6- Time Cost Trade Off
Transcript of 6- Time Cost Trade Off
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Tutorial # 6
Time-Cost Trade-Off
(Time Shortening)
King Saud University
College of Engineering
GE 404 Engineering Management
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Basic Steps for crash calculation
1. Compute the crash cost per time period,considering crash costs are linear over time
2. Using current activity times, find the critical path and identify the
critical activities
3. Select the activity on the critical path of which (a) it can still be crashed,
and (b) it has the smallest crash cost per period.
o If there is more than one critical path, then select one activity from each
critical path such that (a) each selected activity can still be crashed, and (b)the total crash cost of all selected activities is the smallest.
o Note that the same activity may be common to more than one critical path
4. Update all activity times. If the desired due date has been reached, stop. If not,
return to Step 2
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Network Compression Algorithm Update the project network
When a new Critical path is formed:
- Shorten the activity which Falls on Both Critical Paths, OR
- Shorten one activity from each of the critical paths. Use the combined cost
of shortening both activities when determining if it is cost effective to
shorten the project.
At each shortening cycle, compute the new project duration and project cost
Continue until no further shortening is possible
Use the total project cost-time curve to find the optimum time.
Tabulate and Plot the Indirect project Cost on the same time-cost graph
Add direct and indirect cost to find the project cost at each duration.
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Example1:
The below network shows theactivities of a small engineering
project. Data of the project is given inthe below table. The indirect cost is
estimated to be SR 90/day . Determinethe optimum contract duration.
Activity
Code
Time (day) Cost (SR)
Normal Crash Normal Crash
A 7 3 1500 2300
B 9 5 1400 1840
C 8 5 1280 1430
D 14 9 1100 1400
E 4 2 1200 1500
F 9 7 1500 1680
G 7 3 1200 1520
H 11 7 1750 1910
I 11 7 1500 1720
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1- Develop AON, calculate times, find critical path
0 7 7 7 8 15 23 4 27
A 0 C 8 E 2
10 10 17 17 10 25 25 2 29
0 0
0 0 0
0 9 9 9 14 23 18 7 25 29 11 40
B 0 D 0 G 4 I
0 0 9 11 2 25 22 4 29 29 0 40
9 9 18 18 11 29
F 0 H 0
9 0 18 18 0 29
START
Project completion time = 40 working days
Critical Path: B, F, H, I.
ES EF LS LF TF FF CP
A 0 7 10 17 10 0 N
B 0 9 0 9 0 0 YC 7 15 17 25 17 8 N
D 9 23 11 25 2 0 N
E 23 27 25 29 2 2 N
F 9 18 9 18 0 0 Y
G 18 29 22 29 4 4 N
H 18 29 18 29 0 0 YI 29 40 29 40 0 0 Y
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Activity
Code
Time (day) Cost (SR) Time can be
crashed
Slope,
SR/week
Total Crash
Cost, SRNormal Crash Normal Crash
A 7 3 1500 2300 4 200 800
B 9 5 1400 1840 4 110 440C 8 5 1280 1430 3 50 150
D 14 9 1100 1400 5 60 300
E 4 2 1200 1500 2 150 300
F 9 7 1500 1680 2 90 180
G 7 3 1200 1520 4 80 320
H 11 7 1750 1910 4 40 160
I 11 7 1500 1720 4 55 220
∑ 12430 15300 ∑ 2870
2- Calculate cost slope
onash duratiation - Cr Normal dur
t t - Normal CrashCost Slope
coscos
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3- prepare data for crash analysis
Add the crash limit on node
diagram and table of iteration
ES D LS
Act FF
EF TF LF
Crash limit
(d @ cost)
0 7 7 7 8 15 23 4 27
A 0 C 8 E 2
10 10 17 17 10 25 25 2 29
0 0 4@200 3@50 2@150
0 0 0
0 9 9 9 14 23 18 7 25 29 11 40
B 0 D 0 G 4 I
0 0 9 11 2 25 22 4 29 29 0 40
4@110 5@60 4@80 4@55
9 9 18 18 11 29
F 0 H 0
9 0 18 18 0 292@90 4@40
START
Cycle #Activity to
Shorten
Can Be
ShortenedNIL
Week
Shortened
Cost / week,
SR
Cost / Cycle,
SR
Total Direct
Cost, SR
Project
Duration
0 - 12430 40
1
2
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4- Start to Short Critical Activities beginning with activity
having lowest cost activity
a) Find compression time to reduce activity (H) time
Activity (H) can be reduced by 4 days, but non critical activity (E) on
other paths has only FF=2 Then Nil is 2 day
b) Calculate solution and organize data in the table of iteration
table of cycle reduction
Cycle #
Activity to
Shorten
Can Be
Shortened NIL
Week
Shortened
Cost / week,
SR
Cost / Cycle,
SR
Total Direct
Cost, SR
Project
Duration0 - 12430 40
1 H 42 (Due FF of
E)2 40 80 12510 38
2
Cycle1: reduce critical Activity (H) time which has lowcost
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5- Update the project AON
Cycle 1: Modified AON After Time reduction of Activity (H) by 2 days
