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Projects: Critical Paths. Dr. Ron Lembke Operations Management. PERT & CPM. Network techniques Developed in 1950’s CPM by DuPont for chemical plants PERT by U.S. Navy for Polaris missile Consider precedence relationships & interdependencies Each uses a different estimate of activity times.

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projects critical paths

Projects:Critical Paths

Dr. Ron Lembke

Operations Management

pert cpm
PERT & CPM
  • Network techniques
  • Developed in 1950’s
    • CPM by DuPont for chemical plants
    • PERT by U.S. Navy for Polaris missile
  • Consider precedence relationships & interdependencies
  • Each uses a different estimate of activity times
questions answered by pert cpm
Questions Answered by PERT & CPM
  • Completion date?
  • On schedule? Within budget?
  • Probability of completing by ...?
  • Critical activities?
  • Enough resources available?
  • How can the project be finished early at the least cost?
pert cpm steps
PERT & CPM Steps
  • Identify activities
  • Determine sequence
  • Create network
  • Determine activity times
  • Find critical path
    • Earliest & latest start times
    • Earliest & latest finish times
    • Slack
activity on node aon

1

2

3

Activity on Node (AoN)

Project: Obtain a college degree (B.S.)

Receive diploma

Attend class, study etc.

Enroll

1 month

4? Years

1 day

activity on arc aoa

1

2

3

4

Activity on Arc (AoA)

Project: Obtain a college degree (B.S.)

Attend class, study, etc.

Receive diploma

Enroll

1 month

4,5 ? Years

1 day

aoa nodes have meaning

1

2

3

4

AoA Nodes have meaning

Project: Obtain a college degree (B.S.)

GraduatingSenior

Applicant

Student

Alum

liberal arts sidebar
Liberal Arts Sidebar
  • Alum = ?

Alumnus

Alumna

Alumni

Alumnae

Alumni

network example
Network Example

You’re a project manager for Bechtel. Construct the network.

Activity Predecessors A --B A C AD B E BF C G DH E, F

network example aoa

7

2

9

5

1

3

6

8

Network Example - AOA

G

D

B

E

A

H

C

F

4

aoa diagrams

2

2

3

1

5

3

1

4

4

AOA Diagrams

A precedes B and C, B and C precede D

B

A

D

C

B

A

C

D

Add a phantom arc for clarity.

critical path analysis
Critical Path Analysis
  • Provides activity information
    • Earliest (ES) & latest (LS) start
    • Earliest (EF) & latest (LF) finish
    • Slack (S): Allowable delay
  • Identifies critical path
    • Longest path in network
    • Shortest time project can be completed
    • Any delay on activities delays project
    • Activities have 0 slack
network solution
Network Solution

B

D

E

A

G

2

6

3

1

1

C

F

3

4

earliest start finish steps
Earliest Start & Finish Steps
  • Begin at starting event & work forward
  • ES = 0 for starting activities
    • ES is earliest start
  • EF = ES + Activity time
    • EF is earliest finish
  • ES = Maximum EF of all predecessors for non-starting activities
activity a earliest start solution

B

D

E

A

G

2

6

3

1

1

C

F

3

4

Activity A Earliest Start Solution

For starting activities, ES = 0.

latest start finish steps
Latest Start & Finish Steps
  • Begin at ending event & work backward
  • LF = Maximum EF for ending activities
    • LF is latest finish; EF is earliest finish
  • LS = LF - Activity time
    • LS is latest start
  • LF = Minimum LS of all successors for non-ending activities
critical path

B

D

E

A

G

2

6

3

1

1

C

F

3

4

Critical Path
new notation
New notation
  • Compute ES, EF for each activity, Left to Right
  • Compute, LF, LS, Right to Left

ES EF

C 7

LS LF

exhibit 6
Exhibit 6

F 8

C 7

A 21

G 2

B 5

D 2

E 5

exhibit 61
Exhibit 6

21 28

28 36

F 8

C 7

0 21

36 38

A 21

G 2

28 33

21 26

26 28

B 5

D 2

E 5

F cannot start until C and D are done.

G cannot start until both E and F are done.

exhibit 62
Exhibit 6

21 28

28 36

F 8

C 7

21 28

28 36

0 21

36 38

A 21

G 2

0 21

36 38

28 33

21 26

26 28

B 5

D 2

E 5

21 26

26 28

31 36

E just has to be done in time for G to start at 36, so it has slack.

D has to be done in time for F to go at 28, so it has no slack.

gantt chart es
Gantt Chart - ES

A

C

B

D

E

F

G

0 5 10 15 20 25 30 35 40

solved problem 2
Solved Problem 2

B4

E6

G7

C3

A 1

I4

F2

D7

H9

solved problem 21
Solved Problem 2

1 5

511

B4

E6

1118

1 5

511

G7

1118

1 4

0 1

1822

C3

A 1

I4

6 9

0 1

810

1822

F2

1 8

911

817

D7

H9

2 9

918

summary
Summary
  • Activity on Node representation
  • Calculated
    • ES, EF for all activities
    • LS, LF for all activities (working backwards)
    • Slack for each activity
  • Identified critical path(s)