## 4 Numerical Results  
This section conducts experimental computations to illustrate the proposed model and explore different results to investigate the impact of interesting parameters on the optimal values of the decision variables. In the beginning of this section, we introduce numerical data, then we present four subsections. In the first, we investigate the impact of the returned products percentage, \(p\), on the optimal stock capacity for new products, \(S_{A}\)*, and reconditioned products, \(S_{A}\)*. This study analyzes the impact of the quantity of returned worn products on the manufacturing, reconditioning, and stocking decisions. In the second, we examine the influence of the period of mandatory carbon regulation (W) on the optimal stock capacity for new products, \(S_{A}\)*, reconditioned products, \(S_{A}\)*, and the percentage of the returned products, \(p\)*. This study allows a firm leader to determine the optimal production and stocking planning when the mandatory carbon period changes. In the third, we analyze the influence of the limited quantity of carbon emission imposed by the government on optimal values \(S_{A}\)*, \(S_{A}\)*, and \(p\)*. This study proposes the optimal stocking management when the government imposes a quantity limit of carbon emissions. In the fourth, we analyze the impact of the carbon emission cost imposed by the government on optimal values \(S_{A}\)*, \(S_{A}\)*, and \(p\)*. The used input data are:  
* The time simulation, \(T=10^{7}\) periods
* The life cycle of new product, \(\alpha=100\) periods The carbon emission quantity for producing new products, \(q_{pm}=100\) carbon units
* The carbon emission quantity for producing reconditioned products, \(q_{pr}=10\) carbon units
* The quantity limit of carbon emission, \(q_{l}=1000\) carbon units
* The unit carbon emission cost, \(ct=0.01\) monetary unit (for example, dollars or euros)
* The maximum production rate, \(U_{A}=2500\) products/period
* The maximum production rate, \(U_{Ar}=2300\) products/period
* The unit selling price for new products, \(cv_{A}=400\) monetary units
* The unit selling price for reconditioned products, \(cv_{Ar}=180\) monetary units
* The unit storage cost for new products, \(cs_{A}=0.0005\) monetary units
* The unit storage cost for reconditioned products, \(cs_{Ar}=0.0005\) monetary units
* The unit lost sales cost for new products, \(cp_{A}=1200\) monetary unit
* The unit lost sales cost for reconditioned products, \(cp_{Ar}=875\) monetary units
* The unit production cost of new products, \(cu_{A}=50\) monetary unit
* The unit production cost of reconditioned products, \(cu_{Ar}\) = 20 monetary unit
* The unit storage cost for returned product \(cr\) = 0.0003 monetary unit. The demand \(d_{A}(t)\) is generated by truncated normal distribution, in which the average = 15 and the standard deviation = 7. For \(d_{Ar}(t)\), the average = 7 and the standard deviation = 4. The generation of time to repair and time between failures are exponentially distributed. The occurrence of the period of carbon emission limit and length of the period denoted (\(W\)) are generated by truncated normal distribution. For length of the period \(W\), the lower truncated is 40 and the upper truncated is 60, with the average = 50 and standard deviation = 10, and for the occurrence of the period, the upper truncated is 4100 and the lower truncated is 3900, and the standard deviation = 100. As shown in Table 2, the total profit is, at the first time, proportional to the percentage of returned products. Then, as the percentage of returned products increases, the profit again decreases and leads to losses. Indeed, it is observed that we have an optimum when \(p\) is equal to 50%. This is explained by the fact that when \(p\) increases, the number of worn products returned, \(R(t)\), increases and replenishes the recovery inventory.