## 4 Solution for Declining Discrimination of Salvage Ship Supplier Selection
### Limitation of Correction by Diversity Factors  
Application of diversity factors to the adjustment of weights may lead to over correction. Equation (7) was used to correct weights that were obtained through the analytic hierarchy process.  
\[w_{i}^{s}=\frac{w_{i}\cdot\delta_{i}}{\sum\limits_{i=1}^{n}u_{i}} \tag{7}\]  
Comparison between results that were corrected by diversity factors and limited diversity factors were carried out, where A\({}_{i}\)\({}^{0}\) stands for the overall score obtained through analytic hierarchy process, A\({}_{i}\)\({}^{s}\) means that the overall score that was obtained through diversity factors and A\({}_{i}\)\({}^{s}\) refers to the overall score that was obtained through limited diversity factors, as shown in Table 7.  
According to Table 7, the distinction of suppliers with similar scores was realized through application of diversity factors. However, due to strong reduction of two important indexes, Price X\({}_{1}\) and Quality control and production capacity X\({}_{5}\), caused by diversity factors, where the weight of X\({}_{1}\) was reduced from 0.343 to 0.0782 and that of X\({}_{5}\) was changed from 0.338 to 0.1087, final overall scores failed to reflect comprehensive strength of suppliers correctly. It also led to ranking the difference of A\({}_{i}\)\({}^{s}\) and A\({}_{i}\)\({}^{f}\). Through diversity factors, indexes with high scoring difference were adjusted into  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**X** & \(\mathbf{w_{i}}\) & \(\mathbf{w_{i}}\)\({}^{s}\) & \(\mathbf{w_{f}}\)\({}^{f}\) & **S** & \(\mathbf{\mathrm{A_{i}}}\)\({}^{\mathbf{g}}\) & **Rank** & \(\mathbf{\mathrm{A_{i}}}\)\({}^{s}\) & **Rank** & \(\mathbf{\mathrm{A_{i}}}\)\({}^{\mathbf{f}}\) & **Rank** \\ \hline X\({}_{1}\) & 0.343 & 0.0782 & 0.3160 & S\({}_{1}\) & 85.08 & 2 & 80.42 & 9 & 84.55 & 9 \\ X\({}_{2}\) & 0.042 & 0.1110 & 0.0522 & S\({}_{2}\) & 85.06 & 4 & 82.91 & 5 & 84.99 & 2 \\ X\({}_{3}\) & 0.046 & 0.0754 & 0.0561 & S\({}_{3}\) & 85.08 & 2 & 81.79 & 7 & 84.71 & 7 \\ X\({}_{4}\) & 0.077 & 0.2475 & 0.0830 & S\({}_{4}\) & 85.10 & 1 & 83.02 & 4 & 84.79 & 4 \\ X\({}_{5}\) & 0.338 & 0.1087 & 0.3110 & S\({}_{5}\) & 85.04 & 6 & 82.75 & 6 & 85.02 & 1 \\ X\({}_{6}\) & 0.039 & 0.0863 & 0.0498 & S\({}_{6}\) & 85.01 & 7 & 83.44 & 1 & 84.76 & 5 \\ X\({}_{7}\) & 0.073 & 0.1568 & 0.0797 & S\({}_{7}\) & 85.10 & 1 & 83.03 & 3 & 84.63 & 8 \\ X\({}_{8}\) & 0.042 & 0.1361 & 0.0522 & S\({}_{8}\) & 85.07 & 3 & 77.25 & 10 & 84.48 & 10 \\  & & & & S\({}_{9}\) & 85.05 & 5 & 81.19 & 8 & 84.87 & 3 \\  & & & & S\({}_{10}\) & 85.07 & 3 & 83.35 & 2 & 84.72 & 6 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of the Two Revisions.  
important indexes, so that scores of indexes with high scoring difference became important indexes evaluating comprehensive strength of suppliers, leading to ranking that did not accord with actual needs. For instance, the weight of X\({}_{4}\) was adjusted from 0.077 to 0.2475 through diversity factors, making X\({}_{4}\) become the most important index, so that S\({}_{6}\) who got a high score of X\({}_{4}\) (9.1) took the first from the seventh place, ignoring the importance of indexes.  
However, the problems above can be avoided through limited diversity factors. This is because the importance of indexes could be maintained and proper enhancement of weights of indexes with a large difference could be realized through limited diversity factors. In this way, actual needs during bidding can be met.