# Raw Material Purchasing Optimization Using Column Generation
## 5 Conclusions  
Raw material purchasing optimization in steel plants is important because the RMP cost accounts for a significant fraction. In this paper, we proposed a MILP model and a  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Problem** & **LP Value** & **MILP Value** & **Columns** & **Nodes** & **CPU (s)** & **Gap (\%)** \\ \hline P/50/12/1 & 439,090,828,8491 & 439,148,890 & 861 & 4 & 0.4100 & 0.0132 \\ P/50/12/2 & 436,811,265,4539 & 436,983,237 & 18,543 & 22 & 2.8230 & 0.0394 \\ P/50/12/3 & 436,495,314,6475 & 436,992,295 & 4768 & 6 & 0.7600 & 0.1139 \\ P/100/12/1 & 862,867,896,6292 & 862,868,090 & 3068 & 4 & 3.7140 & \(2.24\times 10^{-5}\) \\ P/100/12/2 & 862,858,277.1114 & 862,868,090 & 5907 & 4 & 2.7462 & 0.0011 \\ P/100/12/3 & 862,831,596 & 862,831,596 & 660 & 1 & 0.8774 & 0.0000 \\ P/150/12/1 & 1,311,460,255,2423 & 1,313,850,978 & 1680 & 2 & 4.1843 & 0.1823 \\ P/150/12/2 & 1,309,469,137,4146 & 1,319,050,475 & 233 & 2 & 5.4000 & 0.7317 \\ P/150/12/3 & 1,296,957,435 & 1,296,957,435 & 334 & 1 & 13.7027 & 0.0000 \\ P/200/12/1 & 2,106,130,786,3546 & 2,109,031,624 & 207 & 2 & 0.8354 & 0.1377 \\ P/200/12/2 & 2,094,315,188,635 & 2,096,631,105 & 211 & 2 & 1.1225 & 0.1106 \\ P/200/12/3 & 2,053,716,895,0005 & 2,055,909,857 & 226 & 2 & 2.8562 & 0.1068 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Computational results for the RMP.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Problem** & **LP Value** & \begin{tabular}{c} **MILP** \\ **Value** \\ \end{tabular} & **Columns** & **Nodes** & \
\begin{tabular}{c} **Dual Gap** \\ **(\%)** \\ \end{tabular} &
\begin{tabular}{c} **CPU Time** \\ **(s)** \\ \end{tabular} \\ \hline
1 & 57.4 & 56 & 1139 & 22 & 0.0024 & 0.0236 \\
2 & 57.0 & 57 & 2046 & 38 & 0.0000 & 0.4630 \\
3 & 56.5 & 56 & 183 & 2 & 0.0089 & 0.0039 \\
4 & 57.0 & 57 & 379 & 6 & 0.0000 & 0.0091 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Computational results for example No. 2 (GAP) [33].  
column generation solution for the RMP for a large-scale steel plant. The computational results show that this solution is quite effective. For different varieties and quantities, we recommend several patterns for the selection of raw materials. The results show that it can save a lot in procurement costs, and it is estimated that it can save more than 80 million yuan in procurement costs every year  
During the development of the solution, we note that two issues deserve more attention in the future. First, developing effective heuristics for finding feasible solutions for the lot-size problem is still a good topic, especially with tight capacity constraints. The second is the combination of column generation and neighborhood search techniques.  
Conceptualization, Z.G. and D.L.; data curation, D.L.; formal analysis, D.W.; methodology, Z.G.; experimental design and testing, D.L.; software, D.W. and Z.Y.; supervision, Z.G.; validation, Z.Y.; writing-- original draft, Z.G.; writing--review and editing, D.W. All authors have read and agreed to the published version of the manuscript.  
This study was partly supported by the Major Program of the National Natural Science Foundation of China (72192830, 72192831) and the 111 Project (B16009).  
Data Availability Statement: Data are contained within the article.  
The authors thank the MaSteel Raw Material Supply & Sale Corp. for their help.  
The authors declare no conflicts of interest.