PERT / CPM

A Simple Project

Activity ImmediatePredecessor

ExpectedTime

A - 5

B - 6

C A 4

D A, B 2

Project Network

Activity ImmediatePredecessor

ExpectedTime

A - 5

B - 6

C A 4

D A, B 2

ES Earliest Starting (time)

EF Earliest Finishing

LS Latest Starting

LF Latest Finishing

Slack Extra Time

Earliest Starting/Finishing Times

EF = ES + t

LS = LF - t

a optimistic time

m most likely time

b pessimistic time

t = E(T) expected time = (a + 4m + b)/6

V(T) variance = (b - a)2/36

What if activity times are variable?

Activity TimeExpected Value and Variance

a m b t V(T)

A 4 5 6 5 4/36

B 4 5 12 6 64/36

C 1 4 7 4 36/36

D 1 2 3 2 4/36

Possible Paths and Statistics

Path E(T) = t V(T)

A - C 9 * 40/36

A - D 7 8/36

B - D 8 68/36

• What is the probability that the project takes at

least 10 days?

• What is the probability that the project takes less

than 7 days?

P t P z P z( )/

( . ) . . .

1010 9

40 360 95 0 5 0 3289 0 1711

P t P z P z( )/

( . ) . . .

77 9

40 361 90 0 5 0 4713 0 0287