# Competing Reverse Channels' Performance with Sustainable Recycle Innovation Input
## 5 Comparison and Insights
### Numerical Analysis
#### 5.2.2 Impact of Cost Factor for Recycling Innovation Inputs  
Next, we mainly focus on the investigation of \(R\), the cost factor for recycling innovation inputs, on the performances of the supply chain. The related parameters are assumed that \(\alpha=500\), \(\beta=30\), \(H=1000\), \(K=1\). The value of \(R\) is varied from 0.01 to 2. It is noticed that the optimal level of environmental sustainability of the reverse channel and the direct sale channel, the optimal retail price and the optimal direct sale price decrease with the increase of the cost factor \(R\). In Figure 13, \(b_{1}^{H*}\) and \(b^{BE*}\) decrease with the increase of \(R\), and the gap with \(b_{2}^{H*}\) gradually decreases. \(b_{2}^{H*}\) remains the same as \(R\) increases. Figure 12: Regions comparing profit of the collectors with innovation input with respect to \(K\). As shown in Figure 14, \(p^{H*}\) and \(e^{BE*}\) decrease with the increase of \(R\). When \(R<0.2\), the decrease rate of \(p\) is higher. When \(R\) exceeds 0.2, the decrease of \(p\) is relatively slow, but it remains \(p^{H*}<p^{BE*}\). In Figure 15, \(e^{H*}\) and \(e^{BE*}\) decrease with the increase of \(R\), and the rate of decrease becomes smaller and smaller. When at the same \(R\) value level, the incentive for innovation input of model \(H\) is slightly higher than that in model \(BE\), that is, \(e^{H*}>e^{BE*}\). However, when the value of \(R\) in model \(BE\) is at a lower level, the investment in innovation can exceed that in model \(H\). It can be seen from Figure 16 that even if collector 2 does not invest in innovation, his collection rate also slowly decreases with the increase of \(R\), which means that the cost coefficient of innovation input has a certain impact on collector 2, but the impact is not great. When the \(R\) is low, it means that the collector's investment to recover the innovation input is low, which is an ideal situation with low investment and high return. \(\tau_{1}^{H*}\) and \(\tau^{BE*}\) are at the highest level, both are higher than \(\tau_{2}^{H*}\). It can also be seen that if you want to promote recycle companies to carry out recycling innovation investment, reducing innovation investment costs is a fast-acting method. However, when the \(R\)  
Figure 14: The influences of \(R\) on the retail price \(p\). Figure 13: The influences of \(R\) on the transfer price \(b\). gradually increases, it means that the cost of investing in recycling innovation investment by collectors is gradually increasing, and the barriers to entering the innovation recycling market are gradually rising. Recycling efforts \(\tau_{1}^{H*}\) and \(\tau^{BE*}\) declined rapidly, and \(\tau^{BE*}\) even gradually fell below \(\tau_{2}^{H*}\). At the same time, we also observe that the cost coefficient of innovation investment \(e\) is increasing, and the decreasing trends of \(\tau_{1}^{H*}\) and \(\tau^{BE*}\) are more consistent. Compared with the collector 2 without innovation investment, the rate of decrease is greater. It shows that \(R\) has a significant impact on \(\tau\) with innovation inputs. It also reflects that the excessively high cost of innovation input hinders the recycler's innovation investment in the recycling market. From Figures 17 and 18, comparison of total supply chain profits and manufacturer's profits show the following relationship: \(\Pi_{T}^{H*}>\Pi_{T}^{BE*}\), \(\Pi_{M}^{H*}>\Pi_{M}^{BE*}\). Figure 16: The influences of \(R\) on the collection effort \(\tau\). Figure 15: The influences of \(R\) on the innovation input \(e\). The increase in the investment in recycling innovation has led to an increase in social welfare, which has led to greater profits for the manufacturer in Model \(H\). The recovery volume and recovery rate of collector 2 without innovation input are improved to a certain extent because of the positive externality of innovation input.