1 By: Prof. Y. Peter Chiu Materials Management ~ HOMEWORK SOLUTION ~
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Transcript of 1 By: Prof. Y. Peter Chiu Materials Management ~ HOMEWORK SOLUTION ~
1
By: Prof. Y. Peter Chiu
Materials Management
~ HOMEWORK SOLUTION ~
2
# 3(a)
(b)
CP => A → B → D → F→ G (17)
1
2
4
3
5
6
7
B=5
C=1P1=0
E=3
D=4
F=3
H=4
G=2
3030
4387
8888
128128 16
171213
8383 118
129
15121512
1717
1515
A=3
3
# 3
=> Where is not needed for solution ,
but it is the slack time.
(c)
C
FG
H
AB
DE
A
B
C
D
E
F
G
H0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
4
# 4
1
284
36
5
9
7 10
A=3
B=2
E=6
P2=0
D=4
C=5
P1=0
G=5
F=1
K=5
H=3
I=4
P3=0
J=4
0 31 4
3 87 12
34
78
00
22
7 78 8
22
88
712
712
8 138 13
812
913
13 161714
212
717
13 1713 17
1617
1617
1717
2121
*
*
*
**
5
(a)
A -B -C AD AE BF C , DG D , EH F , GI F ,GJ H , I ,K , LK BL -
(b)
A-C-F-H-J
A-C-F-I-J
A-D-F-H-J
A-D-F-I-J
A-D-G-H-J
A-D-G-I-J
B-E-G-H-J
B-E-G-I-J
B-K-J
L-J
16
17
15
16
19
20
20
21
11
14
*
# 4
6
# 4(c) Activities ti ESi SFi LSi LFi Slack
ABCDEFGHIJKL
3254615344510
003328813131720
32878913161721710
10742128141317127
42128813131717211717
1041040100107
CP= B-E-G-I-J
‧
‧
‧
‧‧
7
# 5(a)
ActivitiesImmediatePredecessor
ABCDEFGHI
--ABD
A , B , ED
C , D , FC , D , F
, G
8
# 5(b)
1
2
3
5
4
6
7
8
A
B
P1
D
E
G
C
F
P2
I
H
9
# 6
(a)
(b)
CP => A→ E→ G (78) C→ F→G (78)
1
2
3
5
6
4
A=32 D=45
G=20
F=28
C=30
B=21E=26
P1=0
320320
77327833
2103211 7858
7858
3232
3232
300300
58325832
5858
3030
10
ABCDEFG
A
B
C
D
E
F
G
800 20 40 60
# 6
(c)
(d) { A , B , C , E , F }
32
30
77 78
58
11
# 8
1 2
3
4
5 6
7
A=3
C=1
P=0B=5
D=4
E=3
F=3
H=4
G=2
00
33
33
88
37
48
88
88
88
1212
89
1112
1212
1515
1213
1617
1515
1717
A-B-P-D-F-G
12
# 8
1
2
4
3
5
6
7
B=5
C=1P1=0
E=3
D=4
F=3
H=4
G=2
3030
4387
8688
128128 16
171213
8383 118
129
15121512
1717
1515
A=3
13
=> Where is not needed for solution ,
but it is the slack time.
# 8
C
FG
H
AB
DE
A
B
C
D
E
F
H
G0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
14
# 8
17 ABDFG
35432
23221
$ 50 125 125 120 100
ReduceA 3→2 costs $50
G 2→1 costs $100
Total $150
‧
*
*
CP ︰ A-B-D-F-G
A-B-D-H
(a)
15
# 8
15 ABDFGH
254314
232212
-$125 125
120 - 150
* If we consider “F” then we must consider “H” along with “F” .
ReduceB by 2
D by 1‧
*
(why ?)
(why not 2 ?)
(refer to Gantt Chart)
(a)
16
# 8(a)
cost $125*2 (B) $125*1 (for D)
Total ︰ $375
CP ︰ A-B-D-F-G A-B-D-H A-B-E-F-G A-B-E-H
Time CPActivities
Courent time
Expedited time
cost
12 ABDEFGH
2333314
2322212
- -$125 50 120 - 150
Cumulative total ︰$525
17
# 8(a) One can consider D&E for $175/wk or F&H for $270/wk.
Even though they are > (return $150 per weak).
