This document describes the process of time-cost tradeoff analysis to minimize the total cost of a project. It involves shortening the duration of critical project activities by paying extra money according to each activity's crash rate or slope. The process begins with creating an activity-on-node network using normal activity durations. It then iteratively selects the cheapest critical activity to crash based on crash rates, updates the network, and identifies the next critical path to determine if further crashing is needed to shorten the project duration. The objective is to determine the combination of critical activities to crash that results in the minimum total project cost.

1. Time-Cost Tradeoff by Examples
INTRODUCTION
1
Chachrist Srisuwanrat
ชาคริต ศรีสุวรรณรัตน์

2. 2
YouTube

3. What is Time-Cost Tradeoff ?
• It is the Exchange between “Time” and “Money”
Introduction to Time-Cost Tradeoff
DirectCost
Project
Duration
76543
500k
600k
700k
800k
900k
1,000k
1,100k
1,200k
1,300k
1,400k
400k
1,500k
1,600k
Cost
(Project Duration) (Cost)
Pay Extra Money to shorten the project
3

4. What is Time-Cost Tradeoff ?
• It is the Exchange between “Time” and “Money”
What is its Objective?
• Find Minimum Total Cost
Introduction to Time-Cost Tradeoff
DirectCost
Total Cost
Project
Duration
76543
500k
600k
700k
800k
900k
1,000k
1,100k
1,200k
1,300k
1,400k
400k
1,500k
1,600k
Cost
(Project Duration) (Cost)
Pay Extra Money to shorten the project
4

5. What is Time-Cost Tradeoff ?
• It is the Exchange between “Time” and “Money”
What is its Objective?
• Find Minimum Total Cost
About Total Cost:
• Total Cost = Direct + Indirect
• Direct Cost: labor, materials, equipment, …
• Indirect Cost : managers, safety, accountants, parking, …
Introduction to Time-Cost Tradeoff
DirectCost
450
600
750
900
1,050
Project
Duration
76543
500k
600k
700k
800k
900k
1,000k
1,100k
1,200k
1,300k
1,400k
400k
1,500k
1,600k
Cost
(Project Duration) (Cost)
Total Cost
IndirectCost150k/m
Pay Extra Cost to shorten the project
5

6. Time-Cost Tradeoff by Examples
Shorten Project by Shorten Critical Activities
+Slope
6

7. How much?
• Different activities have different “Extra Cost”, extra money per shorten duration (day, week, or month)
Shorten “Project Duration” by Shorten “Critical Activity Duration”
Project
Duration
76543
500k
600k
700k
800k
900k
1,000k
1,100k
1,200k
1,300k
1,400k
400k
1,500k
1,600k
Cost
Activity
5 – 7 months
700k – 500k
= Cost
Duration
Normal Duration (ND)
Normal Cost (NC)
Crash Duration (CD)
Crash Cost (NC)
Extra cost/duration = +Slope
500 Direct Cost
7

8. How much?
• Different activities have different “Extra Cost”, extra money per shorten duration (day, week, or month)
Shorten “Project Duration” by Shorten “Critical Activity Duration”
Project
Duration
76543
500k
600k
700k
800k
900k
1,000k
1,100k
1,200k
1,300k
1,400k
400k
1,500k
1,600k
Cost
= Cost
Duration Normal Duration – Crash Duration
Crash Cost – Normal Cost= ND - CD
CC - NC=
Activity
5 – 7 months
700k – 500k
Normal Duration (ND)
Normal Cost (NC)
Crash Duration (CD)
Crash Cost (NC)
Extra cost/duration = +Slope
500 Direct Cost
8

9. How much?
• Different activities have different “Extra Cost”, extra money per shorten duration (day, week, or month)
Shorten “Project Duration” by Shorten “Critical Activity Duration”
Project
Duration
76543
500k
600k
700k
800k
900k
1,000k
1,100k
1,200k
1,300k
1,400k
400k
1,500k
1,600k
Cost
Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
Activity 5 7 700 500 ?
ND - CD
CC - NC 700 - 500
7 - 5
+100 k/m= =+Slope =
Normal Duration – Crash Duration
Crash Cost – Normal Cost== Cost
Duration ND - CD
CC - NC=Extra cost/duration = +Slope
500 Direct Cost
Activity
5 – 7 months
700k – 500k
Normal Duration (ND)
Normal Cost (NC)
Crash Duration (CD)
Crash Cost (NC)
9

10. How much?
• Different activities have different “Extra Cost”, extra money per shorten duration (day, week, or month)
Shorten “Project Duration” by Shorten “Critical Activity Duration”
600
Project
Duration
76543
500k
600k
700k
800k
900k
1,000k
1,100k
1,200k
1,300k
1,400k
400k
1,500k
1,600k
Cost
Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
Activity 5 7 700 500 +100 500 Direct Cost
Normal Duration – Crash Duration
Crash Cost – Normal Cost== Cost
Duration
Extra cost/duration = +Slope
+100k/m
ND - CD
CC - NC 700 - 500
7 - 5
+100 k/m= =+Slope =
ND - CD
CC - NC=
Activity
5 – 7 months
700k – 500k
Normal Duration (ND)
Normal Cost (NC)
Crash Duration (CD)
Crash Cost (NC)
10

11. +100k/m
How much?
• Different activities have different “Extra Cost”, extra money per shorten duration (day, week, or month)
Shorten “Project Duration” by Shorten “Critical Activity Duration”
Project
Duration
76543
500k
600k
700k
800k
900k
1,000k
1,100k
1,200k
1,300k
1,400k
400k
1,500k
1,600k
Cost
Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
Activity 5 7 700 500 +100
600
700
+100
500 Direct Cost
Normal Duration – Crash Duration
Crash Cost – Normal Cost== Cost
Duration
DONE !
Extra cost/duration = +Slope
ND - CD
CC - NC 700 - 500
7 - 5
+100 k/m= =+Slope =
ND - CD
CC - NC=
Activity
5 – 7 months
700k – 500k
Normal Duration (ND)
Normal Cost (NC)
Crash Duration (CD)
Crash Cost (NC)
11

12. Time-Cost Tradeoff by Examples
The Process of Shortening Project
12

13. Process of Shortening Project
P0: Use Normal Duration to create AON
A
3 – 4 m
+100k/m
B
2 – 4 m
+50 k/m
C
3 – 5 m
+75 k/m
D
6 – 8 m
+ 150k/m
13
= shorten Critical Activities by +Slope

