# Supplier Replacement Model in a One-Level Assembly System under Lead-Time Uncertainty
## 6 Managerial Insights  
The proposed model has challenging new settings. In particular we add the purchasing cost depending on supplier reliability. This could be a useful aid for decision makers because it opens the possibility of solving very important problems not currently solved, in particular, to decide to outsource or not, if yes, to which suppliers and countries, but also to negotiate purchase prices versus lead time decisions. The results depend on the behavior of the decision maker and his choices when he/she is faced with uncertainty and risks. If the decision maker is a risk-taking manager (\(risk_{max}\)), he/she will be reluctant to pay more to reduce the uncertainty, and hence will always choose \(APC^{0}\), which is a policy with zero additional purchase cost but with maximum uncertainty. In this case, we have the model proposed in [39] that we used to calculate upper bounds. On the other hand, if the decision maker is risk-averse, he/she will be willing to pay the maximum \(APC^{u_{0}-1}\) (\(risk_{min}\)). In this case, the uncertainty disappears and the problem becomes deterministic. In the deterministic case, ordering just-in-time implies zero inventory holding and backlogging costs, leaving the only cost as \(\sum_{i}APC^{u_{0}-1}_{i}\). Table 8 compares our lead-time uncertainty-reducing pricing and inventory control model with these two strategies on three groups of scenarios. In the first group (G1), we considered a low average APC increase (\(0<\overline{\Delta APC}\leq\frac{H}{5n}\)). In the second group (G2), we considered the case of an average APC increase between \(\frac{2}{3}\frac{H}{n}\) and \(\frac{H}{n}\). Finally, in the third group (G3), we considered the case of an average APC increase greater than holding and backlogging costs (\(2\frac{H}{n}\leq\overline{\Delta APC}\leq 5\frac{H}{n}\)). \begin{table}
\begin{tabular}{c c c} \hline
**Instance Family** & **Mean GAP (\(GA_{H+P}\),LB) (\%)** & **Mean GAP (\(GA_{H+P}\),UB) (\%)** \\ \hline
10 & 10.89 & 145.89 \\
20 & 6.33 & 181.06 \\
30 & 6.00 & 183.49 \\
40 & 8.16 & 185.18 \\
50 & 8.77 & 194.95 \\
60 & 10.24 & 194.31 \\
70 & 12.00 & 192.26 \\
80 & 14.34 & 192.57 \\
90 & 10.97 & 191.04 \\
100 & 10.35 & 190.74 \\ \hline \end{tabular}
\end{table} 
Table 7: Gaps between the results of \(GA_{H+P}\) and upper and lower bounds. \begin{table}
\begin{tabular}{c c c c} \hline
**Instance Group** & **Mean GAP** & **Mean GAP** & **Mean GAP** \\  & **(\(GA_{H+P}\),\(risk_{min}\)) (\%)** & **(\(GA_{H+P}\),\(risk_{max}\)) (\%)** & **(\(risk_{min}\),\(risk_{max}\)) (\%)** \\ \hline G1 & 0.57 & 7014.81 & 6993.03 \\ G2 & 108.20 & 4.04 & -49.68 \\ G3 & 492.31 & \(1.78\cdot 10^{-5}\) & -83.17 \\ \hline \end{tabular}
\end{table} 
Table 8: Decisionmaker behavior analysis. Mean GAPs were computed as follows:  
\[\text{mean GAP}(GA_{H+P},risk_{min}) =\left(\frac{\sum_{k=1}^{K}\frac{risk_{min}^{k}-GA_{H+P}^{k}}{GA_{H+ P}^{k}}}{K}\right)\times 100 \tag{17}\] \[\text{mean GAP}(GA_{H+P},risk_{max}) =\left(\frac{\sum_{k=1}^{K}\frac{risk_{max}^{k}-GA_{H+P}^{k}}{GA_{ H+P}^{k}}}{K}\right)\times 100\] (18) \[\text{mean GAP}(risk_{max},risk_{min}) =\left(\frac{\sum_{k=1}^{K}\frac{risk_{max}^{k}-risk_{min}^{k}} {risk_{min}^{k}}}{K}\right)\times 100 \tag{19}\]  
Comparison of two simple strategies found that when the average APC increase is small, a risk-avoiding strategy is almost 7000% better on average than a risk-taking strategy. Similarly, if the average APC increase is very big, a risk-taking strategy is 83.17% better on average than a risk-avoiding strategy. Obviously, there is no reason to take risks when it is cheaper to pay to reduce the uncertainty. Nevertheless, when the cost of reducing the uncertainty exceeds the inventory holding and backlogging costs caused by the uncertainty, then the decision maker should be open to taking risks. Our algorithm gives practically the same results with a \(risk_{min}\) strategy for group G1 and with a \(risk_{max}\) strategy for group G3.