# 论文中建立模型是什么方法(论文中的研究模型是什么) Refer to 2.2 Joint Payment Contract Mode (O Mode) in the paper "Three-level Supply Chain Dynamic Cooperation Strategies and Comparisons Involved by Big Data Service Providers", and prove Theorem 2.  First, after reading the original paper, familiarize yourself with the joint payment contract model. In this model, manufacturers and retailers and big data providers are still in the form of decentralized decision-making. The first decision is the manufacturer, and the parameters involved are FM and the sharing ratio X. Then the retailer decides the payment level m on the basis of the previous step. Finally, the big data service provider decides FB based on the original FM, X and m.

In this way, the proof of Theorem 2 can also be reversed by induction, starting from the last step, that is, the decision of the big data service provider, to calculate the best response strategy of the manufacturer in the first step. The difference between it and the calculation process of Theorem 1 is that the representation of the objective function of each participating decision-making party changes, and one more optimal value of the decision variable X needs to be solved during retrograde induction. The manufacturer's profit representation in the objective function of Theorem 2 changes.

First show the specific commands, as shown in Figure 3-Figure 9. Figure 3 shows the known functional expressions.  Figures 4-5 show the first step in the proof process: finding the optimal decision variable. Figure 6: Bring the obtained optimal X into the optimal FB, FM and m, but unfortunately, mathematica is not as smart as I thought. Figure 7 shows the solutions to the coefficients of the VR2 and VM2 functions that I calculated by hand.  Figures 8 and 9 show that the results of Figure 7 are known, and the optimal current value profit and optimal current value profit of each decision-making party are obtained. Finally, after hand calculations and software calculations, I obtained the key coefficients of the optimal trajectory of r as shown in Figure 10. In order to verify the correctness of the results, I performed hand calculation verification. The specific verification process is shown in Figure 11.

Next show, how I got the result of Figure 7.   Among them, Figure 12 lists the conditions required to understand the equation, and makes necessary simplifications. Figure 13 shows the process of solving k1 and k2 and b1. Figure 14 shows the simplified b2 obtained by bringing in k1 and k2.

【1】吴成霞,赵道致,潘新宇.大数据服务商参与的三级供应链动态合作策略及其比较[J].控制与决策,2016,31(07):1169-1177.