Project Management

(Part Two)

Harry Kogetsidis

School of Business

Lecture’s topics

• What is project crashing?
• How can we reduce the expected

completion time of a project?

Critical Path Method (CPM)

A simple network-based method which can
estimate how long a project will take and

which

activities are

critical

for its on time

completion.

Expected duration of a project

Once the expected completion time of a

project

has been estimated, it may be necessary or
desirable to try to reduce it.

This would normally imply an extra cost.

Expected duration of a project

Project managers should therefore decide

whether

to use extra resources in order to reduce the
expected completion time of a project.

time/cost trade-of

Project crashing

Project crashing

is the process of reducing

the

expected completion time of a project.

Project crashing

Some points to remember:
• Reducing the expected completion time of a

project will involve shortening a number of its
activities.

• Shortening activities would normally imply a

cost.

• There might be some activities that cannot be

shortened.

Project crashing

Some points to remember:
• The activities to be shortened must be on the

critical path.

• The process of project crashing could create

more critical paths.

Example

Activity Preceding activity Duration

A

-

5

B

-

4

C

A

2

D

C

4

E

B

5

F

B

5

G

B,C 4

H

F

3

CPM network

CPM network

Solution

• Expected project completion time: 12 weeks.

• Critical path: B-F-H

.

• Critical activities: B, F and H

.

slack = 0

• Non-critical activities: A, C, D, E, and G

.

slack =

1

slack = 3

slack = 1 slack = 1 slack = 1

Example (continued)

Activity Normal

Crash Normal Crash

time time cost cost

A

5

4 3000 3300

B

4

3 2100 2450

C

2

1 3250 4000

D

4

4 2200 2200

E

5

3 3400 3900

F

5

2 2800 3400

G

4

3 3000 3650

H

3

1 6000 7500

Bonus ofered

There is a bonus of

€500

if the project is completed in 11

weeks.

What should the project manager do?

Example (continued)

Activity Normal

Crash Normal Crash

Max

time Crash

time time cost cost

reduction

cost/wk

A

5

4 3000 3300

B

4

3 2100 2450

C

2

1 3250 4000

D

4

4 2200 2200

E

5

3 3400 3900

F

5

2 2800 3400

G

4

3 3000 3650

H

3

1 6000 7500

Maximum time reduction

Max. time reduction = normal time – crash

time

(1)

Crash Cost

crash cost – normal cost

Crash cost / week = -----------------------------------

(2)

max. time reduction

Paths in the project

• ACD

5 + 2 + 4 = 11 wks

• ACG

5 + 2 + 4 = 11 wks

• BG

4 + 4 = 8 wks

• BFH

4 + 5 + 3 =12 wks

critical path

• BE

4 + 5 = 9 wks

Example (continued)

Activity Normal

Crash Normal Crash

Max

time Crash

time time cost cost

reduction

cost/wk

A

5

4 3000 3300

1

300

B

4

3 2100 2450

1

350

x

C

2

1 3250 4000

1

750

D

4

4 2200 2200

0

-

E

5

3 3400 3900

2

250

F

5 4 2 2800 3400

3 2 200

x

G

4

3 3000 3650

1

650

H

3

1 6000 7500

2

750

x

Conclusion

• Shorten activity F by one week at a cost of

€200

.

Bonus =

€500

go for the bonus!

Total cost =

€200

Second Bonus ofered

There is another bonus of

€1000

if the project is

completed in

10 weeks.

What should the project manager do?

Paths in the project

• ACD

5 + 2 + 4 = 11 wks

critical path

• ACG

5 + 2 + 4 = 11 wks

critical path

• BG

4 + 4 = 8 wks

• BFH

4 + 5 4 + 3 =11 wks

critical path

• BE

4 + 5 = 9 wks

Example (continued)

Activity Normal

Crash Normal Crash

Max

time Crash

time time cost cost

reduction

cost/wk

A

5 4 4 3000 3300

1 0 300

#

!

B

4

3 2100 2450

1

350

x

C

2

1 3250 4000

1

750

#

!

D

4

4 2200 2200

0

-

#

E

5

3 3400 3900

2

250

F

5 4 3

2 2800 3400

3 2 1

200

x

G

4

3 3000 3650

1

650

!

H

3

1 6000 7500

2

750

x

Conclusion

• Shorten activity F by one week at a cost of

€200

.

• Shorten activity A by one week at a cost of

€300

.

Bonus =

€1000

go for the bonus!

Total cost =

€500

Problem 1

Activity Preceding activity Duration

A

-

3

B

-

6

C

A

2

D

B,C

5

E

D

4

F

E

3

G

B,C

9

H

F,G

3

Problem 1 (continued)

Activity Normal

Crash Normal Crash

time time cost cost

A

3

2 200 250

B

6

4 400 440

C

2

2 400 400

D

5

4 750 850

E

4

3 600 680

F

3

3 460 460

G

9

7 450 520

H

3

3 500 500

Problem 1 (continued)

There is a bonus of

€100

if the project completion time is

reduced by one week.

There is another bonus of

€100

if the project completion time

is

reduced by a second week.

There is a third bonus of

€100

if the project completion time is

reduced by a third week.

What should the project manager do?

Problem 2

Activity Preceding activity

A

-

B

-

C

-

D

B

E

D

F

A

G

A

H

E,C

I

F

J

G,H

Problem 2 (continued)

Activity Normal

Crash Normal Crash

time time cost cost

A

12

11 150 200

B

8

7 200 250

C

14

12 250 300

D

4

2 250 350

E

1

1 400 400

F

12

12 350 350

G

9

7 450 500

H

8

6 400 450

I

3

1 450

500

J

7

5 400 480

Problem 2 (continued)

There is a bonus of

€75

if the project completion time is

reduced by one week.

There is another bonus of

€75

if the project completion

time is

reduced by a second week.

What should the project manager do?

Problem 3

Activity Preceding activity

A

-

B

-

C

-

D

A

E

B

F

B

G

C

H

F,G

I

D

J

D

K

E,I

L

K,H

M

L

Problem 3 (continued)

Activity Normal

Crash Normal Crash

time time cost cost

A

3

2 750 550

B

4

2 600 200

C

3

3 300 300

D

3

2 400 250

E

4

4 400 400

F

3

3 350 350

G

3

2 450 300

H

2

1 400 250

I

4

2 450

250

J

6

4 400 100

K

1

1 550

550

L

1

1 650 650

M

1

1 400 400

Problem 3 (continued)

There is a bonus of

€250

if the project completion time is

reduced by two weeks.

What should the project manager do?