14. Process of Shortening Project
P0: Use Normal Duration to create AON
A
3 – 4 m
+100k/m
0 4
B
2 – 4 m
+50 k/m
4 8
C
3 – 5 m
+75 k/m
4 9
D
6 – 8 m
+ 150k/m
9 17
4 4
5
8
14
= shorten Critical Activities by +Slope

15. Process of Shortening Project
P0: Use Normal Duration to create AON
P1: Consider spend Extra Money (+Slope) on critical activities
A
3 – 4 m
+100k/m
0 4
B
2 – 4 m
+50 k/m
4 8
C
3 – 5 m
+75 k/m
4 9
D
6 – 8 m
+ 150k/m
9 17
4 4
5
8
Step 1 Choices: A+100, C+75, D+150
15
= shorten Critical Activities by +Slope

16. Process of Shortening Project
P0: Use Normal Duration to create AON
P1: Consider spend Extra Money (+Slope) on critical activities
P2: Choose the cheapest critical activity (minimum slope)
A
3 – 4 m
+100k/m
0 4
B
2 – 4 m
+50 k/m
4 8
C
3 – 5 m
+75 k/m
4 9
D
6 – 8 m
+ 150k/m
9 17
4 4
5
8
Step 1 Choices: A+100, C+75, D+150
Choose: C+75
16
= shorten Critical Activities by +Slope

17. Process of Shortening Project
P0: Use Normal Duration to create AON
P1: Consider spend Extra Money (+Slope) on critical activities
P2: Choose the cheapest critical activity (minimum slope)
P3: Update/check/confirm that the +Slope shortens the project
A
3 – 4 m
+100k/m
0 4
B
2 – 4 m
+50 k/m
4 8
C
3 – 5 m
+75 k/m
4 9
D
6 – 8 m
+ 150k/m
9 17
4 4
5
8
--- 4
--- 8
--- 8 --- 16
Step 1 Choices: A+100, C+75, D+150
Choose: C+75
17
= shorten Critical Activities by +Slope

18. Process of Shortening Project
P0: Use Normal Duration to create AON
P1: Consider spend Extra Money (+Slope) on critical activities
P2: Choose the cheapest critical activity (minimum slope)
P3: Update/check/confirm that the +Slope shortens the project
P4: Update AON, Critical Activities, and Critical Paths
A
3 – 4 m
+100k/m
0 4
B
2 – 4 m
+50 k/m
4 8
C
3 – 5 m
+75 k/m
4 9
D
6 – 8 m
+ 150k/m
9 17
4 4
5
8
--- 4
--- 8
--- 8 --- 16
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
18
= shorten Critical Activities by +Slope

19. Process of Shortening Project
P0: Use Normal Duration to create AON
P1: Consider spend Extra Money (+Slope) on critical activities
P2: Choose the cheapest critical activity (minimum slope)
P3: Update/check/confirm that the +Slope shortens the project
P4: Update AON, Critical Activities, and Critical Paths
A
3 – 4 m
+100k/m
0 4
B
2 – 4 m
+50 k/m
4 8
C
3 – 5 m
+75 k/m
4 9
D
6 – 8 m
+ 150k/m
9 17
4 4
5
8
--- 4
--- 8
--- 8 --- 16
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: B+50
Anothercritical pathA-C-D still pushes the project.
Choices: A+100, B&C+125, D150
19
= shorten Critical Activities by +Slope

20. Process of Shortening Project
P0: Use Normal Duration to create AON
P1: Consider spend Extra Money (+Slope) on critical activities
P2: Choose the cheapest critical activity (minimum slope)
P3: Update/check/confirm that the +Slope shortens the project
P4: Update AON, Critical Activities, and Critical Paths
A
3 – 4 m
+100k/m
0 4
B
2 – 4 m
+50 k/m
4 8
C
3 – 5 m
+75 k/m
4 9
D
6 – 8 m
+ 150k/m
9 17
4 4
5
8
--- 4
--- 8
--- 8 --- 16
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: B+50
Anothercritical pathA-C-D still pushes the project.
Choices: A+100, B&C+125, D150
Choose: A+100
20
= shorten Critical Activities by +Slope

21. Process of Shortening Project
P0: Use Normal Duration to create AON
P1: Consider spend Extra Money (+Slope) on critical activities
P2: Choose the cheapest critical activity (minimum slope)
P3: Update/check/confirm that the +Slope shortens the project
P4: Update AON, Critical Activities, and Critical Paths
A
3 – 4 m
+100k/m
0 4
B
2 – 4 m
+50 k/m
4 8
C
3 – 5 m
+75 k/m
4 9
D
6 – 8 m
+ 150k/m
9 17
4 4
5
8
--- 4
--- 8
--- 8 --- 16
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: B+50
Anothercritical pathA-C-D still pushes the project.
Choices: A+100, B&C+125, D+150
Choose: A+100, Project duration = 15--- 3
--- 3 --- 3 --- 7
--- 3 --- 7
--- 7 --- 15
21
= shorten Critical Activities by +Slope

22. Process of Shortening Project
P0: Use Normal Duration to create AON
P1: Consider spend Extra Money (+Slope) on critical activities
P2: Choose the cheapest critical activity (minimum slope)
P3: Update/check/confirm that the +Slope shortens the project
P4: Update AON, Critical Activities, and Critical Paths
A
3 – 4 m
+100k/m
0 4
B
2 – 4 m
+50 k/m
4 8
C
3 – 5 m
+75 k/m
4 9
D
6 – 8 m
+ 150k/m
9 17
4 4
5
8
--- 4
--- 8
--- 8 --- 16
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: B+50
Anothercritical pathA-C-D still pushes the project.
Choices: A+100, B&C+125, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125
--- 3
--- 3 --- 3 --- 7
--- 3 --- 7
--- 7 --- 15
22
= shorten Critical Activities by +Slope

