## 5 Numerical Simulation
### Closed-Loop Supply Chain Differential Pricing Decision  
1. When \(\theta\in[0.7,0.9],g=50\), the optimal retail price, optimal wholesale price and optimal service level of new products, remanufactured products and retreaded products change with \(\theta\) under centralized and decentralized decision making. The situation is shown in Figure 3. Numerical examples show that with the increase in the consumer preference coefficient, the retail price and wholesale price of remanufactured products and refurbished products will increase, and the pricing level of new products will decrease accordingly. It shows that remanufactured products and refurbished products erode the market share of new products, resulting in lower pricing decisions for new products. Simultaneously, as the consumer preference coefficient increases, the service differentiation between new products and remanufactured products or refurbished products decreases, indicating that as consumers favor the remanufactured products and refurbished products, the service strategies of the supply-chain member companies are adjusted accordingly. At this time, the degree of polarization of customer satisfaction is reduced. In addition, lower consumer preferences affect new product pricing decisions and significantly affect remanufactured goods and refurbishment product pricing decisions. This shows that with the increase in consumer preference, the total market demand increases.
2. When \(\theta=0.7\) and \(g\in[50,100]\), the optimal retail price, optimal wholesale price and optimal service level of new products, remanufactured products and refurbished products change with \(g\) in the centralized and decentralized decision making. This scenario is illustrated in Figure 4. The numerical example shows that with the increase in the government subsidy coefficient, the retail price, wholesale price, service level and market demand of the refurbished products have increased, indicating that under the conditions of government subsidies, the surplus of producers and the increase in consumer surplus, the overall supply chain profits rise.
3. When \(\theta\in[0.7,0.9]\) and \(g\in[50,100]\), the total profit of the supply chain under centralized decision making, decentralized R-M decision making and decentralized M-R decision making is shown in Table 4. Numerical examples show that with the increase in consumer preferences \(\theta\) and government subsidies \(g\), the total profits of all members of the supply chain and the supply chain increase, and the profits obtained by the leading ones are higher; the total profit of the supply chain under the R-M decision and M-R decision, individually, is lower than the concentration. Further, decision making shows a double marginal effect, and the supply chain is non-optimal.  
Figure 4: (**a**) Changes in optimal sales price with government subsidies. (**b**) Changes in optimal wholesale prices due to government subsidies. (**c**) Changes in optimal service levels with government subsidies.  
Figure 3: (**a**) Changes in optimal selling prices with consumer preferences. (**b**) Changes in optimal wholesale price with consumer preferences. (**c**) Changes in optimal service levels with consumer preferences.