# Risk Analysis of a Two-Level Supply Chain Subject to Misplaced Inventory
## 6 Numerical Analysis  
In this section, we conduct a numerical analysis to explore the impact of inventory inaccuracy and risk aversion on decision making in terms of information sharing, RFID adoption, and supply chain coordination. We consider the situation when a supplier sells its products to multiple retailers. The retailers are subject to different magnitudes of misplacement errors and have different risk attitudes. In the numerical example, we set the values of the parameters involved as \(p=100\), \(c=40\), \(s=20\), and \(D_{\text{max}}=300\) following the setting used in previous studies [25; 45]. Based on observations of empirical studies [3; 4], we assume the range of \(\beta\) is from 0 to 0.08.  
Figure 1 shows how the supplier's benefit from information sharing is affected by the magnitude of inventory errors and the retailer's degree of risk aversion. The supplier's benefit from information sharing is positively related to the magnitude of inventory errors. In other words, the supplier can benefit more when there exist serious inventory errors in the retail store. However, the supplier may suffer a loss from information sharing (\(\Delta\pi_{IS}^{S}<0\)) when the magnitude of inventory errors is relatively low (\(\beta<0.04\)). The supplier's benefit from information sharing is negatively affected by the retailer's degree of risk aversion. When the retailer is less risk-averse (a higher \(\eta\)), the supplier can benefit more from information sharing, and thus has a stronger desire for information sharing.  
Using Figure 2, we illustrate the supply chain's incentive to adopt RFID technology when the retailer is risk-averse. Figure 2 shows that both parties tolerate higher RFID costs when the inventory errors become serious. From Figure 2, we can also observe that the supplier's incentive to invest in RFID is decreasing in the retailer's degree of risk aversion. Moreover, Figure 2 verifies that the cost savings from RFID implementation are not symmetrically distributed among supply chain participants: the retailer benefits more from RFID compared with the supplier.  
Figure 3 verifies the observation that a risk-averse retailer is willing to share a high portion of his revenue to the supplier, in order to obtain a low wholesale price for avoidance of the risk. This is consistent with the definition of risk-averse, which states that risk-averse decision makers are willing to give up some profits to avoid possible losses.  
The results shown in Table 1 also confirm that a supply chain can always benefit from coordination (\(\Delta\pi_{\text{Co}}^{\text{SC}}>0\)). In particular, the supply chain is expected to benefit more when the retailer is more risk-averse.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\eta\) & \(k\) & \(\Delta\pi_{\text{Co}}^{\text{SC}}\) & \(\Delta\pi_{\text{Co}}^{\text{R}}\) & \(\Delta\pi_{\text{Co}}^{\text{S}}\) \\ \hline
0.1 & 0.05 & 5788.9412 & 5788.9412 & 0 \\
0.2 & 0.05 & 5437.6335 & 2688.2682 & 2749.3652 \\
0.3 & 0.05 & 5055.7772 & 1593.6136 & 3462.1636 \\
0.4 & 0.05 & 4643.3724 & 977.5521 & 3665.8203 \\
0.5 & 0.05 & 4200.4191 & 534.5988 & 3665.8203 \\
0.6 & 0.1 & 3726.9173 & 875.7237 & 2851.1936 \\
0.7 & 0.1 & 3222.8670 & 386.2204 & 2836.6467 \\
0.8 & 0.25 & 2688.2682 & 1313.5856 & 1374.6826 \\
0.9 & 0.25 & 2123.1209 & 629.6386 & 1493.4823 \\
1 & 0.25 & 1527.4251 & 0 & 1527.4251 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Impact of the risk aversion attitude on the profits of the supply chain partners.