Asked by Himani Patel on Jul 01, 2024
Verified
Consider the network described in the table below.
Activity Immediate Predecessor(s) Pessimistic Probable Optimistic J −−15108 K −−987 L J 1065 M J 333 N K, M 951 O K, M 1074 P L, N 1083\begin{array} { | c | c | c | c | c | } \hline \text { Activity } & \begin{array} { c } \text { Immediate } \\\text { Predecessor(s) }\end{array} & \text { Pessimistic } & \text { Probable } & \text { Optimistic } \\\hline \text { J } & - - & 15 & 10 & 8 \\\hline \text { K } & - - & 9 & 8 & 7 \\\hline \text { L } & \text { J } & 10 & 6 & 5 \\\hline \text { M } & \text { J } & 3 & 3 & 3 \\\hline \text { N } & \text { K, M } & 9 & 5 & 1 \\\hline \text { O } & \text { K, M } & 10 & 7 & 4 \\\hline \text { P } & \text { L, N } & 10 & 8 & 3 \\\hline\end{array} Activity J K L M N O P Immediate Predecessor(s) −−−− J J K, M K, M L, N Pessimistic 15910391010 Probable 10863578 Optimistic 8753143 a. Calculate the expected duration of each activity.
b. Calculate the expected duration and variance of the critical path.
c. Calculate the probability that the project will be completed in fewer than 30 time units.
Expected Duration
The estimated time needed to complete a project or task, often considering various uncertainties or risk factors.
Critical Path
A continuity of necessary tasks in a project's agenda that have to be accomplished on time for the project to meet its proposed finalization date.
Pessimistic
An attitude or perspective that tends to see the worst aspect of things or believe that the worst will happen.
- Acquire knowledge of the core concepts and numerical procedures pertinent to the PERT methodology, such as computing expected time, variance, and pinpointing critical pathways.
- Execute variance analysis to determine the potential risks to the project schedule.
- Determine the chance of finalizing a project in the allocated time period through the application of standard deviation and variance.
Verified Answer
GB
Gabin Burgun7 days ago
Final Answer :
(a) See table below.
(b) Tasks J-M-N-P are critical. The sum of their expected durations is 26.00; the sum of their variances is 4.50.
(c) The standard deviation along the path is = 2.12; the probability that Duration < 30 is the probability that z < (30 - 26.00)/2.12 = 1.89. The associated normal curve area is 0.97062.
Task Early Start Early Finish Late Start Late Finish Slack Mean Variance J010.5010.5010.51.361111K085.513.55.58L10.51719.52696.5M10.513.510.513.5030N13.518.513.518.5051.777778O13.520.519265.57P18.52618.52607.51.361111 Project 26 Project 4.5 Std.dev 2.12132\begin{array}{|c|c|c|c|c|c|c|c|}\hline\text { Task } & \begin{array}{c}\text { Early } \\\text { Start }\end{array} & \begin{array}{c}\text { Early } \\\text { Finish }\end{array} & \begin{array}{c}\text { Late } \\\text { Start }\end{array} & \begin{array}{c}\text { Late } \\\text { Finish }\end{array} & \text { Slack } & \text { Mean } & \text { Variance } \\\hline \mathrm{J} & 0 & 10.5 & 0 & 10.5 & 0 & 10.5 & 1.361111 \\\hline \mathrm{K} & 0 & 8 & 5.5 & 13.5 & 5.5 & 8 & \\\hline \mathrm{L} & 10.5 & 17 & 19.5 & 26 & 9 & 6.5 & \\\hline \mathrm{M} & 10.5 & 13.5 & 10.5 & 13.5 & 0 & 3 & 0 \\\hline \mathrm{N} & 13.5 & 18.5 & 13.5 & 18.5 & 0 & 5 & 1.777778 \\\hline \mathrm{O} & 13.5 & 20.5 & 19 & 26 & 5.5 & 7 & \\\hline \mathrm{P} & 18.5 & 26 & 18.5 & 26 & 0 & 7.5 & 1.361111\\\hline &\text { Project } & 26 & & & & \text { Project } & 4.5 \\\hline & & & & & & \text { Std.dev } & 2.12132\\\hline\end{array} Task JKLMNOP Early Start 0010.510.513.513.518.5 Project Early Finish 10.581713.518.520.52626 Late Start 05.519.510.513.51918.5 Late Finish 10.513.52613.518.52626 Slack 05.59005.50 Mean 10.586.53577.5 Project Std.dev Variance 1.36111101.7777781.3611114.52.12132
(b) Tasks J-M-N-P are critical. The sum of their expected durations is 26.00; the sum of their variances is 4.50.
(c) The standard deviation along the path is = 2.12; the probability that Duration < 30 is the probability that z < (30 - 26.00)/2.12 = 1.89. The associated normal curve area is 0.97062.
Task Early Start Early Finish Late Start Late Finish Slack Mean Variance J010.5010.5010.51.361111K085.513.55.58L10.51719.52696.5M10.513.510.513.5030N13.518.513.518.5051.777778O13.520.519265.57P18.52618.52607.51.361111 Project 26 Project 4.5 Std.dev 2.12132\begin{array}{|c|c|c|c|c|c|c|c|}\hline\text { Task } & \begin{array}{c}\text { Early } \\\text { Start }\end{array} & \begin{array}{c}\text { Early } \\\text { Finish }\end{array} & \begin{array}{c}\text { Late } \\\text { Start }\end{array} & \begin{array}{c}\text { Late } \\\text { Finish }\end{array} & \text { Slack } & \text { Mean } & \text { Variance } \\\hline \mathrm{J} & 0 & 10.5 & 0 & 10.5 & 0 & 10.5 & 1.361111 \\\hline \mathrm{K} & 0 & 8 & 5.5 & 13.5 & 5.5 & 8 & \\\hline \mathrm{L} & 10.5 & 17 & 19.5 & 26 & 9 & 6.5 & \\\hline \mathrm{M} & 10.5 & 13.5 & 10.5 & 13.5 & 0 & 3 & 0 \\\hline \mathrm{N} & 13.5 & 18.5 & 13.5 & 18.5 & 0 & 5 & 1.777778 \\\hline \mathrm{O} & 13.5 & 20.5 & 19 & 26 & 5.5 & 7 & \\\hline \mathrm{P} & 18.5 & 26 & 18.5 & 26 & 0 & 7.5 & 1.361111\\\hline &\text { Project } & 26 & & & & \text { Project } & 4.5 \\\hline & & & & & & \text { Std.dev } & 2.12132\\\hline\end{array} Task JKLMNOP Early Start 0010.510.513.513.518.5 Project Early Finish 10.581713.518.520.52626 Late Start 05.519.510.513.51918.5 Late Finish 10.513.52613.518.52626 Slack 05.59005.50 Mean 10.586.53577.5 Project Std.dev Variance 1.36111101.7777781.3611114.52.12132
Learning Objectives
- Acquire knowledge of the core concepts and numerical procedures pertinent to the PERT methodology, such as computing expected time, variance, and pinpointing critical pathways.
- Execute variance analysis to determine the potential risks to the project schedule.
- Determine the chance of finalizing a project in the allocated time period through the application of standard deviation and variance.