Student Information

Name: Khaled Ibrahim Alzahhar

Course: Quantitative Business Analysis

Assignment: EX2 - PERT and CPM Analysis

Supervised by: Dr. Sayed El-Khouly

Project Management Network Analysis: PERT and CPM

Interactive tool to calculate project completion probabilities and guaranteed dates using Program Evaluation and Review Technique (PERT)

How to Use This Tool

This tool calculates project completion probabilities based on activity time estimates. You can edit the values in the Activity Time Estimates table and click "Update Calculations" to see new results.

Step-by-Step Solution

1
Calculate estimated time (te) for each activity using the formula:
te = (O + 4M + P) / 6
2
Calculate variance for each activity using the formula:
Variance = [(P - O) / 6]²
3
Determine the critical path (longest path through the network):
Critical Path: 1 → 2 → 6 → 7
4
Calculate total expected time (TE) and total variance (V) for the critical path:
TE = 10 + 7 + 4 = 21 weeks
V = 1.00 + 4.00 + 1.00 = 6.00
5
Calculate standard deviation (σ) for the critical path:
σ = √V = √6.00 ≈ 2.45 weeks
6
Calculate Z-scores for desired completion times:
Z = (T - TE) / σ
For 14 weeks: Z = (14 - 21) / 2.45 ≈ -2.86
For 17 weeks: Z = (17 - 21) / 2.45 ≈ -1.63
7
Find probabilities using standard normal distribution table:
P(14 weeks) = P(Z ≤ -2.86) ≈ 0.0021 or 0.21%
P(17 weeks) = P(Z ≤ -1.63) ≈ 0.0516 or 5.16%
8
Find completion time for 80% probability:
Z for 80% = 0.84
T = TE + Z × σ = 21 + 0.84 × 2.45 ≈ 23.06 weeks

Answers to QBA EX2 Questions

a) Probability of finishing the project in 14 weeks and 17 weeks

After calculating the estimated times and critical path, we find:

b) Guaranteed date for 80% certainty

To be 80% sure that the project will be completed by a guaranteed date, we need to find the date corresponding to a probability of 0.8.

The Z-score for 80% probability is 0.84.

Using the formula: T = TE + Z × σ = 21 + (0.84 × 2.45) ≈ 23.06 weeks

Therefore, management should quote 23.06 weeks to be 80% sure of project completion.

Activity Time Estimates (Weeks) - Editable

Activity Optimistic (O) Most Likely (M) Pessimistic (P)
1-2
1-3
1-4
2-6
3-6
3-7
3-5
4-5
5-7
6-7

Calculate Completion Probability

Results

Expected Project Duration: 21 weeks

Standard Deviation: 2.45 weeks

Probability of completion by desired date: -

PERT Calculations

Estimated Activity Times (te)

te = (O + 4M + P) / 6

Activity te (weeks) Variance

Critical Path Analysis

Critical Path: 1 → 2 → 6 → 7

Total Expected Time: 21 weeks

Total Variance: 6.00

Calculate Guaranteed Completion Date

Results

Guaranteed completion date: -

Project Network Diagram

graph LR 1((1)) -->|10| 2((2)) 1 -->|10| 3((3)) 1 -->|5| 4((4)) 2 -->|7| 6((6)) 3 -->|5| 6 3 -->|7| 7((7)) 3 -->|2| 5((5)) 4 -->|5| 5 5 -->|8| 7 6 -->|4| 7 style 1 fill:#3498db,color:white style 2 fill:#3498db,color:white style 3 fill:#3498db,color:white style 4 fill:#3498db,color:white style 5 fill:#3498db,color:white style 6 fill:#3498db,color:white style 7 fill:#3498db,color:white