hti management dr/Mahmoud malik & Eng/ Ahmed Nagy

1. Crash
Activity Successor Normal
duration
Crash
duration
Normal
cost (LE)
Crash
Cost (LE)
Constraint
Z A 4 2 2660 2800 -
A B,D 10 7 5000 5750 -
B - 5 3 3500 4900 F4,D2A
D - 8 6 7150 8150 D3C,L4E
E D 10 6 2800 3200 D5X
X E 4 2 4000 4300 F5
Y C 5 5 5000 5000 F5
C D 7 4 5000 5600 -
A project has the following activities and relationships
Contract time 20 days, Penalty Value300 LE/Day, What is your
recommendation?

2. Finish
X
C
E
Y
AZ B
D
Start
4
0 5
5
0 5
10
10 20
7
5 12
0
0 0
4
0 4
10
4 14
5
16 21
8
16 24
0
24 24
F5
L4
D3
D5
D2
F5
Activity Successor
Z A
A B,D
B -
D -
E D
X E
Y C
C D
15
16
14
24
21
F4

3. If we don’t crash the project the total cost will be as following :
Total cost = Total normal cost + Penalty cost
Total normal cost = Ʃ Normal cost for each activity
=2660+5000+3500+7150+2800+4000+5000+5000= 35110 L.E.
Penalty cost = Penalty cost per month * No. of delayed month
= 300 * 4 = 1200 L.E.
Total cost = Total normal cost + Penalty cost
= 35110 + 1200 = 36310 L.E.
In This case total time of the project will be 24 w and Contractor will
deliver the project 4 month later than the time in the contract.
To avoid this delay the crash will be applied to this network to deliver
the project as possible as contract time.

4. The Crash rules :
1) Apply Crash only on activities which affect the total time.
2) Crash the least cost activity according to the least cost slope
Cost Slope =
𝑪𝒓𝒂𝒔𝒉𝒆𝒅 𝒄𝒐𝒔𝒕 𝑪.𝑪. −𝑵𝒐𝒓𝒎𝒂𝒍 𝑪𝒐𝒔𝒕(𝑵.𝑪.)
𝑵𝒐𝒓𝒎𝒂𝒍 𝑫𝒖𝒓𝒂𝒕𝒊𝒐𝒏 (𝑵.𝑫.) −𝑪𝒓𝒂𝒔𝒉𝒆𝒅 𝑫𝒖𝒓𝒂𝒕𝒊𝒐𝒏 (𝑪.𝑫.)
L.E unite time
3) Activity will be crashed according to it’s crashability
Crashability = Normal Duration(N.D.) – Crash Duration (C.D.)

5. The Path which need to be crashed are the paths gives total time more
than contract time (20 w)
X E D (24w 20w)
2
500
4
100
Y C D
2
500
3
200
Z A D
2
500
3
250
2
70
(23 20)
(22 20)
Z A B
1
700
3
250
2
70
(21 20)
4E = 4*100 = 400 L.E.
3C = 3 * 200 = 600 L.E.
2Z = 2 * 70 = 140 L.E.
This path is already crashed 2Z from
the previous path (Z is Shared
activity in the two paths)
Total Crashed Cost = 600 + 400 + 140 = 1140 L.E.

6. Another Scenario to reach contract time 20 w
X E D (24 20)
2
500
4
100
Y C D
2
500
3
200
Z A D
2
500
3
250
2
70
(23 20)
(22 20)
Z A B
2
700
3
250
2
70
(21 20)
1C = 1 * 200 = 200 L.E.
NO need for crashing this path
1Z = 70 L.E.
2E = 2 * 100 = 200 L.E.
Act. D is
shared
Act.
2D =
2*500=
1000 L.E.
Total Crashed Cost for this scenario = 1000 + 400 + 200+70 = 1470 L.E.

7. X E D (24w 23w)
2
500
4
100
Y C D
2
500
3
200
Z A D
2
500
3
250
2
70
(23 23)
(22 23)
Z A B
1
700
3
250
2
70
(21 23)
Total Crashed Cost = 100 L.E.
1E = 1 * 100 = 100 L.E.
NO need for crashing this path
NO need for crashing this path
NO need for crashing this path
Scenario of ending the project with in 23 w

8. X E D (24w 22w)
2
500
4
100
Y C D
2
500
3
200
Z A D
2
500
3
250
2
70
(23 22)
(22 22)
Z A B
1
700
3
250
2
70
(21 22)
Total Crashed Cost = 200 + 200 = 400 L.E.
2E = 2 * 100 = 200 L.E.
1C = 200 L.E.
NO need for crashing this path
NO need for crashing this path
Scenario of ending the project with in 22 w

9. X E D (24w 21w)
2
500
4
100
Y C D
2
500
3
200
Z A D
2
500
3
250
2
70
(23 21)
(22 21)
Z A B
1
700
3
250
2
70
(21 21)
Total Crashed Cost = 300 + 400 + 70 = 770 L.E.
3E = 3* 100 = 300 L.E.
2C = 2 * 200 = 400 L.E.
1Z = 70 L.E.
NO need for crashing this path
Scenario of ending the project with in 21 w

10. Total time
Total
Normal
Cost
Total
crashed
cost
Total Penalty
Value
Total cost
24 35110 0 1200 36310
23 35110 100 900 36110
22 35110 400 600 36110
21 35110 770 300 36180
20 35110 1140 0 36250
Scenarios of the different completion time of the project can be
estimated according to this table:
Respect reputation and apply scenario 20 w

11. Finish
X
C
E
Y
AZ B
D
Start
4
0 5
5
0 5
10 16
4
5 9
0
0 0
2
0 2
10
2 12
5
14 19
8
12 20
0
20 20
F5
L4
D3
D5
D2
F5
12
12
12
20
19
F4
6
The final executed Network

12. UPDATE
Feedback form site at day 5 as following:
1) Activity C will start late by 2days
2) Activity A will finish late by 2 days
Finish
X
C
E
Y
AZ B
D
Start
4
0 5
5
0 5
10 16
4
7 11
0
0 0
2
0 2
10
2 14
5
16 21
8
14 22
0
22 22
F5
L4
D3
D5
D2
F5
14
12
14
22
21
F4
6

13. According to feedback at day 5 during construction
the project will finish in 22 day (2 days late from
contract time) , so we need to apply crash again but
take in your consideration :
1) The activities which have been finished.
Ex: Activity X,Y and Z finished before the feedback
date and Activity C not started yet according to
feedback (not allowed to be crashed) and Activity A
has been started but will finish late according to
feedback (allowed to be crashed if possible).
1) The activities which have been crashed before.
Ex: Activity E,C and Z

14. Y C D
2
500
0
200
Z A D
2
500
3
250
0
70
(22 20)
(22 20)
Z A B
1
700
3
250
0
70
(21 20)
2D = 2 * 500 = 1000 L.E.
This path is already crashed 2D from
the previous path (D is Shared
activity in the two paths)
1B = 1 * 700 = 700 L.E.
Total Crashed Cost = 1000 + 700 = 1700 L.E.

15. The network after update
Finish
X
C
E
Y
AZ B
D
Start
4
0 5
5
0 5
10 16
4
7 11
0
0 0
2
0 2
10
2 14
4
16 20
6
14 20
0
20 20
F5
L4
D3
D5
D2
F5
14
12
14
20
20
F4
6