## 4 Experimental Results
In step 2 and step 3, the \(S_{j}\) and \(P_{j}\) range values indicated in Table 1 are maintained. Also, for each job \(j\), \(d_{j}\) is determined using the random integer value from the closed interval from the corresponding range values given by Table 1. We then proceed to the final step. 4. After randomly determining the resource allocations made based on Table 1 (i.e., after generating random integers from the closed intervals of \(|\mathbf{Q}|\), \(U_{\mathbf{Q}}\), \(K_{\mathbf{Q}}\) in a similar process to step 1), the values of NC, RF, and RS of the network are determined. The additional arcs are further added randomly in the network to reach a desired NC, and resource allocations for each job are further tuned to achieve the needed combination value. For J9001, NC \(=1.50\), RF \(=0.25\), and RS \(=0.20\) must be achieved by tuning the number of arcs and resource values. Readers may refer \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & \multicolumn{4}{c}{**Levels**} \\ \hline NC & 1.50 & 1.80 & 2.10 & \\ \hline RF & 0.25 & 0.50 & 0.75 & 1.00 \\ \hline RS & 0.20 & 0.50 & 0.70 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Variable parameter setting for ProGen. to [70] for simple formulas to calculate these values and a detailed description of the parameters and their realizations. This process (i.e., steps 1-4) was computed using ProGen software as it is computationally expensive. In addition, in this study, to meet the practicality of the data, two additional values (i.e., cost and income) were determined. The monetary cost of executing each activity is determined as follows:  
\[C_{i}:=\frac{d_{i}\!\sum\boldsymbol{q}_{i}}{\sum_{k=1}^{J}d_{k}\!\sum \boldsymbol{q}_{k}}\times 100 \tag{13}\]  
In Equation (13), \(d_{i}\) and \(\boldsymbol{q}_{i}\) have the same meanings as defined in Equations (1) and (2). For each project, we randomly select a set of three, four, five, and six activities as events. For each set of events, we assign an income from performing these activities to random positive numbers such that the total income always comes to 100. (Files containing detailed information regarding each income for each event for all projects can be downloaded along with the dataset and associated results using the link provided at the end of this paper). Using just cost and incomes in this setting has no reward for a contractor as the sum of costs equals the income without taking into account the time value of money. To reward a contractor, a final settlement of \(C_{J+1}\) is computed using Equation (14):  
\[C_{J+1}:=\frac{30\times\mathrm{J}}{|\mathrm{E}|} \tag{14}\]  
where \(|\mathrm{E}|\) denotes the total number of events or jobs that generate income for the contractor, in our case, \(|\mathrm{E}|\in\{3,4,5,6\}\). The client pays the contractor without any delay whenever the contractor executes activities specified in the event set. In this study, we set \(|\Theta|\!=\!2(J-|\boldsymbol{C}\cup\boldsymbol{A}|)\) where \(C\) and \(A\) denote the completed and active jobs, respectively. That is, \(|\Theta|=2\) when the state is \(S_{0}\) and \(|\Theta|=0\) when the state is \(S_{F}\), and \(|\Theta|\) decreases linearly as a function of the state \(S_{v}\). The numerical experiment is designed to investigate the effectiveness of six different models developed in this study. These models include: 1. ADP with random priority rule, 2. ADP with EDA as priority rule, 3. ADP with ACO as priority rule, 4. ADP-DCS with random priority rule, 5. ADP-DCS with EDA as priority rule, and 6. ADP-DCS with ACO as priority rule. ADP-DCS indicates the improvements made by DCS after the ADP process. The experiments were conducted on an AMD Ryzen Threadripper 3970X 32-core processor, 128 GB RAM machine in the Julia language. We note that a direct comparison between models associated with ADP and ADP-DCS cannot be made as ADP-DCS tries to make improvements on ADP solutions by generating additional schedules.