Operations Research · Unit 5
Network Analysis and Project Management
Exam-focused notes for Network Analysis and Project Management (Operations Research, ORS255): what the TU syllabus asks and how it has actually been tested, with 10 solved past questions from this unit.
What this unit covers
- Network diagram construction
- Activity relationships and predecessors
- Critical path identification
- Critical activities and bottleneck activities
- Slack time and float calculations
- Project completion time estimation
- PERT network diagrams
- Time duration analysis
Critical path identification
Project Network Analysis
The table gives the information about the activities, their predecessors and time duration required to complete the activities of the project. Find the shortest time duration of the project within which the project can be completed.
| Activity | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| Predecessor | - | - | B | B | B | E | A,D,C |
| Time (in days) | 18 | 8 | 14 | 14 | 16 | 10 | 20 |
[5]
Activity Predecessor Duration (days) ---------------------------------------- A - 18 B - 8 C B 14 D B 14 E B 16 F E 10 G A, D, C 20 $EF = ES + \text{Duration}$, and $ES = \max(EF \text{ of predecessors})$ Activity Predecessor ES EF -------------------------...
Full solved answer →Critical Path Analysis
The following activities must be completed to complete the project. Determine the critical path and time duration of the project.
| Activity | Predecessor | Time (in a week) |
|---|---|---|
| A | - | 3 |
| B | - | 8 |
| C | A,B | 4 |
| D | B | 2 |
| E | A | 1 |
| F | C | 7 |
| G | E,F | 5 |
| H | D,F | 6 |
| I | G,H | 8 |
| J | I | 9 |
[5]
Activity Predecessor Duration (weeks) ----------------------------------------- A - 3 B - 8 C A, B 4 D B 2 E A 1 F C 7 G E, F 5 H D, F 6 I G, H 8 J I 9 $ES$ = max of predecessors' $EF$; $EF = ES + \text{duration}$. Activity Dur ES EF -----------------------...
Full solved answer →Network Diagram and Critical Path Analysis
Activity A B C D E F G ------------------------------- Predecessors - A A A B,C C,D E,F Time (days) 7 4 5 6 7 5 6 Logical structure of dependencies: - A starts the project. - B, C, D all follow A. - E follows B and C. - F follows C and D. - G follows E and ...
Full solved answer →Network Diagram and Critical Path Analysis
Activity Predecessor Duration (weeks) ----------------------------------------- A - 5 B - 12 C A 6 D B 3 E A, D 2 F B 6 G C, E, F 14 H G 22 Using $EF = ES + t$ and $ES = \max(EF \text{ of predecessors})$: Activity Dur Predecessor ES EF ---------------------...
Full solved answer →Critical Path Analysis
The following activities must be completed in the order to complete the project. Determine critical path and time duration of the project.
| Activity | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| Predecessor | - | - | A,B | B | A | C | E,F | D,F | G,H | I |
| Time (in week) | 3 | 8 | 4 | 2 | 1 | 7 | 5 | 6 | 8 | 9 |
[5]
Activity Predecessor(s) Duration (weeks) ------------------------------------------- A - 3 B - 8 C A, B 4 D B 2 E A 1 F C 7 G E, F 5 H D, F 6 I G, H 8 J I 9 $EF = ES + \text{Duration}$, and $ES = \max(EF \text{ of predecessors})$. Activity Predecessors ES E...
Full solved answer →Critical Path Analysis
The following activities must be completed in order to complete the project. Determine the critical path and time duration of the project based on slack time of the activity.
| Activity | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| Predecessor | - | - | A, B | B | A | C | E, F | D, F | G, H | I |
| Time (in days) | 3 | 8 | 4 | 2 | 1 | 7 | 5 | 6 | 8 | 9 |
[10]
Activity A B C D E F G H I J ---------------------------------------- Predecessor − − A,B B A C E,F D,F G,H I Duration (days) 3 8 4 2 1 7 5 6 8 9 $ES = \max(EF \text{ of predecessors})$, $EF = ES + \text{Duration}$ Activity Dur ES EF -----------------------...
Full solved answer →PERT network diagrams
Project Completion Time and Variance Analysis
A project consists of nine activities whose time estimates (in weeks) and other characteristics are given below. What is the expected project completion time and its variance?
| Activities | A | B | C | D | E | F | G | H | I |
|---|---|---|---|---|---|---|---|---|---|
| Preceding activities | - | - | - | A | A | B,D | B,D | C,F | E |
| Optimistic time | 2 | 6 | 6 | 2 | 11 | 8 | 3 | 9 | 4 |
| Most likely time | 4 | 6 | 12 | 5 | 14 | 10 | 6 | 15 | 10 |
| Pessimistic time | 6 | 6 | 24 | 8 | 23 | 12 | 9 | 27 | 16 |
[5]
Activity Predecessors $to$ $tm$ $tp$ -------------------------------------------- A - 2 4 6 B - 6 6 6 C - 6 12 24 D A 2 5 8 E A 11 14 23 F B, D 8 10 12 G B, D 3 6 9 H C, F 9 15 27 I E 4 10 16 $$te = \frac{to + 4tm + tp}{6}, \qquad \sigma^2 = \left(\frac{tp ...
Full solved answer →PERT Network Analysis Problem
A project consists of nine activities whose time estimates (in weeks) and other characteristics are given below:
| Activities | A | B | C | D | E | F | G | H | I |
|---|---|---|---|---|---|---|---|---|---|
| Preceding activities | - | - | - | A | A | B, D | B, D | C, F | E |
| Optimistic time | 2 | 6 | 6 | 2 | 11 | 8 | 3 | 9 | 4 |
| Most likely time | 4 | 6 | 12 | 5 | 14 | 10 | 6 | 15 | 10 |
| Pessimistic time | 6 | 6 | 24 | 8 | 23 | 12 | 9 | 27 | 16 |
(a) Show the PERT network diagram for the project.
(b) Identify the critical activities.
(c) What is the expected project completing time and its variance?
[10]
Activity Predecessors a (opt) m (likely) b (pess) ------------------------------------------------------ A - 2 4 6 B - 6 6 6 C - 6 12 24 D A 2 5 8 E A 11 14 23 F B, D 8 10 12 G B, D 3 6 9 H C, F 9 15 27 I E 4 10 16 Note: Activities G and I have no successor...
Full solved answer →Network diagram construction
Network Diagram Project
The following activities must be completed in order to complete the project. Draw network diagram to reflect the inter relationship between activities of the project.
| Activity | P | Q | R | S | T | U | V | W | X |
|---|---|---|---|---|---|---|---|---|---|
| Predecessor | - | - | P, Q | Q | P | R | T, U | S, U | V, W |
[5]
To draw the network diagram, I need to identify the precedence relationships and create nodes and arrows showing the sequence of activities. Activity Predecessor Dependencies ------------------------------------- P - Start (no predecessor) Q - Start (no pre...
Full solved answer →A work project consists of twelve activities labeled through L. Upon being asked to specify the order in which the jobs had to be done, the manager answered as follows: A, B, and C are the first activities of the project and can start simultaneously and immediately; A and B precede D while B precede E, F and H. Activities F and C precede G while E and H precede I and J. The activities C, D, F and J precede K which, in turn, precedes L. Further I, G and L are the terminal activities of the project. Draw a network diagram corresponding to the project. [5]
From the manager's specifications: Activity Predecessors ------------------------ A None (start) B None (start) C None (start) D A, B E B F B G F, C H B I E, H J E, H K C, D, F, J L K Terminal activities: I, G, L Level 0 (Start): A, B, C Level 1: D (from A,...
Full solved answer →Make Unit 5 stick
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