operation management Homework

OPRE 6302: Homework Assignment 5
Problem1
a) Draw the project network diagram
C(2)
E(8)

A(3)

B(4)

G(4)

H(9)
D(6)

F(7)

b) List all the paths in the network diagram. Say which one(s) is(are) the critical path(s) and what the minimum project duration is.
 PATHS
ACEG=3+2+8+4=17 months
ACEH=3+2+8+9=22 months
BDEG=4+6+8+4=22 months
BDEH=4+6+8+9=27 months
BDFH=4+6+7+9=26 months
 Critical path: BDEH
 Minimum project duration: 27 months

c) For each activity compute ES, EF, LS LF and slack. Then, say which activities are critical.
3
0
5

8

3

5

10 18

10

10 18

C(2)

8

18 22
23 27

G(4)

E(8)

A(3)

18

0
0

B(4)

4
4

4
4

18

10
10

10
11

D(6)

17
18

27
27

H(9)

F(7)

ES EF
LS LF

A
B
C
D
E
F
G
H

ES
0
0
3
4
10
10
18
18

EF
3
4
5
10
18
17
22
27

 Critical activities: B,D,E,H

LS
5
0
8
4
10
11
23
18

LF
8
4
10
10
18
18
27
27

Slack
5
0
5
0
0
1
5
0

d) What is the cost of competing the project if its duration is what you obtained in (b)?
 Total cast:
700+900+1100+600+800+1300+500+800=6700($)
e) Project needs to be completed in 24 months. Determine which activities need to be crashed and what will be the incremental cost.
Activity Normal duration(months) A 3
B 4
C 2
D 6
E 8
F 7
G 4
H 9

Crash duration(months) 1
4
1
5
6
5
4
6

Normal cost($) 700
900
1100
600
800
1300
500
800

Crash cost($) 750
900
1150
700
1100
1700
500
2300

Crash cost/month 25
0
50
100
150
200
0
500

Max # of crashes 2
0
1
1
2
2
0
3

Crash activities so that the project is completed in 24 months.
PATHS
ACEG
ACEH
BDEG
BDEH
BDFH
MIN. PROJECT
DURATION(MONTHS)
CRITICAL PATHS
ACTIVITIES CRASHED
INCREMENTAL COST($)
TOTAL COST($)

START
17
22
22
27
26
27

1ST CRASH
16
21
21
26
26
26

2ND CRASH
16
21
20
25
25
25

3RD CRASH
15
20
19