After reduction other critical Path is developed: B, D, E, I
0 7 7 7 8 15 23 4 27
A 0 C 8 E 0
8 8 15 15 8 23 23 0 27
0 0 4@200 3@50 2@150
0 0 0
0 9 9 9 14 23 18 7 25 27 11 38
B 0 D 0 G 2 I
0 0 9 9 0 23 22 2 27 27 0 38
4@110 5@60 4@80 4@55
9 9 18 18 9 27
F 0 H 0
9 0 18 18 0 27
2@90 2@40
START
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4- Start to Short Critical Activities beginning with activity
having lowest cost activity
a) Find compression time to reduce activity (I) time
Activity (I) can be reduced by 4 days, without any constraint for FF,
Then NIL =4
b) Calculate solution and organize data in the table of iteration
table of cycle reduction
Cycle #Activity to
Shorten
Can Be
ShortenedNIL
Week
Shortened
Cost / week,
SR
Cost / Cycle,
SR
Total Direct
Cost, SR
Project
Duration0 - 12430 40
1 H 42 (Due FF
of E)2 40 80 12510 38
2 I 4 4 4 55 220 12730 34
3
Cycle2: reduce critical Activity (I) time which has low cost
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5- Update the project AON
Cycle 2: Modified AON After Time reduction of Activity (I) by 4 days
0 7 7 7 8 15 23 4 27
A 0 C 8 E 0
8 8 15 15 8 23 23 0 27
0 0 4@200 3@50 2@150
0 0 0
0 9 9 9 14 23 18 7 25 27 7 34B 0 D 0 G 2 I
0 0 9 9 0 23 22 2 27 27 0 34
4@110 5@60 4@80 0
9 9 18 18 9 27
F 0 H 09 0 18 18 0 27
2@90 2@40
START
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4- Start to Short Critical Activities beginning with activity
having lowest cost activity
a) Find compression time to reduce activity (H,D) time
b) Calculate solution and organize data in the table of iteration
table of cycle reduction
Cycle #Activity to
Shorten
Can Be
ShortenedNIL
Week
Shortened
Cost / week,
SR
Cost / Cycle,
SR
Total Direct
Cost, SR
Project
Duration0 - 12430 40
1 H 42 (Due FF
of E)2 40 80 12510 38
2 I 4 4 4 55 220 12730 34
3 H,D (2,2)2(Due FF
of G)2 (40,60) 200 12930 32
Cycle3: reduce critical Activities (H,D) times which have
low cost and satisfy the Critical Paths
Activity (H,D) can be reduced by 2 days. Also, Activity (G) has
FF=2, Then NIL =2
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5- Update the project AON
Cycle 3: Modified AON After Time reduction of Activity (H,D) by 2 days
After reduction other critical Path is developed: B, F, G, I
0 7 7 7 8 15 21 4 25A 0 C 6 E 0
6 6 13 13 6 21 21 0 25
0 0 4@200 3@50 2@150
0 0 0
0 9 9 9 12 21 18 7 25 25 7 32
B 0 D 0 G 0 I0 0 9 9 0 21 18 0 25 25 0 32
4@110 3@60 4@80 0
9 9 18 18 7 25
F 0 H 0
9 0 18 18 0 252@90 0
START
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4- Start to Short Critical Activities beginning with activity
having lowest cost activity
a) Find compression time to reduce activity (B) time
b) Calculate solution and organize data in the table of iteration
table of cycle reduction
Cycle #Activity to
Shorten
Can Be
ShortenedNIL
Week
Shortened
Cost / week,
SR
Cost / Cycle,
SR
Total Direct
Cost, SR
Project
Duration0 - 12430 40
1 H 42 (Due FF
of E)2 40 80 12510 38
2 I 4 4 4 55 220 12730 34
3 H,D (2,2)2(Due FF
of G)2 (40,60) 200 12930 32
4 B 4 4 4 110 440 13370 28
Cycle4: reduce critical Activity (B) time which has low cost
and satisfies the Critical Paths
Activity (B) can be reduced by 4 days. Then NIL=4
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5- Update the project AON
Cycle 4: Modified AON After Time reduction of Activity (B) by 4 days
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4- Start to Short Critical Activities beginning with activity
having lowest cost activity
a) Find compression time to reduce activities (D,F) times
b) Calculate solution and organize data in the table of iterationtable of cycle reduction
Cycle #Activity to
Shorten
Can Be
ShortenedNIL
Week
Shortened
Cost / week,
SR
Cost / Cycle,
SR
Total Direct
Cost, SR
Project
Duration
0 - 12430 40
1 H 4 2 (Due FFof E) 2 40 80 12510 38
2 I 4 4 4 55 220 12730 34
3 H,D (2,2)2(Due FF
of G)2 (40,60) 200 12930 32
4 B 4 4 4 110 440 13370 28
5 D,F (2,2) 2 2 (60,90) 300 13670 26
Cycle5: reduce critical Activities (D,F) times which have low cost and
satisfy the Critical Paths
Activities (D,F) can be reduced by 2 days, Since the FF of activity C
is 6, Then NIL=2
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5- Update the project AON
Cycle 5: Modified AON After Time reduction of Activity (B) by 4 days
After reduction other critical Path is developed: A, C, E, I
0 7 7 7 8 15 15 4 19
A 0 C 4 E 0
0 4 7 7 4 15 15 0 19
0 0 4@200 3@50 2@150
0 0 0
0 5 5 5 10 15 12 7 19 19 7 26
B 0 D 0 G 0 I
0 0 5 5 0 15 12 0 19 19 0 26
0 1@60 4@80 0
5 7 12 12 7 19
F 0 H 0
5 0 12 12 0 19
0 0
START
Remark:
All Activity on network are critical and no further reduction is possible
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