23. Process of Shortening Project
P0: Use Normal Duration to create AON
P1: Consider spend Extra Money (+Slope) on critical activities
P2: Choose the cheapest critical activity (minimum slope)
P3: Update/check/confirm that the +Slope shortens the project
P4: Update AON, Critical Activities, and Critical Paths
A
3 – 4 m
+100k/m
0 4
B
2 – 4 m
+50 k/m
4 8
C
3 – 5 m
+75 k/m
4 9
D
6 – 8 m
+ 150k/m
9 17
4 4
5
8
--- 4
--- 8
--- 8 --- 16
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: B+50
Anothercritical pathA-C-D still pushes the project.
Choices: A+100, B&C+125, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
--- 3
--- 3 --- 3 --- 7
--- 3 --- 7
--- 7 --- 15
--- 3
--- 3
--- 6
--- 6 --- 14
6
---
23
= shorten Critical Activities by +Slope

24. Process of Shortening Project
P0: Use Normal Duration to create AON
P1: Consider spend Extra Money (+Slope) on critical activities
P2: Choose the cheapest critical activity (minimum slope)
P3: Update/check/confirm that the +Slope shortens the project
P4: Update AON, Critical Activities, and Critical Paths
A
3 – 4 m
+100k/m
0 4
B
2 – 4 m
+50 k/m
4 8
C
3 – 5 m
+75 k/m
4 9
D
6 – 8 m
+ 150k/m
9 17
4 4
5
8
--- 4
--- 8
--- 8 --- 16
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: B+50
Anothercritical pathA-C-D still pushes the project.
Choices: A+100, B&C+125, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
Step 4 Choice: B+50, D+150
Choose: D+150
--- 3
--- 3 --- 3 --- 7
--- 3 --- 7
--- 7 --- 15
--- 3
--- 3
--- 6
--- 6 --- 14
6
---
24
= shorten Critical Activities by +Slope

25. Process of Shortening Project
P0: Use Normal Duration to create AON
P1: Consider spend Extra Money (+Slope) on critical activities
P2: Choose the cheapest critical activity (minimum slope)
P3: Update/check/confirm that the +Slope shortens the project
P4: Update AON, Critical Activities, and Critical Paths
A
3 – 4 m
+100k/m
0 4
B
2 – 4 m
+50 k/m
4 8
C
3 – 5 m
+75 k/m
4 9
D
6 – 8 m
+ 150k/m
9 17
4 4
5
8
--- 4
--- 8
--- 8 --- 16
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: B+50
Anothercritical pathA-C-D still pushes the project.
Choices: A+100, B&C+125, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
Step 4 Choice: B+50, D+150
Choose: D+150, Project duration = 13
--- 3
--- 3 --- 3 --- 7
--- 3 --- 7
--- 7 --- 15
--- 3
--- 3
--- 6
--- 6 --- 14--- 13
--- 7
6
---
25
= shorten Critical Activities by +Slope

26. Process of Shortening Project
P0: Use Normal Duration to create AON
P1: Consider spend Extra Money (+Slope) on critical activities
P2: Choose the cheapest critical activity (minimum slope)
P3: Update/check/confirm that the +Slope shortens the project
P4: Update AON, Critical Activities, and Critical Paths
A
3 – 4 m
+100k/m
0 4
B
2 – 4 m
+50 k/m
4 8
C
3 – 5 m
+75 k/m
4 9
D
6 – 8 m
+ 150k/m
9 17
4 4
5
8
--- 4
--- 8
--- 8 --- 16
--- 3
--- 3 --- 3 --- 7
--- 3 --- 7
--- 7 --- 15
--- 3
--- 3
--- 6
--- 6 --- 14--- 13
--- 7
6
---
Step 5 Choice: B+50, D+150
Choose: D+150
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: B+50
Anothercritical pathA-C-D still pushes the project.
Choices: A+100, B&C+125, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
Step 4 Choice: B+50, D+150
Choose: D+150, Project duration = 13
26
= shorten Critical Activities by +Slope

27. Process of Shortening Project
P0: Use Normal Duration to create AON
P1: Consider spend Extra Money (+Slope) on critical activities
P2: Choose the cheapest critical activity (minimum slope)
P3: Update/check/confirm that the +Slope shortens the project
P4: Update AON, Critical Activities, and Critical Paths
A
3 – 4 m
+100k/m
0 4
B
2 – 4 m
+50 k/m
4 8
C
3 – 5 m
+75 k/m
4 9
D
6 – 8 m
+ 150k/m
9 17
= shorten Critical Activities by +Slope
4 4
5
8
--- 4
--- 8
--- 8 --- 16
--- 3
--- 3 --- 3 --- 7
--- 3 --- 7
--- 7 --- 15
--- 3
--- 3
--- 6
--- 6 --- 14--- 13
--- 7
6
---
Step 5 Choice: B+50, D+150
Choose: D+150, Project duration= 12
12
---
--- 6
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: B+50
Anothercritical pathA-C-D still pushes the project.
Choices: A+100, B&C+125, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
Step 4 Choice: B+50, D+150
Choose: D+150, Project duration = 13
27

28. Time-Cost Tradeoff by Examples
Minimum Total Cost
28

29. Total Cost = Direct Cost + Indirect Cost
A
3 – 4 m
+100k/m
B
2 – 4 m
+50 k/m
C
3 – 5 m
+75 k/m
D
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
29

30. Total Cost = Direct Cost + Indirect Cost
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
Step 4 Choice: B+50, D+150
Choose: D+150, Project duration= 13
Step 5 Choice: B+50, D+150
Choose: D+150, Project duration = 12
A
3 – 4 m
+100k/m
B
2 – 4 m
+50 k/m
C
3 – 5 m
+75 k/m
D
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
30

31. Total Cost = Direct Cost + Indirect Cost
A
3 – 4 m
+100k/m
B
2 – 4 m
+50 k/m
C
3 – 5 m
+75 k/m
D
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
125 x Duration
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
Step 4 Choice: B+50, D+150
Choose: D+150, Project duration= 13
Step 5 Choice: B+50, D+150
Choose: D+150, Project duration = 12
31

32. Total Cost = Direct Cost + Indirect Cost
A
3 – 4 m
+100k/m
B
2 – 4 m
+50 k/m
C
3 – 5 m
+75 k/m
D
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
125 x Duration
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
Step 4 Choice: B+50, D+150
Choose: D+150, Project duration= 13
Step 5 Choice: B+50, D+150
Choose: D+150, Project duration = 12
32

