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Project ManagementA Managerial Approach
Resource Allocation
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Critical Path Method - Crashinga Project
CPM includes a way of relating theproject schedule to the level
ofphysical resources allocated to the
project
This allows the project manager totrade time for cost, or vice
versa
In CPM, two activity times and twocosts are specified, if
appropriate foreach activity
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Critical Path Method - Crashinga Project
The first time/cost combination is callednormal, and the second
set is referred to
as crash Normal times are normal in the same
sense as the m time estimate of the three
times used in PERT Crash times result from an attempt to
expedite the activity by the application of
additional resources
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Critical Path Method - Crashinga Project
Careful planning is critical whenattempting to expedite (crash)
a project
Expediting tends to create problems;and the solution to one
problem oftencreates several more problems thatrequire
solutions
Some organizations have more thanone level of crashing
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Slope =( crash cost - normal cost)/(crash time normal time)
That is, the cost per day of crashing aproject. Negative slope
indicates that asthe time required for a project task isdecreased,
the cost is increased.
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1
3
24
Given the following network, determine the first activity tobe
crashed by the following priority rules:
D5
C7
B3
A4
a. Shortest task first b. Minimum slack firstc. Most critical
followers d. Most successors
Exercise 1
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Exercise 2
Using the previous network and theadditional information below,
find:
The crash cost per day.
Which activities should be crashed tomeet a project deadline of
13 days atminimum cost. Assume partial crashingis allowed.
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Activity Crashtime
(days)
Crashedcost
(total)
NormalTime
(days)
Normalcost
A 3 $500 4 $300
B 1 325 3 250
C 4 550 7 400
D 3 250 5 150
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Activity Crash days=normaltime-crash time
Crashcost
Crashcost/day
A 1 200 200
B 2 75 37.5
C 3 150 50
D 2 100 50
Crash cost per day
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Task B is on the critical path and has thelowest crash cost per
day.
Hence crashing task B will implyadditional crash cost of $75
only.
Crashing B by 2 days reduces theduration to 13 days without
making anyother new tasks critical.
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Exercise 3: Given the following network(time in days).Find the
lowest cost to complete the project in 10 days.
1
2
3
4
a
bc
d
e
Activity Crash time,cost$ Normaltime,cost Partialcrashing
a 3, 60 3, $60 No
b 6, 80 7, 30 Yes
c 2, 90 5, 50 No
d 5, 50 6, 30 No
e 2, 100 4, 40 Yes
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Current time & cost: 12 days & $ 210.
1 4
2a
b5
d
e
0
3
12
3
8
3
7
6c
4
Since the critical path is a-c-e, we initially
need consider only these 3 activities:
a: cannot be crashed
c: can cut 3days at an extra cost of $ 40 but only results
in project completion by day 11, due to b. to reach 10days, cut
b by 1 day, total extra cost $90.
e: can cut e by 2 days for an extra cost of $60 & results
inproject completion by day 10.
Hence best solution:Cut e by 2 daysat a cost of $60
