## 4 Materials and Methods
### Proposed SMSRS Model
#### 4.1.2 Integrating the SRA Model with MSRS  
This section explains the integration of the SRA model with the MSRS algorithm. To integrate the SRA with the MSRS algorithm, the stochastic activity durations obtained from the SRA model were used as input for the computational steps involved in the integration as described below:  
1. Determine project duration, start and finish times of each activity \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Activity** & **Pred.** & \(a\) & \(m\) & \(b\) & \begin{tabular}{c} **Rand** \\ **(0-1)** \\ \end{tabular} & \
\begin{tabular}{c} **Random** \\ **Duration** \\ \end{tabular} &
\begin{tabular}{c} **Average** \\ **Duration** \\ \end{tabular} & **Distribution** \\ \hline A & - & 2 & 3 & 5 & 0.25 & 2.86 & 3.31 & _Triangular_ \\ B & - & 3 & 4 & 6 & 0.07 & 3.44 & 4.27 & _Triangular_ \\ C & - & 4 & 5 & 8 & 0.68 & 6.05 & 5.71 & _Triangular_ \\ D & A & 1 & 2 & 3 & 0.24 & 1.69 & 1.93 & _Triangular_ \\ E & A & 2 & 3 & 5 & 0.76 & 3.81 & 3.32 & _Triangular_ \\ F & B & 3 & 4 & 6 & 0.97 & 5.54 & 4.33 & _Triangular_ \\ G & D.F & 2 & 3 & 5 & 0.55 & 3.29 & 3.28 & _Triangular_ \\ H & C & 5 & 6 & 9 & 0.01 & 5.24 & 6.65 & _Triangular_ \\ I & C & 3 & 4 & 6 & 0.38 & 4.07 & 4.32 & _Triangular_ \\ J & E,H & 2 & 3 & 5 & 0.62 & 3.36 & 3.33 & _Triangular_ \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of SRA for project A. The project duration, start and finish times based on the stochastic durations of each activity were computed using the forward and backward pass approach with the aid of Microsoft excel using Equations (2a)-(2d). The result is shown in Table 4.  
\(EST_{i}=\) MAX (IF (ISERR (FIND (activity range, 1 st pred. ))), 0, EFT range)) (2a) \[EFT_{i}=EST_{i}+Duration_{i}\] (2b) \[LFT_{i}=\) MIN (IF (ISERR (FIND (1 st activity, pred. range)), MAX (EFT range), LST range)) (2c) \[LST_{i}=LFT_{i}-Duration_{i}\] (2d)  
where Pred., EST, EFT, LST, and LFT are predecessor, early start time, early finish time, late start time, and late finish time of each activity. (ii) Schedule each activity  
Each activity was scheduled accordingly using the stochastic activity durations. MSRS algorithm was adopted at the instances of resource conflicts based on the resource substitution rule of the project in Table 2. After scheduling all the activities considering the resource constraints the project duration was 19.49 days as shown in Table 5. This duration is the expected project duration considering risk and uncertainty and resource constraints. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Activity** & **Pred.** & **Duration** & **EST** & **EFT** & **LST** & **LFT** & **Slack** \\ \hline A & - & 3.31 & 0 & 3.31 & 5.73 & 9.04 & 5.73 \\ B & - & 4.27 & 0 & 4.27 & 3.81 & 8.08 & 3.81 \\ C & - & 5.71 & 0 & 5.71 & 0 & 5.71 & 0 \\ D & A & 1.93 & 3.31 & 5.24 & 10.48 & 12.41 & 7.17 \\ E & A & 3.32 & 3.31 & 6.63 & 9.04 & 12.36 & 5.73 \\ F & B & 4.33 & 4.27 & 8.6 & 8.08 & 12.41 & 3.81 \\ G & D,F & 3.28 & 8.6 & 11.88 & 12.41 & 15.69 & 3.81 \\ H & C & 6.65 & 5.71 & 12.36 & 5.71 & 12.36 & 0 \\ I & C & 4.32 & 5.71 & 10.03 & 11.37 & 15.69 & 5.66 \\ J & E,H & 3.33 & 12.36 & 15.69 & 12.36 & 15.69 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of the forward and backward pass for the stochastic durations.