## 4 Numerical Results
### Optimal Ordered Date of Used/End-of-Life Product and Release Dates Plan of Components at Level 2  
To calculate the optimal ordered date of used/end-of-life product and the vector of release dates for components at level 2, we implement a genetic algorithm with a simulation method. These components at level 2 must be ordered following the destruction of certain components after the disassembly process. The algorithm is implemented within JAVA language to resolve \(EC[[T_{PR},X]]\). Figure 6 illustrates the proposed algorithm. Indeed, the choice of the genetic algorithm is decided upon from its widespread use to solve discrete optimization problems, which proves that it is among the most used algorithms [34] considering that is a relevant, accurate and fast algorithm. The objective of using the classical simulation method is to evaluate all possible values of the decision variables one by one. Indeed, our search space for the decision variable \(T_{PR}\) is very reasonable, which helps us to calculate the total expected cost for each value, whereas the decision vector \(X=\left\{X_{j,2}\right\},\ j\in N_{2}\) depends on \(T_{PR}\) and other deterministic and stochastic parameters of the system, which seems impossible to list all the possible combinations of the vector. This vector depends too on the number of components to be ordered. Therefore, as indicated in the flowchart of Figure 6, we initialize at first the set of optimal solutions founded for each value of \(T_{PR}\). Then, we generate a random vector that represents the state of each component of the disassembled product. As mentioned above in Figure 5, the proposed product consists of 10 parts at level 2, so among its components, we have remanufacturable and unremanufacturable parts. Then, we apply the genetic algorithm steps (selection, crossing, mutation) to find the best vector \(X=\left\{X_{j,2}\right\}\). The parameters of the genetic algorithms are noted in Figure 6. In the second step, to calculate the optimal number of preventive maintenance actions, we implement the mathematical function \(C_{M}\) within the \"Wolfram Mathematica\" tool.  
The results found are shown in tables below (Tables 7 and 8). In Table 7, the disassembly process is not considered; all components of level 2 are ordered from suppliers (external resources). On the other hand, Table 8 shows results of the proposed model. The number of remanufactured components is generated randomly. As shown, the vector of dates of new components ordered from external suppliers consists of five dates, which proves that the disassembly of the used/end-of-life product has given us five remanufacturable components. Indeed, the optimal ordered date of the used/end-of-life product founded with the proposed algorithm is given in the table. We also observe the difference between costs, which proves the advantage of integrating the disassembly and remanufacturing process.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \(j\) & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline \(Ca_{j}\) & 20 & 10 & 12 & 21 & 36 & 17 & 16 & 11 & 30 & 32 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The purchasing cost of components at level 2.  
Figure 6: Flowchart of the proposed algorithm.