6 & 171,167.5 & 147,719.5 & 147,140 \\ LM & 348,834.2 & 348,645.5 & 375,848.3 & 377,246.8 \\ LL & 500,176.5 & 498,802 & 538,598.2 & 540,171.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mean and median NP value of each category of problems for before and after buffer size tuning. this problem in a multi-item production environment. The proposed heuristic is adopted to make the customer order delivery schedule in each planning horizon and obtain a production order release sequence for the upstream resources of the production system. The proposed heuristic is tested on different real-life problems. End results indicate that the proposed heuristic method outperforms the other considered heuristics in literature, and it can achieve more significant results. Uncertainty in the demand of products is considered in the current research. However, in real production shops, various uncertain factors, such as the uncertain variety and processing time, and random arrival time may also exist. Therefore, in future research, these uncertain factors can be introduced to the order scheduling problem. Furthermore, integrating the rule-based heuristics and the intelligent algorithms is also an interesting direction to further improve the performance of the production system. Conceptualization, L.Y. and J.M. ; Data curation, G.X. and J.M. ; Formal analysis, Y.C. ; Investigation, Y.C. ; Methodology, L.Y. and G.X. ; Project administration, T.Z. ; Resources, T.Z. ; Supervision, T.Z. ; Validation, L.Y. ; Writing--original draft, L.Y. ; Writing--review and editing, L.Y., G.X. and J.M. ; Funding acquisition, L.Y. All authors have read and agreed to the published version of the manuscript. This research was funded by the Youth Program of National Natural Science Foundation of China (Grant No. 51905196). Not applicable. The authors declare that they have no competing  
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