This document discusses crashing vs fast-tracking construction projects and the relationship between activity duration and cost. It provides an example of crashing the duration of a sample ABCD project: 1) The initial critical path is ACD at 14 days. Crashing A by 1 day reduces duration to 13 days at a cost of 25 units. 2) Further crashing A and crashing D reduces the duration to 12 days and 11 days respectively. 3) Crashing C reduces the critical path to 10 days at a cost of 175 units. 4) Continued crashing of C, B, and A reaches the minimum duration of 8 days at a total crashing cost of 700 units.

1. MODULE 8
CONSTRUCTION COSTS
Lesson 1
Fast-Tracking vs. Crashing, Relationship
between Activity Direct Cost & Activity
Duration – Assumptions
(PROF. R K CHOUDHARY
GCE GAYA)

2. Learning Objectives
• Fast-tracking vs Crashing
• Relationship between activity direct cost &
activity duration – Assumptions
• Procedure for finding minimum direct cost for
crashed project durations
• Influence of indirect cost and relationship
between total cost and project duration
3

3. 5 4d 9
B
7 11
5d 5
A
11 3d
D
5 11
5 6d 11
C
5 11
0 14
0 14
Activity Duration Predecessor
A 5 -
B 4 A
C 6 A
D 3 B,C
Consider the ABCD Project
Current duration : 14 days
Expected duration : 10 days
How can it be done ?

4. Reducing Project Duration
• Fast-Tracking
– Preforming activities in parallel in order to reduce project duration
• Crashing
– Reducing duration of activities in order to reduce project duration
Change of execution sequence or duration will have cost implication.
Time-Cost Trade-Off analysis is used to find the minimum
overall project cost for a specified project duration
Focus is on Crashing 5

5. Crash Cost
Cost of completing activity in
minimum duration
Terminology
6
Normal Cost
Cost of completing activity in
normal duration
CRASHING
Reducing activity time by
expending additional resources
Normal Duration
Normal activity duration
Crash Duration
Minimum duration

6. Activity Duration Reduction
• Construction Method Selection
• Alternate Construction Materials
• Working Multiple Shifts
• Overtime work (Late hours or Weekends)
• Bringing in Higher Capacity Equipment
• Additional Workers or Equipment
7
Reducing duration will require additional expenditure

7. Activity: Time vs Cost - Relationship
Crash cost
Linear - Assumption
Piecewise Linear - Assumption
Actual Relationship
Normal
cost
Crash time Normal
time
Activity time
8
Cost Slope = cost / time
= (Crash cost – Normal cost)
(Normal time – Crash time)

8. Lesson 2
Time-Cost trade-off: ABCD Example
Project, Steps for Crashing

9. B
7 11
5d 5
A
5
113d
D
11
5 6d 11
C
5 11
Act ND
days
Pred CD
days
NC
u
CC
u
A 5 - 3 250 300
B 4 A 3 300 375
C 6 A 3 350 875
D 3 B,C 2 300 350
5 4d 9
0 14
0 14
Back to the ABCD Project
Determine Minimum Cost of Completing Project in 13, 12…8 days.2

10. B
7 11
5d 5
A
5
113d
D
11
5 6d 11
C
5 11
CC/day = (CC-NC) /(ND-CD)
Act ND
days
Pred CD
days
NC
u
CC
u
Crash
Days
Crash
Cost /
day
A 5 - 3 250 300 2 25
B 4 A 3 300 375 1 75
C 6 A 3 350 875 3 175
D 3 B,C 2 300 350 1 50
5 4d 9
0 14
0 14
Crashing the ABCD Project
Paths : ABD – Non Critical 12 days
ACD – Critical 14 days

11. B
11
5
4d
A
4
5
11
03d
D
11
0
4
5 6d 11
C
4
5 11
0
Act ND
days
Pred CD
days
NC
u
CC
u
Crash
Days
Crash
Cost /
day
A 5 - 3 250 300 2 25
B 4 A 3 300 375 1 75
C 6 A 3 350 875 1 175
D 3 B,C 2 300 350 1 50
4d 8
9
0
0
14
3
14
Step 1: Crash the critical path
ACD.
Options available to crash
A= u 25
C= u 175
D= u 50
Crash A by 1 day: Cost = u 25
Still the critical path is ACD (13 days)
ABCD Project Crash Duration - 13 days
7
6

12. 4
3 4d 8
7
B
1
90
4
3d
A
A
4
3
10
1
903d
D
D
9
4 6d 10
3 6d 9
C
4 C
3 9
10
6
5
4
3
Act ND
days
Pred CD
days
NC
u
CC
u
Crash
Days
Crash
Cost /
day
A 5 - 3 250 300 2 25
B 4 A 3 300 375 1 75
C 6 A 3 350 875 3 175
D 3 B,C 2 300 350 1 50
0 12
0
0 1
13
2
Step 2: Crash the critical path
ACD.
Options available to crash
A= u 25
C= u 175
D= u 50
Crash A by 1 day: Cost = u 25
(A cannot be crashed any further)
Still the critical path is ACD (12 days)
ABCD Project Crash Duration - 12 days

13. 3 4d 7
B
9
3d
A
3
9 2
3d
D
9
3 6d 9
C
3 9
5
3
Act ND
days
Pred CD
days
NC
u
CC
u
Crash
Days
Crash
Cost /
day
A 5 - 3 250 300 2 25
B 4 A 3 300 375 1 75
C 6 A 3 350 475 1 125
D 3 B,C 2 300 350 1 50
0 11
2
Step 3: Crash the critical path
ACD.
Options available to crash
A= u 25
0 11
(A cannot be crashed any further)
C= u 175
D= u 50
Crash D by 1 day: Cost = u 50
(D cannot be crashed any further)
Still the critical path is ACD (11 days)
ABCD Project Crash Duration - 11 days

