No Slide TitleProject Management
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:
If so, how!
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.
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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?
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How? Path: 1-2-3 = 5+6=11 weeks
Path: 1-3 = 5 weeks
1
3
2
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Path 1-2-3 = 1 + 3 = 4
Path 1-3 = 0
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If we used all 4 days, then path 1-2-3 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?
4(0)
3(0)
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Because path 1-2-3 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 1-2-3 completion time to the same time
as path 1-3. (HOW?)
6(3)
8(0)
Solution:
We can only reduce total time for path 1-2-3 = 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
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Figure 8.6
House Showing Concurrent Activities
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Project Crashing and Time-Cost Trade-Off
Example Problem (1 of 5)
Figure 8.19 The Project Network for Building a House
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Table 8.4
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Figure 8.20
Crash cost & crash time have a linear relationship:
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General Relationship of Time and Cost (2 of 2)
Figure 8.23
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Figure 8.21 Network with Normal Activity Times and Weekly Crashing Costs
Project Crashing and Time-Cost Trade-Off
Example Problem (4 of 5)
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Figure 8.22
Project Crashing and Time-Cost Trade-Off
Example Problem (5 of 5)
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Exhibit 8.16
Project Crashing with QM for Windows
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Figure 8.6
House Showing Concurrent Activities
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Example Problem Formulation and Data (1 of 2)
Figure 8.24
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subject to:
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
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Minimize Z = xi
xi, xj 0
tij = time of activity i j
The objective is to minimize the project duration (critical path time).
The CPM/PERT Network
i
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subject to:
y23 3 y23 + x3 - x2 8 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
Project Crashing with Linear Programming
Example Problem – Model Formulation
Objective is to minimize the cost of crashing
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