# The Common Warehouse Model and Profit Distribution of the Express Industry
## 4 Simulation Experiment  
The results of the correction method are verified by examples and experiments. The experiment proves that when the weights of different factors change, the improved Shapley value method can make the enterprises making more contributions to factors with higher weights get more profits. Now assume that there are three express enterprises 1, 2, and 3, and their operating expenses are CNY 170,000, CNY 250,000, and CNY 300,000 respectively. Their cooperation may be as follows:  
1. Enterprises 1, 2 carry out cooperation, and enterprise 3 carries out business alone. The total cost at this time is CNY 500,000. 2. Enterprises 1, 3 carry out cooperation, and enterprise 2 carries out business alone. The total cost at this time is CNY 520,000. 3. Enterprises 2, 3 carry out cooperation, and enterprise 1 carries out business alone The total cost at this time is CNY 450,000. 4. Enterprises 1, 2, 3 carry out cooperation The total cost at this time is CNY 320,000. Figure 4: Three identified risk factors. According to the traditional Shapley value method, the following calculation can be carried out to obtain the distribution profits of enterprises 1, 2, and 3 in the alliance in Tables 1-3. Therefore, according to the traditional Shapley value method, the profits of enterprises can be obtained as \(\varphi_{1}=0+3.67+3.33+4.33=11.33\) (ten thousand CNY) \(\varphi_{1}=0+3.67+4.5+6.67=11.33\) (ten thousand CNY) \(\varphi_{1}=0+3.67+4.5+6.67=11.33\) (ten thousand CNY). Hence, we get three \(\varphi_{i}\) in the correction algorithm. The following experiment shows the benefit distribution effect of the modified algorithm in the case of this example. This paper assumes that \(k_{1}=0.2,k_{2}=0.1,k_{3}=0.7\) and the values in Table 4. The piecewise function of the investment fund contribution and innovation research contribution in Equation (8) is also given. The specific value of risk contribution is determined by Equation (8). When constructing functions \(f(\theta_{i})\) and \(g(\rho_{i})\), combined with practical considerations, the following expression can be obtained:  
\[f(\theta_{i})=\left\{ \begin{array}{ll}\frac{3}{5}\theta_{i},0\leq\theta_{i}< \frac{1}{3}\\ \frac{4}{9}\theta_{i}-\frac{1}{15},\frac{1}{3}\leq\theta_{i}<\frac{1}{2}\\ \frac{4}{3}\theta_{i}-\frac{1}{3},\frac{1}{2}\leq\theta_{i}\leq 1\end{array} \right. \tag{12}\]  
\[g(\rho_{i})=\left\{ \begin{array}{ll}\frac{1}{6},0\leq\rho_{i}<\frac{1}{3}\\ \frac{5}{12},\frac{1}{3}\leq\rho_{i}<\frac{1}{2}\\ \frac{7}{2},\frac{1}{2}\leq\rho_{i}<\frac{2}{3}\\ 1,\frac{2}{3}\leq\rho_{i}\leq 1\end{array} \right. \tag{13}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**(s)** & **(1)** & **(1, 2)** & **(1, 3)** & **(1, 2, 3)** \\ \hline \(v(s)\) & 0 & 22 & 20 & 40 \\ \(v(s-\{1\})\) & 0 & 0 & 0 & 27 \\ \(v(s)-v(s-\{1\})\) & 0 & 22 & 20 & 13 \\ \(|s|\) & 1 & 2 & 2 & 3 \\ \(\omega(|s|)[v(s)-v(s-\{1\})]\) & 0 & 3.67 & 3.33 & 4.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Profit distribution table of enterprise 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**(s)** & **(2)** & **(1, 2)** & **(2, 3)** & **(1, 2, 3)** \\ \hline \(v(s)\) & 0 & 22 & 27 & 40 \\ \(v(s-\{2\})\) & 0 & 0 & 0 & 20 \\ \(v(s)-v(s-\{2\})\) & 0 & 22 & 27 & 20 \\ \(|s|\) & 1 & 2 & 2 & 3 \\ \(v(s)-In the experiment, we fixed the above data (enterprise cost, \(k_{i}\), \(\theta_{i}\) and \(\rho_{i}\) of three enterprises, \(f(\theta_{i})\) and \(g(\rho_{i})\)). Then we modified the weights of different factors, and traversed all \((\delta_{1},\delta_{2},\delta_{3})\) satisfying \(\delta_{1}+\delta_{2}+\delta_{3}=1\). After that we combined and calculated the corresponding profit distribution results, as is shown in Figure 5.  
In Figure 5, the change of the benefit distribution result (axis \(z\)) with the weight of each factor is plotted (axis \(x\) refers to \(\delta_{1}\), axis \(y\) refers to \(\delta_{2}\), accordingly; \(\delta_{3}=1-\delta_{1}-\delta_{2}\)).