1. Project Management
Chapter 8 (Crashing)

2. Project Crashing Basic Concept
In last lecture, we studied on how to use CPM and PERT to identify critical path for a project problem
Now, the question is:
Question: Can we cut short its project completion time?
If so, how!
Chapter 8 - Project Management

3. Project Crashing Solution!
Yes, the project duration can be reduced by assigning more resources to project activities. But, doing this would somehow increase our project cost!
How do we strike a balance?
Project crashing is a method for shortening project duration by reducing one or more critical activities to a time less than normal activity time.

4. Trade-off concept Here, we adopt the “Trade-off” concept
We attempt to “crash” some “critical” events by allocating more resources to them, so that the time of one or more critical activities is reduced to a time that is less than the normal activity time.
How to do that:
Question: What criteria should it be based on when deciding to crashing critical times?

5. Example – crashing (1)
Max weeks can be crashed
The critical path is 1-2-3, the completion time =11
How? Path: = 5+6=11 weeks
Path: 1-3 = 5 weeks
Now, how many days can we “crash” it?
Normal weeks 2
6(3)
5 (1) 3 1
5(0)

6. Example – crashing (1) 6(3) 5 (1) 5(0)2
6(3)
5 (1) 3 1
5(0)
The maximum time that can be crashed for:
Path = = 4
Path 1-3 = 0
Should we use up all these 4 weeks?

7. Example – crashing (1) 6(3) 5 (1) 5(0) 3(0) 4(0)2
6(3)
5 (1) 3 1
5(0)
If we used all 4 days, then path has
(5-1) + (6-3) = 7 completion weeks
Now, we need to check if the completion time for path 1-3 has lesser than 7 weeks (why?)
Now, path 1-3 has (5-0) = 5 weeks
Since path 1-3 still shorter than 7 weeks, we used up all 4 crashed weeks
Question: What if path 1-3 has, say 8 weeks completion time?

8. Example – crashing (1) Such as 6(3) 5 (1) 8(0)2
6(3)
5 (1) 3 1
8(0)
Now, we cannot use all 4 days (Why?)
Because path will not be critical path anymore as
path 1-3 would now has longest hour to finish
Rule: When a path is a critical path, it will not stay as a critical path
So, we can only reduce the path completion time to the same time
as path (HOW?)

9. Example – crashing (1) Solution: 6(3) 5 (1) 8(0)2
6(3)
5 (1) 3 1
8(0)
We can only reduce total time for path = path 1-3,
that is 8 weeks
If the cost for path 1-2 and path 2-3 is the same then
We can random pick them to crash so that its completion
Time is 8 weeks

10. Example – crashing (1) Solution: 4(0) 4(1) 6(3) 5 (1) 8(0) 3(0) OR2
6(3)
5 (1) 3 1
8(0)
3(0) OR
5 (1)
6(3) 2 1 3
8(0)
Now, paths and 1-3 are both critical paths

11. AOA Network for House Building Project
The Project Network
AOA Network for House Building Project
Figure 8.6
Expanded Network for Building a
House Showing Concurrent Activities
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12. Project Crashing and Time-Cost Trade-Off Example Problem (1 of 5)
Figure The Project Network for Building a House

13. Project Crashing and Time-Cost Trade-Off Example Problem (3 of 5)
Table 8.4

14. Project Crashing and Time-Cost Trade-Off Example Problem (2 of 5)
Crash cost & crash time have a linear relationship:
Figure 8.20
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15. Project Crashing and Time-Cost Trade-Off
General Relationship of Time and Cost (2 of 2)
Figure 8.23
The Time-Cost Trade-Off
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16. Project Crashing and Time-Cost Trade-Off Example Problem (4 of 5)
Figure 8.21 Network with Normal Activity Times and Weekly Crashing Costs

17. Project Crashing and Time-Cost Trade-Off Example Problem (5 of 5)
As activities are crashed, the critical path may change and several paths may become critical.
Figure 8.22
Revised Network with Activity 1 Crashed

18. Project Crashing and Time-Cost Trade-Off
Project Crashing with QM for Windows
Exhibit 8.16

19. Formulating as a Linear Programming Model
AOA Network for House Building Project
Figure 8.6
Expanded Network for Building a
House Showing Concurrent Activities
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

20. Formulating as a Linear Programming Model
Example Problem Formulation and Data (1 of 2)
Figure 8.24
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21. Example Problem Formulation and Data (2 of 2)
The CPM/PERT Network
Example Problem Formulation and Data (2 of 2)
Minimize Z = x1 + x2 + x3 + x4 + x5 + x6 + x7
subject to:
x2 - x1  12
x3 - x2  8
x4 - x2  4
x4 - x3  0
x5 - x4  4
x6 - x4  12
x6 - x5  4
x7 - x6  4
xi, xj  0
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22. Formulating as a Linear Programming Model
The CPM/PERT Network
Formulating as a Linear Programming Model
The objective is to minimize the project duration (critical path time).
General linear programming model with AOA convention:
Minimize Z = xi
subject to:
xj - xi  tij for all activities i  j
xi, xj  0
Where:
xi = earliest event time of node i
xj = earliest event time of node j
tij = time of activity i  j i
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23. Project Crashing with Linear Programming
Example Problem – Model Formulation
Minimize Z = $400y y y y y y y67
subject to:
y12  5 y12 + x2 - x1  x7  30
y23  3 y23 + x3 - x2  xi, yij ≥ 0
y24  1 y24 + x4 - x2  4
y34  0 y34 + x4 - x3  0
y45  3 y45 + x5 - x4  4
y46  3 y46 + x6 - x4  12
y56  3 y56 + x6 - x5  4
y67  1 x67 + x7 - x6  4
xi = earliest event time of node i
xj = earliest event time of node j
yij = amount of time by which activity i  j is crashed
Objective is to minimize the cost of crashing
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