14. 3 4d 7
B
9
8
3d
A
3
8
9 2d
D
8
9
3 5
6d 9
8
C
3 9
8
5
4
3
Act ND
days
Pred CD
days
NC
u
CC
u
Crash
Days
Crash
Cost /
day
A 5 - 3 250 300 2 25
B 4 A 3 300 375 1 75
C 6 A 3 350 475 1 125
D 3 B,C 2 300 350 1 50
0 11
0
0 11
0
ABCD Project Crash Duration - 10 days
Step 4: Crash the critical path ACD.
Options available to crash
A= u 25 (A cannot be crashed any further)
C= u 175
D= u 50 (D cannot be crashed any further)
Crash C by 1 day: Cost = u 175
Still the critical path is ACD (10 days)

15. 3 4d 7
B
7
8
3d
A
3
7
8 2d
D
8
7
3 5
4d 8
7
C
3 7
8
3
4
3
Act ND
days
Pred CD
days
NC
u
CC
u
Crash
Days
Crash
Cost /
day
A 5 - 3 250 300 2 25
B 4 A 3 300 375 1 75
C 6 A 3 350 475 1 125
D 3 B,C 2 300 350 1 50
0 1
90
Step 5: Crash the critical path ACD.
Options available to crash
A= u 25
0 1
90
(A cannot be crashed any further)
C= u 175
D= u 50 (D cannot be crashed any further)
Crash C by 1 day: Cost = u 175
Both ABD & ACD are Critical (9
days)
ABCD Project Crash Duration - 9 days

16. 3 4
3d 6
7
B
7
6
3d
A
3
6
7 2d
D
7
6
3 4
3d 6
7
C
3 7
6
3
4
3
Act ND
days
Pred CD
days
NC
u
CC
u
Crash
Days
Crash
Cost /
day
A 5 - 3 250 300 2 25
B 4 A 3 300 375 1 75
C 6 A 3 350 475 1 125
D 3 B,C 2 300 350 1 50
0 8
9
0 8
9
Step 6: Crash the critical path ACD
& ABD.
Options available to crash
A= u 25 (A cannot be crashed any further)
C= u 175 & B= u 75
D= u 50 (D cannot be crashed any further)
Crash C & B by 1 day: Cost = u 250
MAX CRASH
ABCD Project Crash Duration - 8 days

17. Crashing Cost - Summary
2000
1750
1500
1250
1000
7 8 9 10 11 12 13 14 15
Project Duration days
Project
Direct
Cost
u
Step
No.
Project
Duration
days
Activity
Crashed
Crash
Cost
u
Cumulat
ive
Crash
Cost u
Total
Project
Direct
Cost u
0 14 None 0 0 1200
1 13 A by 1 25 25 1225
2 12 A by 1 25 50 1250
3 11 D by 1 50 100 1300
4 10 C by1 175 275 1475
5 9 C by 1 175 450 1650
6 8 C & B by 1 250 700 1900

18. 11
2000
Effect of Crashing on Direct cost
1900
1800
1700
1600
1500
250
 In later stages, when
multiple paths are tied
(larger cost slope).
175
 In the early stages of
1400
1300
175
50
compression (lesser cost
slope).
1200
25
25
1100
1000 Project Duration days
7 8 9 10 11 12 13 14 15
Project
Direct
Cost
u

19. INDIRECT COSTS
 Project overhead
 Staff, manager, project engineer salary.
 Office equipment and temporary utilities like
electricity, phone.
 General overhead
 Main office expenses- rent, maintenance.
 Site equipment and vehicles.
 Lawyers and accountants, Advertising and Social activities.
 Contingency fees
 Additional cost allocated for unknown events.
Not directly related to activities 12

20. Effect of crashing on Indirect cost
 These expenses are
constant for each day
of the project
 When the project
duration is decreased
total indirect cost will
decrease
13
Total Overhead Cost

21. Total Project Cost – Direct + Indirect
Ste
p
No.
Project
Duration
days
Activity
Crashed
Crash
Cost
u
Cumul
ative
Crash
Cost u
Total
Project
Direct
Cost u
Indirect
Cost /
day
Total
Indirect
Cost
Total Cost
(Direct +
Indirect)
0 14 None 0 0 1200 100 1400 2600
1 13 A by 1 25 25 1225 100 1300 2525
2 12 A by 1 25 50 1250 100 1200 2450
3 11 D by 1 50 100 1300 100 1100 2400
4 10 C by1 175 275
1475 100 1000 2475
5 9 C by 1 175 450
1650 100 900 2550
6 8 C & B by 1 250 700
1900 100 800 2700
14

22. Cost
u
Time-Cost Curve
3000
2500
Total Cost
2000
1500 Indirect Cost
1000 Direct Cost
500
0
7 8 9 10 11 12 13 14 15
Project Duration days 15

23. Steps for Crashing
• Identify activities on Critical path(s)
1
• Compare unit cost of crashing (critical) activities/combinations
2 available for crashing*
• Select activity/combination with minimum unit cost. In case of a
3 tie activity which influences more paths.
• Reduce duration of activity/ combination. (ensure no other path
4 becomes critical if duration reduction is by more that 1 day)
• Recalculate network parameters and go to Step-1.
5
16
*Repeat Steps until activity/combination cannot
undergo further crashing