1. Project Management: PERT/CPM
Chapter 9
Project Management: PERT/CPM

2. Project Planning & Scheduling
Projects consist of numerous separate jobs
Managers schedule/coordinate activities for on time completion of the project
Interdependence of activities make this difficult
Answer questions such as:
Total time to complete the project
Start and finish dates
Critical activities
Delay of noncritical activities before they become critical

3. Elements Of Project Planning
Define project objective(s)
Identify activities
Establish precedence relationships
Make time estimates
Determine project completion time
Compare project schedule objectives
Determine resource requirements to meet objective 5

4. Project Scheduling What to do? Critical Path Method (CPM)
DuPont & Remington-Rand (1956)
deterministic task times
activity-on-node network construction (AON)
Project Evaluation & Review Technique (PERT)
U.S. Navy, Booz, Allen & Hamilton
multiple task time estimates (probabilistic)
activity-on-arrow network construction (AOA)

5. PERT/CPM Develop a network model Determine activity times
Uncertain times use an estimating method
Certain times use CPM
Analyze Network
Find critical path
Variability
Time/Cost Trade offs

6. Networks and PERT/CPM Network analysis Simple PERT analysis
Shortest route problem
Minimal spanning tree
Maximum flow Algorithm
Simple PERT analysis
Finding critical path using CPM
Sensitivity analysis
critical/gating activities
time/cost tradeoffs

7. PERT/CPM CPM Shortest Route problem Minimal Spanning Tree Maximal Flow
minimizes the distance from an origin to a destination
Minimal Spanning Tree
most economical way to find a connecting route
transportation networks
computer/communication networks
distribution networks
Maximal Flow
problems involving restrictions on flow between nodes

8. Monitoring & Gantt Charts
Popular tool for project scheduling
Graph with bar for representing the time for each task
Provides visual display of project schedule
shows both planned and completed activities against a time scale
Shows slack for activities
(amount of time activity can be delayed without delaying project) 7

9. A Gantt Chart 4 10 6 8 3 1 5 7 9 Month Activity 2 Design house and4 10 6 8 3 1 5 7 9
Month
Activity
Design house and
obtain financing
Lay foundation
Order and receive
Materials
Build house
Select paint
Select carpet
Finish work 8

10. Critical Path
A path is a sequence of connected activities running from the start to the end node in a network
The critical path is the path with the longest duration in the network
A project cannot be completed in less than the time of the critical path 13

11. Network Construction
In AON, nodes represent activities & arrows show precedence relationships
In AOA, arrows represent activities & nodes are events for points in time
An event is the completion or beginning of an activity
A dummy shows precedence for two activities with same start & end nodes 11

12. Precedence Table Job Precedence Time 1 Contact Client - 4 2
Write Proposal 3
Obtain Approval
Complete Programming 12 5
Complete Industry Review 10 6
Write Final Draft
4, 5 7
Complete Oral Report 11

13. Project Network/Precedence Diagram
Complete Industry Review
Complete Oral Report 5 7
Complete Programming
Write Proposal 1 2 4 6
Contact Client 3
Write Final Draft
Obtain Approval 12

14. Early Start Times ES - earliest time activity can start
Forward pass starts at beginning of network to determine ES times
EF = ES + activity time
ESj = maximum (EF)
EFi = ESi + ti
ES1 = 0
EF1 = ES1 + t1 = = 4 days 16

15. Computing Early Times ES2 = max (EF1) = 4 days
EF2 = ES2 + t2 = = 6 days
EF3 = ES3 + t3 = = 9 days
EF4 = ES4 + t4 = = 21 days 17

16. Earliest Start Times Table
Job ES EF 1
Contact Client 4 2
Write Proposal 6 3
Obtain Approval 9
Complete Programming 21 5
Complete Industry Review 10
Write Final Draft 27 7
Complete Oral Report 26 11

17. Late Times LS - latest time activity can start & not delay project
Backward pass starts at end of network to determine LS times
LF - latest time activity can be completed & not delay project
LSi = LFi - ti
LFi = minimum (LS) 18

18. Computing Late Times LF7 = 27 days LS67 = LF7 - t6 = 27 - 5 = 22 days
LF5 = minimum (LS6, LS7) = min(21,22) = 21 days
LS5 = LF5 - t5 = = 11 days 19

19. Latest Start Times Table
Job LS LF 1
Contact Client 4 2
Write Proposal 6 3
Obtain Approval 9
Complete Programming 21 5
Complete Industry Review 11
Write Final Draft 27 7
Complete Oral Report 22 11

20. Activity Slack Activities on critical path
ES = LS
EF = LF
slack = 0
Activities not on critical path have slack
Si = LSi - ESi or Si = LFi - EFi
S5 = LS5 - ES5 = = 11 days
S7 = LS7 - ES7 = = 1 day 21

21. 1--->2--->3--->4--->6
The Critical Path
The critical path is the path with the longest duration in the network
A project cannot be completed in less than the time of the critical path
Therefore,
1--->2--->3--->4--->6
is the critical path for the project 13

22. Project Crashing
Shorten durations of critical tasks by adding more resources ($) or changing task scope
Crashing refers to analyzing the tradeoff of compressing the duration of tasks versus cost to compress those tasks
Managers use this technique to balance project time constraints with project budget constraints