33. Total Cost = Direct Cost + Indirect Cost
A
3 – 4 m
+100k/m
B
2 – 4 m
+50 k/m
C
3 – 5 m
+75 k/m
D
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
125 x Duration
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
Step 4 Choice: B+50, D+150
Choose: D+150, Project duration= 13
Step 5 Choice: B+50, D+150
Choose: D+150, Project duration = 12
33

34. Total Cost = Direct Cost + Indirect Cost
A
3 – 4 m
+100k/m
B
2 – 4 m
+50 k/m
C
3 – 5 m
+75 k/m
D
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
125 x Duration
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
Step 4 Choice: B+50, D+150
Choose: D+150, Project duration= 13
Step 5 Choice: B+50, D+150
Choose: D+150, Project duration = 12
34

35. Total Cost = Direct Cost + Indirect Cost
A
3 – 4 m
+100k/m
B
2 – 4 m
+50 k/m
C
3 – 5 m
+75 k/m
D
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
125 x Duration
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
Step 4 Choice: B+50, D+150
Choose: D+150, Project duration= 13
Step 5 Choice: B+50, D+150
Choose: D+150, Project duration = 12
35

36. Total Cost = Direct Cost + Indirect Cost
A
3 – 4 m
+100k/m
B
2 – 4 m
+50 k/m
C
3 – 5 m
+75 k/m
D
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
Min Total Cost
125 x Duration
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
Step 4 Choice: B+50, D+150
Choose: D+150, Project duration= 13
Step 5 Choice: B+50, D+150
Choose: D+150, Project duration = 12
36

37. Time-Cost Tradeoff by Examples
S-Curve at Min Total Cost
37

38. Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
Step 4 Choice: B+50, D+150
Choose: D+150, Project duration= 13
Step 5 Choice: B+50, D+150
Choose: D+150, Project duration = 12
S-Curve at Min Total Cost
A
4
3 – 4 m
+100k/m
B
4
2 – 4 m
+50 k/m
C
5
3 – 5 m
+75 k/m
D
8
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
38

39. A
4
3 – 4 m
+100k/m
B
4
2 – 4 m
+50 k/m
C
5
3 – 5 m
+75 k/m
D
8
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
--- 4
-------- 375
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
39
S-Curve at Min Total Cost

40. A
4
3 – 4 m
+100k/m
B
4
2 – 4 m
+50 k/m
C
5
3 – 5 m
+75 k/m
D
8
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
--- 4
--- 3
-------- 500
-------- 375
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
40
S-Curve at Min Total Cost

41. A
4
3 – 4 m
+100k/m
B
4
2 – 4 m
+50 k/m
C
5
3 – 5 m
+75 k/m
D
8
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
--- 4
--- 3 --- 3
--- 3
-------- 500
-------- 375-------- 450
-------- 150
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
41
S-Curve at Min Total Cost

42. A
4
3 – 4 m
+100k/m
B
4
2 – 4 m
+50 k/m
C
5
3 – 5 m
+75 k/m
D
8
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
--- 4
--- 3 --- 3
--- 3
-------- 500
-------- 375-------- 450
-------- 150
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
42
S-Curve at Min Total Cost

43. A
4
3 – 4 m
+100k/m
B
4
2 – 4 m
+50 k/m
C
5
3 – 5 m
+75 k/m
D
8
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
--- 4
--- 3 --- 3
--- 3
-------- 500
-------- 375-------- 450
-------- 150
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
43
S-Curve at Min Total Cost

44. A
4
3 – 4 m
+100k/m
B
4
2 – 4 m
+50 k/m
C
5
3 – 5 m
+75 k/m
D
8
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
--- 4
--- 3 --- 3
--- 3
-------- 500
-------- 375-------- 450
-------- 150
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
44
S-Curve at Min Total Cost

45. A
4
3 – 4 m
+100k/m
B
4
2 – 4 m
+50 k/m
C
5
3 – 5 m
+75 k/m
D
8
6 – 8 m
+ 150k/m
400k 100k 300k
300k
Indirect cost= 125 k/m
--- 4
--- 3 --- 3
--- 3
-------- 500
-------- 375-------- 450
-------- 150
Step 1 Choices: A+100, C+75, D+150
Choose: C+75, Project duration = 16
Step 2 Choices: A+100, B+50, C+75, D+150
Choose: A+100, Project duration = 15
Step 3 Choices: B&C+125, D+150
Choose: B&C+125, Project duration= 14
45
S-Curve at Min Total Cost

46. Time-Cost Tradeoff by Examples
Example 1-A: Direct Cost
A B C
Activity Duration Cost
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
Indirect cost= 65 k/m46

47. Example 1-A
A B C
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
47

48. Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
Example 1-A: Calculate +Slope
A B C
+70 k/m +80 k/m + 50 k/m
+70
+80
+50
3 – 4 m 10 – 12 m 6 – 8 m
48

49. Example 1-A: Start with “Normal Duration” for all activities
A B C
+70 k/m +80 k/m + 50 k/m
3 – 4 m 10 – 12 m 6 – 8 m
4 12 8
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
49

50. Example 1-A: Perform CPM
A B C
+70 k/m +80 k/m + 50 k/m
0 4
3 – 4 m 10 – 12 m 6 – 8 m
4 12 8
4 16 16 24
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
50

51. Example 1-A: Identify critical activities and critical path
A B C
+70 k/m +80 k/m + 50 k/m
0 4
3 – 4 m 10 – 12 m 6 – 8 m
4 12 8
4 16 16 24
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
51

52. Example 1-A: Shortening Project = Shortening critical activities
Step 1 Choices: A+70, B+80, C+50
Choose: C+50
A B C
+70 k/m +80 k/m + 50 k/m
0 4
3 – 4 m 10 – 12 m 6 – 8 m
4 12 8
4 16 16 24
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
52

53. Example 1-A: Shortening Project = Shortening critical activities
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
A B C
+70 k/m +80 k/m + 50 k/m
--- 7
0 4
3 – 4 m 10 – 12 m 6 – 8 m
4 12 8
4 16 16 24--- 23
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
53

54. Example 1-A: Shortening Project = Shortening critical activities
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50
A B C
+70 k/m +80 k/m + 50 k/m
--- 7
0 4
3 – 4 m 10 – 12 m 6 – 8 m
4 12 8
4 16 16 24--- 23
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
54

