# The Common Warehouse Model and Profit Distribution of the Express Industry
## 4 Simulation Experiment
For every eligible \((\delta_{1},\delta_{2},\delta_{3})\), the corresponding result of profit distribution can be directly drawn from the graph as a line perpendicular to plane \(xy\) and its intersection point is \((\delta_{1},\delta_{2})\). The value \(\varphi\) corresponding to the three intersection points of the plane in the figure is the final benefit distribution result \(\varphi_{i}^{\prime}\). It can be seen from the figure that the correction algorithm conforms to our expectation. For example, we can find from the form of the blue curved surface that as \(\delta_{1}\) increases, the shared interests of enterprise 1 is in decline, because the increase of \(\delta_{1}\) represents that when allocating profits, the alliance focuses on distributing more benefits to the enterprises that contribute more capital. Among the three enterprises, the investment capital contribution of enterprise 1 only accounts for 10% of the whole alliance, so as the alliance pays more attention to the input capital contributions, the benefits of enterprise 1 will decrease. In the previous chapter, the weight of each factor was obtained by comparing the given importance matrix with AHP. Since the expert score cannot be obtained, this experiment traverses the possible weight space to study the influences of different weights on the final benefit distribution. As the results in this experiment contain all weighing possibilities, that is, the ratings given by possible experts, they are more general and broader. In addition, in order to more intuitively reflect the relationship between the results of benefit distribution and different variables, we drew three groups of experimental results, as shown in Figures 6-8, respectively, showing the changes of the results of benefit distribution with a certain factor. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Enterprise 1** & **Enterprise 2** & **Enterprise 3** \\ \hline \(\theta_{i}\) & 0.1 & 0.4 & 0.5 \\ \(\rho_{i}\) & 0.5 & 0.4 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Assumed \(\theta_{i}\) and \(\rho_{i}\) of three enterprises. Figure 5: The variation of the result of profit distribution with the weight of each factor. Among them, the horizontal axis represents the weight of change and the vertical axis represents the result of profit distribution. In each figure, the weight of one factor was fixed at 0.5 to change other weights, and the final profit distribution results were compared under the conditions of power being one and power being two. However, this experiment has given the specific values of three factors of three enterprises, so the experiment fails to reflect the influence of the power in the algorithm. Figure 8: The result of the distribution of profits varies with \(\delta_{2}\) (\(\delta_{1}\) is fixed). Figure 6: The result of the distribution of profits varies with \(\delta_{1}\) (\(\delta_{3}\) is fixed). Figure 7: The result of the distribution of profits varies with \(\delta_{3}\) (\(\delta_{2}\) is fixed). \[ \begin{split}&\varphi_{2}^{\prime}=\varphi_{2}+\Delta\lambda_{2}\times v (s)\\ &=\varphi_{2}+\left(\delta_{1}\theta_{2}+\delta_{2}\theta_{2}^{ \sharp}+\delta_{3}\rho_{2}-\frac{1}{N}\right)\times v(s)\end{split}  \tag{14}\]  
Take Figure 7 for example. It can be seen that when \(\delta_{2}=0.5\) is fixed, the profits of enterprise 2 remain unchanged along with the change of \(\delta_{3}\). This is due to the numerical particularity of the examples used in this experiment, since Equation (14) is used to calculate the interests of enterprise 2 when the power is 1 and the power is 2 (where \(N\) is the number of participating enterprises and the value is 3). Besides, the weight of risk \(\delta_{2}\) is fixed. As the weight of innovation research contribution factor \(\delta_{3}\) changes, the weight of capital investment factor \(\delta_{1}=0.5-\delta_{3}\) also changes.