Concept explainers
Interpretation: The total project completion time is to be calculated along with the lowest cost solution if the project is to be completed
Concept Introduction:
Project
Explanation of Solution
The activity with their immediate predecessor and estimated time, crash time, crash cost and normal cost is tabulated below.
Activity | Immediate Predecessor | Estimated Normal Time | Crash Time | Normal Cost | Crash Cost |
A | - | ||||
B | A | ||||
C | A | ||||
D | - | ||||
E | B, D, C | ||||
F | D | ||||
G | D | ||||
H | E | ||||
I | F, G, H |
Table (1)
The network diagram for the activity shown in table (1) is shown below.
Figure (1)
Therefore, the network diagram of the given project is shown in Figure (1).
The expression for the cost slope is given by,
The cost slope for each activity is tabulated below.
Activity | Immediate Predecessor | Estimated Normal Time | Crash Time | Normal Cost | Crash Cost | Cost Slope |
A | - | |||||
B | A | |||||
C | A | |||||
D | - | |||||
E | B, D, C | |||||
F | D | |||||
G | D | |||||
H | E | |||||
I | F, G, H |
Table (2)
Consider figure (1), the different paths and their completion times is tabulated below.
Path | Completion time (weeks) |
Table (3)
From Table (3), the maximum completion time is taken by path
Therefore, the critical path is
Now the project is to be completed
Consider the critical path activities.
The lowest crash cost per week is of activity B and activity H.
Crash Activity B by
And,
Thus, the additional cost of crashing the activity by
The new network diagram is shown in figure below.
Figure (2)
Consider figure (2), the different paths and their completion times is tabulated below.
Path | Completion time (weeks) |
Table (4)
From Table (4), the maximum completion time is taken by path
Therefore, the critical path is
But the desired project duration is
Try different option.
Crash Activity B by
And,
And,
Thus, the additional cost of crashing the activity by
The new network diagram is shown in figure below.
Figure (3)
Consider figure (3), the different paths and their completion times is tabulated below.
Path | Completion time (weeks) |
Table (4)
From Table (4), the maximum completion time is taken by path
Therefore, the critical path are
Therefore, the crashing cost of the project is
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