55. Example 1-A: Shortening Project = Shortening critical activities
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
A B C
+70 k/m +80 k/m + 50 k/m
--- 7
0 4
3 – 4 m 10 – 12 m 6 – 8 m
4 12 8
4 16 16 24--- 23
--- 6
--- 22
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
55

56. Example 1-A: Shortening Project = Shortening critical activities
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
Step 3 Choices: A+70, B+80
Choose: A+70
A B C
+70 k/m +80 k/m + 50 k/m
--- 7
0 4
3 – 4 m 10 – 12 m 6 – 8 m
4 12 8
4 16 16 24--- 23
--- 6
--- 22
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
56

57. Example 1-A: Shortening Project = Shortening critical activities
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
Step 3 Choices: A+70, B+80
Choose: A+70, Project duration= 21
A B C
+70 k/m +80 k/m + 50 k/m
--- 7
0 4
3 – 4 m 10 – 12 m 6 – 8 m
4 12 8
4 16 16 24--- 23
--- 6
--- 22
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
--- 3
--- 3 --- 3 --- 15 --- 15 --- 21
57

58. Example 1-A: Shortening Project = Shortening critical activities
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
Step 3 Choices: A+70, B+80
Choose: A+70, Project duration= 21
Step 4 Choices: B+80
Choose: B+80
A B C
+70 k/m +80 k/m + 50 k/m
--- 7
0 4
3 – 4 m 10 – 12 m 6 – 8 m
4 12 8
4 16 16 24--- 23
--- 6
--- 22
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
--- 3
--- 3 --- 3 --- 15 --- 15 --- 21
58

59. Example 1-A: Shortening Project = Shortening critical activities
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
Step 3 Choices: A+70, B+80
Choose: A+70, Project duration= 21
Step 4 Choices: B+80
Choose: B+80, Project duration = 20
A B C
+70 k/m +80 k/m + 50 k/m
--- 7
0 4
3 – 4 m 10 – 12 m 6 – 8 m
4 12 8
4 16 16 24--- 23
--- 6
--- 22
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
--- 3
--- 3 --- 3 --- 15 --- 15 --- 21
--- 11
--- 14
14
---
20
---
59

60. Example 1-A: Shortening Project = Shortening critical activities
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
Step 3 Choices: A+70, B+80
Choose: A+70, Project duration= 21
Step 4 Choices: B+80
Choose: B+80, Project duration = 20
Step 5 Choices: B+80
Choose: B+80
A B C
+70 k/m +80 k/m + 50 k/m
--- 7
0 4
3 – 4 m 10 – 12 m 6 – 8 m
4 12 8
4 16 16 24--- 23
--- 6
--- 22
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
--- 3
--- 3 --- 3 --- 15 --- 15 --- 21
--- 11
--- 14
14
---
20
---
60

61. Example 1-A: Shortening Project = Shortening critical activities
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
Step 3 Choices: A+70, B+80
Choose: A+70, Project duration= 21
Step 4 Choices: B+80
Choose: B+80, Project duration = 20
Step 5 Choices: B+80
Choose: B+80, Project duration = 19
A B C
+70 k/m +80 k/m + 50 k/m
--- 7
0 4
3 – 4 m 10 – 12 m 6 – 8 m
4 12 8
4 16 16 24--- 23
--- 6
--- 22
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
--- 3
--- 3 --- 3 --- 15 --- 15 --- 21
--- 11
--- 14
14
---
20
---
--- 10
--- 13
--- 13 --- 19
61

62. Time-Cost Tradeoff by Examples
Example 1-B: Minimum Total Cost
Indirect cost= 65 k/m62

63. Example 1-B: Minimum Total Cost
400k 300k 500k
A B C
+70 k/m +80 k/m + 50 k/m
3 – 4 m 10 – 12 m 6 – 8 m
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
(Indirectcost = 65 k/m)
Normal Direct Cost = 400 + 300 + 500 = 1,200 k
63

64. Example 1-B: Minimum Total Cost
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
Step 3 Choices: A+70, B+80
Choose: A+70, Project duration= 21
Step 4 Choices: B+80
Choose: B+80, Project duration = 20
Step 5 Choices: B+80
Choose: B+80, Project duration = 19
400k 300k 500k
A B C
+70 k/m +80 k/m + 50 k/m
3 – 4 m 10 – 12 m 6 – 8 m
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
(Indirectcost = 65 k/m)
Normal Direct Cost = 400 + 300 + 500 = 1,200 k
64

65. Example 1-B: Minimum Total Cost
400k 300k 500k
A B C
+70 k/m +80 k/m + 50 k/m
3 – 4 m 10 – 12 m 6 – 8 m
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
(Indirectcost = 65 k/m)
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
Step 3 Choices: A+70, B+80
Choose: A+70, Project duration= 21
Step 4 Choices: B+80
Choose: B+80, Project duration = 20
Step 5 Choices: B+80
Choose: B+80, Project duration = 19
Normal Direct Cost = 400 + 300 + 500 = 1,200 k
65

66. Example 1-B: Minimum Total Cost
400k 300k 500k
A B C
+70 k/m +80 k/m + 50 k/m
3 – 4 m 10 – 12 m 6 – 8 m
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
(Indirectcost = 65 k/m)
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
Step 3 Choices: A+70, B+80
Choose: A+70, Project duration= 21
Step 4 Choices: B+80
Choose: B+80, Project duration = 20
Step 5 Choices: B+80
Choose: B+80, Project duration = 19
Normal Direct Cost = 400 + 300 + 500 = 1,200 k
66

67. Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
Step 3 Choices: A+70, B+80
Choose: A+70, Project duration= 21
Step 4 Choices: B+80
Choose: B+80, Project duration = 20
Step 5 Choices: B+80
Choose: B+80, Project duration = 19
Example 1-B: Minimum Total Cost
400k 300k 500k
A B C
+70 k/m +80 k/m + 50 k/m
3 – 4 m 10 – 12 m 6 – 8 m
Activity Duration Cost +Slope
Crash (CD) Normal(ND) Crash (CC) Normal(NC)
A 3 4 470 400
B 10 12 460 300
C 6 8 600 500
+70
+80
+50
(Indirectcost = 65 k/m)
Normal Direct Cost = 400 + 300 + 500 = 1,200 k
67

68. Example 1-B: Minimum Total Cost
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
400k 300k 500k
A B C
+70 k/m +80 k/m + 50 k/m
3 – 4 m 10 – 12 m 6 – 8 m
Min Total Cost
(Indirectcost = 65 k/m)
68