#Time CP
ActivitiesCourent time
Expedited time
cost
10 ABDEFGH
2322213
2322212
- - - - - - 150
Cumulative total ︰$970
CP ︰ A-B-D-F-G A-B-D-H A-B-E-F-G A-B-E-H
18
# 8(b)
Activity Normal cost
ABCDEFGH
$200 600 100 650 450 500 500 600
19
# 8(b) Direct cost $3600 for 17 days.
For 12 days optimal project schedule
AddAGBD
1121
$50 = 50$100 = 100$125 = 250$125 = 125
$525
Direct cost $3600+$525 = $4125 for 12 days.
Indirect cost $150*12 = $1800
Total costs = $5925.vs.$6150 #
20
# 10
(a)
1
2
3
5
6
4
A=32 D=45
G=20
F=28
C=30
B=21E=26
P1=0
320320
77327833
2103211 7858
7858
3232
3232
300300
58325832
5858
3030
‧
‧
‧
‧
21
# 10(b)
Activities
A
B
C
D
E
F
G
-
-
-
A
A , B
C
E , F
ti ES EF LS LF Slack
32
21
30
45
26
28
20
0
0
0
32
32
30
58
32
21
30
77
58
58
78
0
11
0
33
32
30
58
32
32
30
78
58
58
78
0
11
0
1
0
0
0
CP=A-P1-E-G
C-F-G
22
# 10
ABCDEFG
10 20 30 40 50 # 70 80
: A-E-G :CP
: C-F-G :CP
: A-D
23
# 10
Time Act. Current Exp.-time cost/dy
78 A-E-GC-F-G
A
C
E
F
G
32
30
26
28
20
26
30
20
24
18
$50
-
110
40
75
‧Reduce G one day cost $75.
CP : A-D* A-E-G C-F-G
*
24
# 10
Time Act. Current Exp.-time cost/dy
77 A-D
A-E-G
C-F-G
A
C
D
E
F
G
32
30
45
26
28
19
26
30
40
20
24
18
$50
-
60
110
40
75
*
*
‧Reduce A & F by 4 day cost $90*4= $360.
25
# 10Time Current Exp.-time costActivitiesCP
73 A-DA-E-GC-F-G
ACDEFG
283045262419
263040202418
$50 -$60$110 -$75
DONE﹗Original 78 days cost $3300+ $100(78)= $11,100
New expedited project scheduce 73 days.
Cost Direct cost +75+360= $3735
Indirect 73*$100= $7300
Total : $11,035.
26
# 18
Pr T﹛ I ( 25 – 15 ) = 10 = ?≦ ﹜
E (TI) = 9.17 Var (TI) = 4.69
?
69.4
17.91010
Pr Z 0.383 =( 0.50+0.1492) =0.649﹛ ≦ ﹜
( P.530 )
27
# 19
(a)
1 2
4
3 5
6
7A=5
B=6
C=5
P1
F=7
D=4 G=2
H=6
By lnspection CP => A → B → E → G → H (25)
E=6
28
# 19
(b) Pr{ T 28 weeks| CP=ABEGH }=≦ ?
Pr{ T 32 weeks| CP=ABEGH }=≦ ?
Activities a m b μ =(a+4m+b)/6 σ2=(b-a)2/36
A 2 5 9 5.167‧ 1.361
B 1 6 8 5.5 ‧ 1.361
C 3 5 12 5.833 2.25D 2 4 12 5 2.778
E 4 6 8 6 ‧ 0.444
F 6 7 8 7 0.111
G 1 2 6 2.5 ‧ 0.694
H 4 6 16 7.333‧ 4
29
# 19
(c)
A → B → E → G → H Length = 26.5
Σσ2A-B-E-G-H=7.860 => σ=2.804
Pr{Z ≦ =0.535}=0.7037= 70.37﹪
Pr{Z =1.962}=0.9751= ≦ 97.51﹪
Pr{T X weeks| CP=ABEGH} = 95 ≦ ﹪
=1.645 ∴ X=31.11 weeks 804.2
5.26X Z ≦
804.2
5.2628
804.2
5.2632
#
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The EndThe End