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

#

30

The EndThe End