69. Time-Cost Tradeoff by Examples
Example 1-C: S-Curve at Min Total Cost
69

70. Example 1-C: S-Curve
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
400k 300k 500k
A
4
B
12
C
8
+70 k/m +80 k/m + 50 k/m
3 – 4 m 10 – 12 m 6 – 8 m
(Indirectcost = 65 k/m)
70

71. Example 1-C: S-Curve
400k 300k 500k
A
4
B
12
C
8
+70 k/m +80 k/m + 50 k/m
3 – 4 m 10 – 12 m 6 – 8 m
-------- 550
--- 7
(Indirectcost = 65 k/m)
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
71

72. Example 1-C: S-Curve
400k 300k 500k
A
4
B
12
C
8
+70 k/m +80 k/m + 50 k/m
3 – 4 m 10 – 12 m 6 – 8 m
-------- 550-------- 600
--- 7--- 6
(Indirectcost = 65 k/m)
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
72

73. Example 1-C: S-Curve
400k 300k 500k
A
4
B
12
C
8
+70 k/m +80 k/m + 50 k/m
3 – 4 m 10 – 12 m 6 – 8 m
(Indirectcost = 65 k/m)
-------- 550-------- 600
--- 7--- 6
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
73

74. Example 1-C: S-Curve
400k 300k 500k
A
4
B
12
C
8
+70 k/m +80 k/m + 50 k/m
3 – 4 m 10 – 12 m 6 – 8 m
(Indirectcost = 65 k/m)
-------- 550-------- 600
--- 7--- 6
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
74

75. Example 1-C: S-Curve
400k 300k 500k
A
4
B
12
C
8
+70 k/m +80 k/m + 50 k/m
3 – 4 m 10 – 12 m 6 – 8 m
(Indirectcost = 65 k/m)
-------- 550-------- 600
--- 7--- 6
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
75

76. Example 1-C: S-Curve
400k 300k 500k
A
4
B
12
C
8
+70 k/m +80 k/m + 50 k/m
3 – 4 m 10 – 12 m 6 – 8 m
(Indirectcost = 65 k/m)
-------- 550-------- 600
--- 7--- 6
Step 1 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 23
Step 2 Choices: A+70, B+80, C+50
Choose: C+50, Project duration= 22
76

77. Time-Cost Tradeoff by Examples
Example 2-A: Direct Cost
77

78. B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
Example 2-A
78

79. Example 2-A: Perform CPM
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
13 18
79

80. Example 2-A: Identify critical path and critical activities
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
13 18
80

81. B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
13 18
81
Example 2-A: Direct Cost

82. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
--- 6
13 18
--- 12
12
---
17
---
82

83. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
--- 6
13 18
--- 12
12
---
17
---
83

84. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
--- 6
13 18
--- 12
12
---
17
---
84

85. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
--- 6
13 18
--- 12
12
---
17
---
--- 4
16
---
85

86. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
--- 6
13 18
--- 12
12
---
17
---
--- 4
16
---
86

87. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
--- 6
13 18
--- 12
12
---
17
---
--- 4
16
---
--- 5
5
---
11
---
5
---
11
---
15
---
11
---
87

88. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
--- 6
13 18
--- 12
12
---
17
---
--- 4
16
---
--- 5
5
---
5
---
11
---
11
---
15
---
11
---
88

89. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
--- 6
13 18
--- 12
12
---
17
---
--- 4
16
---
--- 5
5
---
5
---
11
---
11
---
15
---
11
---
89

90. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
--- 6
13 18
--- 12
12
---
17
---
--- 4
16
---
--- 5
5
---
5
---
11
---
11
---
15
---
11
---
90

91. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
--- 6
13 18
--- 12
12
---
17
---
--- 4
16
---
--- 5
5
---
5
---
11
---
11
---
15
---
11
---
91

92. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
--- 6
13 18
--- 12
12
---
17
---
--- 4
16
---
--- 5
5
---
5
---
11
---
11
---
15
---
11
---
92

93. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
--- 6
13 18
--- 12
12
---
17
---
--- 4
16
---
--- 5
5
---
5
---
11
---
11
---
15
---
11
---
93

94. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
--- 6
13 18
--- 12
12
---
17
---
--- 4
16
---
--- 5
5
---
5
---
11
---
11
---
15
---
11
---
94

95. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 6
5 11
6 13
6 12
--- 6
13 18
--- 12
12
---
17
---
--- 4
16
---
--- 5
5
---
5
---
11
---
11
---
15
---
11
---
--- 1
--- 5
--- 10
--- 4
--- 4 --- 10
--- 4 --- 10
10
---
14
---
95

96. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 4
5 10
4 10
4 10
--- 6
10 14
--- 4
--- 1
--- 5
96

97. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
Step 5 Choices: A+155, B&E&F+150,
D&E&F+125
Choose D&E&F+125
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 4
5 10
4 10
4 10
--- 6
10 14
--- 4
--- 1
--- 5
97

98. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
Step 5 Choices: A+155, B&E&F+150,
D&E&F+125
Choose D&E&F+125, Project duration = 13
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 4
5 10
4 10
4 10
--- 6
10 14
--- 4
--- 1
--- 5--- 4
--- 5
--- 5
--- 9
--- 9
--- 9
9
---
13
---
98

99. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
Step 5 Choices: A+155, B&E&F+150,
D&E&F+125
Choose D&E&F+125, Project duration = 14
Step 6 Choices: A+155, B&E&F+150
Choose B&E&F+150
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 4
5 10
4 10
4 10
--- 6
10 14
--- 4
--- 1
--- 5--- 4
--- 5
--- 5
--- 9
--- 9
--- 9
9
---
13
---
99

100. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
Step 5 Choices: A+155, B&E&F+150,
D&E&F+125
Choose D&E&F+125, Project duration = 13
Step 6 Choices: A+155, B&E&F+150,
Choose B&E&F+150, Project duration = 12
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 4
5 10
4 10
4 10
--- 6
10 14
--- 4
--- 1
--- 5--- 4
--- 5
--- 5
--- 9
--- 9
--- 9
9
---
13
------ 4 --- 8
--- 4
--- 1
--- 4
--- 4
--- 8
--- 8
8
---
12
---
100

101. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
Step 5 Choices: A+155, B&E&F+150,
D&E&F+125
Choose D&E&F+125, Project duration = 13
Step 6 Choices: A+155, B&E&F+150,
Choose B&E&F+150, Project duration = 12
Step 7 Choices: A+155
Choose A+155
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 4
5 10
4 10
4 10
--- 6
10 14
--- 4
--- 1
--- 5--- 4
--- 5
--- 5
--- 9
--- 9
--- 9
9
---
13
---
--- 1
--- 4 --- 4 --- 8
--- 4
--- 8
--- 4
--- 8
8
---
12
---
101

102. Example 2-A: Direct Cost
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
--- 2
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
Step 5 Choices: A+155, B&E&F+150,
D&E&F+125
Choose D&E&F+125, Project duration = 13
Step 6 Choices: A+155, B&E&F+150,
Choose B&E&F+150, Project duration = 12
Step 7 Choices: A+155
Choose A+155, Project duration = 11
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
0 3 3 5
3 4
5 10
4 10
4 10
--- 6
10 14
--- 4
--- 1
--- 5--- 4
--- 5
--- 5
--- 9
--- 9
--- 9
9
---
13
---
--- 1
--- 4 --- 4 --- 8
--- 4
--- 8
--- 4
--- 8
8
---
12
---2
---
2
---
3
---
2
---
3
---
3
---
7
---
3
---
7
---
3
---
7
---
7
---
11
---
--- 2
102

103. Time-Cost Tradeoff by Examples
Example 2-B: Minimum Total Cost
103

104. Example 2-B: Minimum Total Cost (Indirectcost = 120 k/m)
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
104

105. Example 2-B: Minimum Total Cost (Indirectcost = 120 k/m)
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
245k 175k
160k
300k 340k
325k
700k
Normal Direct Cost = 245 + 175 + 160 + 300 + 325 + 700 + 340 = 2,245 k
105

106. Example 2-B: Minimum Total Cost (Indirectcost = 120 k/m)
B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
245k 175k
160k
300k 340k
325k
700k
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
Step 5 Choices: A+155, B&E&F+150,
D&E&F+125
Choose D&E&F+125, Project duration = 13
Step 6 Choices: A+155, B&E&F+150,
Choose B&E&F+150, Project duration = 12
Step 7 Choices: A+155
Choose A+155, Project duration = 11
Normal Direct Cost = 245 + 175 + 160 + 300 + 325 + 700 + 340 = 2,245 k
106

107. Example 2-B: Minimum Total Cost (Indirectcost = 120 k/m)
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
Step 5 Choices: A+155, B&E&F+150,
D&E&F+125
Choose D&E&F+125, Project duration = 13
Step 6 Choices: A+155, B&E&F+150,
Choose B&E&F+150, Project duration = 12
Step 7 Choices: A+155
Choose A+155, Project duration = 11107

108. Example 2-B: Minimum Total Cost (Indirectcost = 120 k/m)
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
Step 5 Choices: A+155, B&E&F+150,
D&E&F+125
Choose D&E&F+125, Project duration = 13
Step 6 Choices: A+155, B&E&F+150,
Choose B&E&F+150, Project duration = 12
Step 7 Choices: A+155
Choose A+155, Project duration = 11108

109. Example 2-B: Minimum Total Cost (Indirectcost = 120 k/m)
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
Step 5 Choices: A+155, B&E&F+150,
D&E&F+125
Choose D&E&F+125, Project duration = 13
Step 6 Choices: A+155, B&E&F+150,
Choose B&E&F+150, Project duration = 12
Step 7 Choices: A+155
Choose A+155, Project duration = 11109

110. Example 2-B: Minimum Total Cost (Indirectcost = 120 k/m)
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
Step 5 Choices: A+155, B&E&F+150,
D&E&F+125
Choose D&E&F+125, Project duration = 13
Step 6 Choices: A+155, B&E&F+150,
Choose B&E&F+150, Project duration = 12
Step 7 Choices: A+155
Choose A+155, Project duration = 11
Min Total Cost
110

111. Time-Cost Tradeoff by Examples
Example 2-C: S-Curve at Min Total Cost
111

112. Example 2-C: S-Curve (Indirectcost = 120 k/m)
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
Step 5 Choices: A+155, B&E&F+150,
D&E&F+125
Choose D&E&F+125, Project duration = 13
Step 6 Choices: A+155, B&E&F+150,
Choose B&E&F+150, Project duration = 12
Step 7 Choices: A+155
Choose A+155, Project duration = 11
Min Total Cost
112

113. B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
245k 175k
160k
300k 340k
325k
700k
Example 2-C: S-Curve (Indirectcost = 120 k/m)
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
Step 5 Choices: A+155, B&E&F+150,
D&E&F+125
Choose D&E&F+125, Project duration = 13
Step 6 Choices: A+155, B&E&F+150,
Choose B&E&F+150, Project duration = 12
Step 7 Choices: A+155
Choose A+155, Project duration = 11113

114. B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
245k 175k
160k
300k 340k
325k
700k
Example 2-C: S-Curve (Indirectcost = 120 k/m)
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
--- 6
--------- 350
114

115. B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
245k 175k
160k
300k 340k
325k
700k
Example 2-C: S-Curve (Indirectcost = 120 k/m)
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
--- 6
--------- 350
--- 4
--------- 400
115

116. B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
245k 175k
160k
300k 340k
325k
700k
Example 2-C: S-Curve (Indirectcost = 120 k/m)
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
--- 6
--------- 350
--- 4
--------- 400
--- 2
--------- 230
116

117. B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
245k 175k
160k
300k 340k
325k
700k
Example 2-C: S-Curve (Indirectcost = 120 k/m)
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
--- 6
--------- 350
--- 4
--------- 400
--- 2
--------- 230
--- 1
--------- 300
--- 5
--------- 350
117

118. B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
245k 175k
160k
300k 340k
325k
700k
Example 2-C: S-Curve (Indirectcost = 120 k/m)
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
--- 6
--------- 350
--- 4
--------- 400
--- 2
--------- 230
--- 1
--------- 300
--- 5
--------- 350
0 3 3 5 5 10
3 4 4 10
4 10
10 14
118

