Exercise $2$: Project Bid Analysis Using PERT Method

Bill Fredlund, president of Lincoln Log Construction, is considering placing a bid on a building project. Bill has determined that five tasks would need to be performed to carry out the project. Using the PERT three$-$estimate approach, he has obtained the following estimates for task durations along with their precedence relationships:Optimistic Estimate $(\backslash (\backslash$mathrm$\{$t$\}\_\{0\}\backslash ))$Most Likely Estimate $(\backslash (\backslash$mathbf$\{$t$\}\_\{\backslash$mathbf$\{$m$\}\}\backslash ))$Pessimistic Estimate $(\backslash (\backslash$mathrm$\{$t$\}\_\{\backslash$mathrm$\{$p$\}\}\backslash ))$

If the project is not completed within $\backslash (\backslash$mathbf$\{11\}\backslash )$ weeks, there is a penalty of $\backslash (\backslash$mathbf$\{\backslash$$ $500,000\}\backslash ).$ Therefore, Bill is very interested in determining the likelihood that his company can complete the project in time.

$($a$)$ Construct the project network for this project.

$($b$)$ Compute the expected duration and variance for each activity.

$($c$)$ Find the critical path.

$($d$)$ Determine the probability that the project will be completed within $11$ weeks.

$($e$)$ Bill needs to decide whether to bid based on financial considerations. If the project is completed within $11$ weeks, the company would make $\backslash (\backslash$mathbf$\{\backslash$$ $250,000\}\backslash ).$ However, if the project takes longer, they would lose $\backslash (\backslash$mathbf$\{\backslash$$ $250,000\}\backslash )$ due to the penalty. Should Bill bid on the project if he wants at least a $\backslash (\backslash$mathbf$\{50\backslash \%\}\backslash )$ chance of meeting the deadline?