## 5 Analysis of Simulation Experiments
Therefore, it was reasonable to replicate every experiment scenario 15 times, stockpiling 6 million goods in the second storage facility. The values assumed by parameters of the experimental setup are listed in Table 3. Considering the table's notation, \(X_{\alpha}^{coef}\) and \(X_{\beta}^{coef}\) are the product manufacturing and storing cost coefficients, \(X_{\gamma}^{coef}\), \(X_{\delta_{p}}^{coef}\) and \(X_{e}^{coef}\) are the relative cost coefficients related to raw materials, maintenance, and repair, \(X_{\zeta}^{coef}\), \(X_{\gamma}^{coef}\) denote the coefficients of remanufacturing and refurbishing costs, \(K_{\alpha}^{coef}\), \(K_{\beta}^{coef}\), and \(K_{\gamma}^{coef}\) represent coefficients of profits procured after selling standard products, remanufactured, and refurbished goods. Finally, \(F_{\alpha}^{coef}\) is the fee coefficient relevant to returned items. Finally, the experimental analysis presented in later sections compares different versions of the presented mechanism. The implemented mechanism versions are: (a) RL(EK-CBM), (b) RL(EK-CM), (c) RL(EK-PM), (d) RL(BS-PM), (e) RL(BS-CM), (f) RL(BS-CBM), (g) RL(\((s,S)\)-CBM), (h) RL(\((s,S)\)-PM), (i) RL(\((s,S)\)-CM), (j) RL(KANBAN-CBM), (k) RL(KANBAN-PM), (l) RL(KANBAN-CM), (m) RL(CBM), (n) RL(PM), (o) RL(CM), (p) RL(R-Learning). Table 4 disseminates the ad hoc production and maintenance policies that are integrated in the RL-based mechanisms, excluding RL(R-Learning). Using these policies, the RL agent initiates production and maintenance in the system according to (2) and (3). RL(CBM), RL(PM), RL(CM), and RL(R-Learning) were adapted from the approaches presented in [26; 60; 66]. Elaborately, as presented in [26; 66], RL(R-Learning) integrates a single R-Learning-based agent for the joint control optimization of single-stage production systems. Similarly, RL(CBM), RL(PM), and RL(CM) employ one agent for deriving policies. This agent follows the RL-based decision-making approach [60], which involved ad hoc production policies instead of maintenance ones. Given the above, the behavior of RL(CBM), RL(PM), RL(CM), and RL(R-Learning) was accordingly adjusted for the purposes of the present study. Note, in the following figures, that each illustrated quantity is associated with its respective unit. Analytically, the average inventory is measured in parts; the average event rates (e.g., \(\mu^{p}\)) are measured in time units; the obtained revenues and costs are associated with monetary units; the simulation scenarios are dimensionless. For readability reasons, these units, except for \"parts\", are abbreviated, and the following notation is utilized: \"t.u.\" denotes time unit, \"m.u.\" represents monetary unit, and \"d.u.\" refers to dimensionless unity. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**Facility** & \(S_{\text{max}}\) & \(X_{\alpha}^{coef}\) & \(X_{\beta}^{coef}\) & \(X_{\gamma}^{coef}\) & \(X_{\delta_{p}}^{coef}\) & \(X_{e}^{coef}\) & \(X_{\zeta}^{coef}\) & \(X_{\gamma}^{coef}\) & \(X_{\gamma}^{coef}\) & \(F_{\alpha}^{coef}\) & \(K_{\alpha}^{coef}\) & \(K_{\beta}^{coef}\) & \(K_{\gamma}^{coef}\) & \(\gamma\) & \(\beta\) & \(e\) \\ \hline
1 & 500 & 12.5 & 6.5 & - & 6.5 & 6.5 & 8.5 & - & - & - & - & - & 0.005 & 0.005 & 0.1 \\ \hline
2 & 1050 & 12.5 & 6.5 & 7 & 6.5 & 6.5 & 8.5 & 8.5 & 40.5 & 110 & 60 & 40 & 0.05 & 0.005 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameter setup.