PERT / CPM

PERT / CPM or Network Analysis

CPM Critical Path Method Developed in 1957 by Du Pont First used in the construction of a new chemical

plant PERT Program Evaluation Review

Technique Developed in 1958 by Navy Used in the POLARIS missile program

Planning, Scheduling & Control Useful for project management

How long will it take to complete? What are the critical task that can delay the

completion? How long can certain task be prolonged before

becoming critical?

Network Implementation Define project and all significant activities or

tasks with single start and stop times. Develop the relationships between tasks. Draw the network with single start and end. Assign time or cost for each task. Compute the longest path through the

network. This is the critical path. Use network to plan, schedule and manage

project.

Useful Questions Building the Network

Is this a start activity? Is it a finish activity? Which activity precedes this one? Which activity follows it? Which activity is concurrent?

Drawing the Network Network begins with a single event and ends

with a single event. Each activity is represented by an arrow. Events are represented by circles and

precede and follow each activity. Consecutive activities must be separated by

events. No pair of events can be directly connected

by more than one activity without intervening events.

Parallel Paths Require Event

Rules for Network Construction (continued)

If an activity R precedes several otherwise unrelated activities S & T, then they must be separate by event.

If several otherwise unrelated activities R & S both precede activity T, then they must be separate by event.

Example

RS

TR

S

T

Dummy Activities Some precedence relations will require one

or more dummy activities. Dummy activities have 0 duration and are

represented by dashed arrows. Contribute to number of alternate paths but

not duration. Example:

A precedes D A and B precede E B and C precede F

Dummy Activity Example

A

B

C

D

E

F

Example Network Table

Activity Duration Preceded ByA 3B 3 AC 4D 1 CE 3 B, DF 2 A, B, DG 2 C, FH 4 GI 1 CJ 3 E, GK 5 F, H, I

CPM Example Network

A

B E

J

C

D

I

F

G

H K

3

3

4

1

3

2

1

24

3

5

Example: Alternate Paths

Path LengthA-B-E-J 12

A-B-F-G-dummy-J 13A-B-F-G-H-K 19

C-D-E-J 11C-D-F-G-dummy-J 12

C-D-F-G-H-K 18C-I-K 10

Path LengthA-B-E-J 12

A-B-F-G-dummy-J 13A-B-F-G-H-K 19

C-D-E-J 11C-D-F-G-dummy-J 12

C-D-F-G-H-K 18C-I-K 10

CPM Example NetworkCritical Path

A

B E

J

C

D

I

F

G

H K

3

3

4

1

3

2

1

24

3

5

Alternate Paths Evaluation alternative paths relative to critical

path Earlist Start (ES) for each activity trace forward

from start to beginning of the activity. When several paths exist use longest.

Latest Start (LS) for each activity trace backwards from project end to tail of each activity. When several paths exist use longest. Subtract from critical path time.

Total Float (TL): TL = LS ES

CPM Example Network

A

B E

J

C

D

I

F

G

H K

3

3

4

1

3

2

1

24

3

5

F: ES=3+3=6; LS=19-(5+4+2+2)=6; TF=0

CPM Example Network Table

Activity Duration ES LS TFA 3 0 0 0B 3 3 3 0C 4 0 1 1D 1 4 5 1E 3 6 13 7F 2 6 6 0G 2 8 8 0H 4 10 10 0I 1 4 13 9J 3 10 16 6K 5 14 14 0

Project Duration =19

PERT Program Evaluation and Review Technique

Allows uncertainity to be included in activity times

Assume a Beta probability distribution Defined with three parameters:

ts shortest time to accomplish activity

tl longest time to complete activity

tm most likely time

Expected duration; te = ( ts + 4tm + tl ) / 6 Standard deviation; = (tl ts) / 6

PERT Example Network

A

B E

J

C

D

I

F

G

H K

1-3-5

2-3-4

3-4-101-1-5

2-3-6

1-2-7

0-1-3

1-2-43-4-6

1-3-6

3-5-12

PERT Example Network TableActivity Expected Time Variance ES LS TF

A 3.00 0.44 0.00 0.50 0.50B 3.00 0.11 3.00 3.50 0.50C 4.83 1.36 0.00 1.00 0.00D 1.67 0.44 4.83 4.83 0.00E 3.33 0.44 6.50 14.84 8.34F 2.67 1.00 6.50 6.50 0.00G 2.17 0.25 9.17 9.17 0.00H 4.17 0.25 11.34 11.34 0.00I 1.17 0.25 4.83 14.34 9.51J 3.17 0.69 11.34 18.17 6.83K 5.83 2.25 15.51 15.51 0.00

Project Duration = 21.34