## 4 Case Application and Benefit-Cost Analysis
### Application and Benefit-Cost Analysis of the Stage of Sample Product Performance Evaluation
\tag{9}\]  
where \(SCPC(e_{31})\leq 0.03\), \(SCPC(e_{32})\leq 0.06\), \(0.02\leq NPC(e_{31})\leq 0.08\), \(0.005\leq NPC(e_{32})\leq 0.02\), \(0.02\leq NPC(e_{33})\leq 0.07\), \(0.005\leq NPC(e_{34})\leq 0.02\), \(C_{m}(w_{I31})=0.96+70.94\text{exp}(-23.84\text{w}_{I31})\), \(C_{m}(w_{I32})=0.96+70.94\text{exp}(-23.84\text{w}_{I32})\), \(C_{m}(w_{I33})=43.71+165.28\text{exp}(-271.07\text{w}_{I33})\), \(C_{m}(w_{I34})=43.71+165.28\text{exp}(-271.07\text{w}_{I34})\), \(C(w_{I31})=(32/0.05^{2})\)\(w_{I31}^{2}\), \(C(w_{I32})=(55/0.05^{2})\)\(w_{I32}^{2}\), \(C_{l}(w_{I33})=(35/0.05^{2})\)\(w_{I33}^{2}\), and \(C_{l}(w_{I34})=(35/0.05^{2})\)\(w_{I34}^{2}\). The NSGI-II algorithm has been applied for optimizing the calculation, and after multiple runs, the results are almost the same. The quality loss after optimization is \(M(C_{l})=\text{CNY 33.861}\), and the processing cost is \(M(C_{m})=\text{CNY 64.248}\); meanwhile, the manufacturing accuracies of single node enterprises are \(w_{I31}=0.027829\), \(w_{I32}=0.032264\), \(w_{I33}=0.013456\), and \(w_{I34}=0.014989\). Based on Table 3, the total manufacturing cost for the counterweight blocks and balance shaft provided by the existing supplier is CNY 93. After optimization, the cost decreases by 30%, which meets the requirement of reducing the cost while ensuring the balance performance. Based on the mathematical model of Formula (7) in Section 3.2.2, the impact of the balance shaft system sales price on the maximum profits of three-cylinder engine assembly suppliers, balance shaft system suppliers, and the manufacturing supply chain are obtained. Table 5 shows the decision-making results under various conditions, for example, when the engine assembly supplier assembles directly without testing the quality, and when the assembly quality is considered. It can be seen from Table 5 that when the three-cylinder engine assembly supplier directly installs the balance shaft system without considering the process quality, the maximum profits of the engine assembly supplier, the balance shaft system small assembly supplier, and the manufacturing supply chain are CNY 2500, CNY 3700, and CNY 5300, respectively. When the impact of the process quality is considered, the maximum profits of the engine assembly supplier, the balance shaft system small assembly supplier, and the manufacturing supply chain are all 1-2 times higher. When the three-cylinder engine assembly supplier considers the impact of assembly quality and maximizes the profit of the manufacturing supply chain, the maximum profits of the balance shaft small assembly supplier and the manufacturing supply chain are both higher than when the three-cylinder engine assembly supplier dominates. Moreover, in this situation, the overall maximum profit of the manufacturing supply chain can be increased by around 7%, with the wholesale price of the three-cylinder engine balance shaft system remaining unchanged. The above shows that it is more conducive to the management of process quality in the manufacturing supply chain to consider the impact of the assembly quality of the balance shaft system. The analysis indicates that the process quality control model for the three-cylinder engine balance shaft system proposed in this paper is feasible. At the stage of preparation before product processing, when the impact of both process quality and testing quality of the balance shaft system are considered, and other conditions remain unchanged, the maximum profit of the manufacturing supply chain is twice that, without considering the testing quality. At the stage of product performance evaluation, the profit of the manufacturing supply chain is higher when the process quality is considered, and the result remains unchanged, whether the three-cylinder engine assembly dominates or the maximum profit of the manufacturing supply chain dominates.