119. B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
245k 175k
160k
300k 340k
325k
700k
Example 2-C: S-Curve (Indirectcost = 120 k/m)
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
--- 6
--------- 350
--- 4
--------- 400
--- 2
--------- 230
--- 1
--------- 300
--- 5
--------- 350
0 3 3 5 5 10
3 4 4 10
4 10
10 14
119

120. B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
245k 175k
160k
300k 340k
325k
700k
Example 2-C: S-Curve (Indirectcost = 120 k/m)
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
--- 6
--------- 350
--- 4
--------- 400
--- 2
--------- 230
--- 1
--------- 300
--- 5
--------- 350
0 3 3 5 5 10
3 4 4 10
4 10
10 14
120

121. B
2
+75 k/m
A
3
+155 k/m
2 – 3 m 1 – 2 m
D
6
+50 k/m
4 – 6 m
C
3
+70 k/m
1 – 3 m
F
6
+50 k/m
2 – 6 m
E
7
+25 k/m
3 – 7 m
G
5
+60 k/m
4 – 5 m
245k 175k
160k
300k 340k
325k
700k
Example 2-C: S-Curve (Indirectcost = 120 k/m)
Step 1 Choices: A+155, C+70, E+25, G+60
Choose: E+25, Project duration = 17
Step 2 Choices: A+155, C+70, E&F+75, G+60
Choose: G+60, Project duration= 16
Step 3 Choices: A+155, C+70, E&F+75
Choose: C+70, Project duration = 15
Step 4 Choices: A+155, B&C+145, D&C+120,
B&E&F+150, D&E&F+125
Choose D&C+120, Project duration = 14
--- 6
--------- 350
--- 4
--------- 400
--- 2
--------- 230
--- 1
--------- 300
--- 5
--------- 350
0 3 3 5 5 10
3 4 4 10
4 10
10 14
121

122. Example 2-C: S-Curve
122
(Indirectcost = 120 k/m)

123. Time-Cost Tradeoff by Examples
Example 2-D: Excel Solver
123

124. Time-Cost Tradeoff by Examples
Example 2-D: Activate Excel Solver
124

125. Check if there is “Solver” button
If not, go to File menu
125

126. Select “Options”
126

127. 127

128. Select “Add-ins”, and choose “Excel Add-ins”, then click “Go…”
1
2
3
128

129. Check “Solver Add-in” checkbox, and click “OK” button
4
5
129

130. Finish activating “Solver”
130

131. The “Solver”
131

132. The “Solver”
Actual Duration (AD)2. Variables
AD >= CD
AD <= ND
AD must be “Integer”.
Project Duration= …
3. Constraints
1. Objective: Minimize… Project Direct Cost
132

133. Time-Cost Tradeoff by Examples
Example 2-D: Let’s Start
133

134. Create table, add initial data, and calculate +Slope if necessary
+Slope = (Crash Cost – Normal Cost)
(Normal Duration – Crash Duration)
134

135. Setup Columns for Actual Duration & Actual Cost
+Slope = (Crash Cost – Normal Cost)
(Normal Duration – Crash Duration)
Actual Cost = Normal Cost +Slope x (Normal Duration – Actual Duration)
Actual Duration could be any number between “Crash” and “Normal” durations.
Variables in Solver
135

136. Add Formula for CPM: ESD and EFD
+Slope = (Crash Cost – Normal Cost)
(Normal Duration – Crash Duration)
Actual Cost = Normal Cost +Slope x (Normal Duration – Actual Duration)
Actual Duration could be any number between “Crash” and “Normal” durations.
Variables in Solver
136

137. Find the Normal and Crash Durations of the Project
Normal Duration of the Project = 18
Crash Duration of the Project = 11
Therefore, we will analyze the project
between 11 to 18 months.
137

138. Create a table for Total Cost = Direct + Indirect
138

139. Activate Solver by going to “Data” menu -> Solver
139

140. Set Objective, Variables, and Constraints in Excel Solver
1. Objective: Minimize Actual Direct Cost
140

141. Set Objective, Variables, and Constraints in Excel Solver
2. Variables
1. Objective: Minimize Actual Direct Cost
141

142. Set Objective, Variables, and Constraints in Excel Solver
2. Variables
1. Objective: Minimize Actual Direct Cost
3. Constraints:
Actual duration<= ND
Actual duration must be “Integer”
Actual duration >= CD
Project duration= 18
142

143. Set Objective, Variables, and Constraints in Excel Solver
2. Variables
1. Objective: Minimize Actual Direct Cost
3. Constraints:
Actual duration<= ND
Actual duration must be “Integer”
Actual duration >= CD
Project duration= 18
143

144. Set Objective, Variables, and Constraints in Excel Solver
2. Variables
1. Objective: Minimize Actual Direct Cost
3. Constraints:
Actual duration<= ND
Actual duration must be “Integer”
Actual duration >= CD
Project duration= 18
144

145. Set Objective, Variables, and Constraints in Excel Solver
2. Variables
4. Click “Solve” button
1. Objective: Minimize Actual Direct Cost
3. Constraints:
Actual duration<= ND
Actual duration must be “Integer”
Actual duration >= CD
Project duration= 18
145

146. Manually type the Cost in the table after finish solving
Click “OK” button
And type in the number.
146

147. Change “Constraint of Project Duration” to the next one, 17
Constraints
Actual duration<= ND
Actual duration must be “Integer”
Actual duration >= CD
Project duration= 17
1. Select the constraint
and click“Change” button
2. Click “Solve” button
147

148. 148

149. Keep Solving until reaching the Crash Duration of the Project
149

150. Finish Solving
150

151. Calculate Total Cost and indicate the Minimum Total Cost
151

152. Calculate Total Cost and indicate the Minimum Total Cost
Minimum Total Cost
With the shortest duration
152

153. Use Solver to determine activities’ duration & cost at Min Total Cost
Minimum Total Cost
With the shortest duration
153
2. Click “Solve” button
1. Change

154. Actual Duration & Cost at Minimum Total Cost
Minimum Total Cost
With the shortest duration
154

155. Rate: Cost/Duration
Minimum Total Cost
With the shortest duration
155

156. Bar Chart with Cost/Duration
Minimum Total Cost
With the shortest duration
156

157. Bar Chart with Cost/Duration
157

158. Sum Direct, Indirect, and Total Cost
158

159. Calculate Cumulative Cost
159

160. Time-Cost Tradeoff by Examples
THANK YOU
160