Gestão de Operações

UCP-FCEE
Soluções Exercícios aulas práticas 16
Gestão de Operações
1.
a. Create an activity-on-arc (AOA) network diagram for this project.
See diagram below
b. Calculate the early start (ES), early finish (EF), late start (LS), and late finish (LF) for
each activity. Add these values to your path diagram.
See Diagram below, boxes contain data on ES, EF, LS, and LF
c. Determine the critical path for the project. What is its length (in weeks)?
Critical path is shown in red and is 69 weeks long.
I 15
ES 12 EF 27
LS 48 LF 63
A 12
ES 0
LS 2
F 10
ES 12
EF 22
LS 53 LF 63
6
EF 12
LF 14
C 10
ES 12 EF 22
LS 14 LF 24
Start
B9
ES 0 EF 9
LS 0 LF 9
2
Dummy 0
ES 27 EF 27
LS 63 LF 63
8
D 10
ES 9
LS 9
EF 19
LF 19
5
G 35
ES 22
LS 24
7
3
H 40
ES 19
LS 19
EF 59
LF 59
J4
ES 59
LS 59
4
d. Calculate the slack for each activity not on the critical path.
A: 2-0 =2, C: 14-12=2, E: 35-9=26, F: 53-12=41, G: 24-22=2, I: 48-12=36
a. What is the crash cost per week for all activities in the network?
MAXIMUM
TIME
ACTIVITY REDUCTION
A
1
B
2
C
5
D
2
E
10
F
4
G
10
H
5
I
5
J
3
EF 69
LF 69
Finish
EF 57
LF 59
E 24
ES 9
EF 33
LS 35 LF 59
2.
K6
ES 63
LS 63
COST TO
CRASH CRASH PER
COST
WEEK
$ 1,000
$ 1,000
14,000
7,000
3,000
600
4,000
2,000
80,000
8,000
6,000
1,500
30,000
3,000
60,000
12,000
12,500
2,500
3,000
1,000
EF 63
LF 63
UCP-FCEE
Soluções Exercícios aulas práticas 16
Gestão de Operações
K
1
4,000
4,000
b. Which activities did you crash to achieve the 63 weeks?
J – D – K selected in order of increasing cost per week to crash
c. What is the added cost of completing the project in 63 weeks?
J – 3 weeks @ $1000 / Wk
D – 2 weeks @ $2000 / Wk
K – 1 week @ $4000 / Wk
Total cost $11,000
d. What will it cost to decrease the schedule to 62 weeks from 63 weeks?
Both activities B and C need to be crashed, since there are now two critical paths through
the network (A-C-G-J-K and B-D-H-J-K). The cost is $7000 for B plus $600 for C for a
total of $7,600 to go from 63 weeks to 62 weeks.
3.
a) The activity-on-arc network is as follows:
[15, 18]
(15, 18)
7
2
[0, 3]
(2, 5)
1
[3, 3]
(5, 5)
0
A
B
[0, 5]
(0, 5)
[7, 11]
(11, 15)
3
G
C
[5, 7]
(5, 7)
4
[7, 12]
(7, 12)
0
D
J
[15, 15]
(15, 15)
[7, 13]
(9, 15)
E
H
8
6
[12, 15]
(12, 15)
I
[15,1 9]
(16, 20)
9
[18, 20]
(18, 20)
K
[20, 22]
(20, 22)
F
5
b) The ES, LS, EF and LF values are given in the table below as well as on the
network diagram above.
10
UCP-FCEE
Soluções Exercícios aulas práticas 16
Gestão de Operações
Activity
A
B
C
D
E
F
G
H
I
J
K
ES
0
0
5
7
7
12
7
15
15
18
20
EF
3
5
7
13
12
15
11
18
19
20
22
LS
2
0
5
9
7
12
11
15
16
18
20
LF
5
5
7
15
12
15
15
18
20
20
22
Slack
2
0
0
2
0
0
4
0
1
0
0
c) The critical path for the project is B-C-E-F-(6,7) dummy-H-J-K, with a length of 22
weeks.
d) The slacks for the non-critical path activities (A, D, G, I) are given in the table in
part (b). Note that only the non-critical path activities have non-zero slack.
4.
a) The following solution provides the step by step process used to obtain the required
18-week project length.
Step 1 – list all path lengths in the network prior to crashing:
Path
B-C-G-H-J-K
B-C-D-I-K
B-C-D-(6, 7) dummy-H-J-K
B-C-E-F-(6, 7) dummy-H-J-K
B-C-E-F-I-K
A-(2, 3) dummy-C-G-H-J-K
A-(2, 3) dummy-C-D-I-K
A-(2, 3) dummy-C-D-(6, 7) dummy-H-J-K
A-(2, 3) dummy-C-E-F-(6, 7) dummy, H-J-K
A-(2, 3) dummy-C-E-F-I-K
Length
(weeks)
18
19
20
22
21
16
17
18
20
19
Step 2 – Crash the activity on the critical path with the minimum crash cost/week. This is activity E,
which can be crashed at a cost of $475/week. We crash activity E by 2 weeks because this is the amount
until another path, B-C-D-(6,7) dummy-H-J-K, becomes critical. This costs $950 ($475*2 weeks). The
new list of path lengths is as follows:
Path
B-C-G-H-J-K
B-C-D-I-K
B-C-D-(6, 7) dummy-H-J-K
B-C-E-F-(6, 7) dummy-H-J-K
B-C-E-F-I-K
A-(2, 3) dummy-C-G-H-J-K
A-(2, 3) dummy-C-D-I-K
A-(2, 3) dummy-C-D-(6, 7) dummy-H-J-K
A-(2, 3) dummy-C-E-F-(6, 7) dummy, H-J-K
A-(2, 3) dummy-C-E-F-I-K
Length
(weeks)
18
19
20
20
19
16
17
18
18
17
UCP-FCEE
Gestão de Operações
Soluções Exercícios aulas práticas 16
Step 3 – The critical paths are now B-C-D-(6, 7) dummy-H-J-K and B-C-E-F-(6, 7)
dummy-H-J-K. Activity C is now the activity on the critical path with the lowest crash
cost/week. Crash C to its maximum extent since all path lengths contain this activity.
This costs $750 ($500*1.5 weeks), and yields the following path lengths:
Path
B-C-G-H-J-K
B-C-D-I-K
B-C-D-(6, 7) dummy-H-J-K
B-C-E-F-(6, 7) dummy-H-J-K
B-C-E-F-I-K
A-(2, 3) dummy-C-G-H-J-K
A-(2, 3) dummy-C-D-I-K
A-(2, 3) dummy-C-D-(6, 7) dummy-H-J-K
A-(2, 3) dummy-C-E-F-(6, 7) dummy, H-J-K
A-(2, 3) dummy-C-E-F-I-K
Length
(weeks)
16.5
17.5
18.5
18.5
17.5
14.5
15.5
16.5
16.5
15.5
Step 4 – The critical paths remain as B-C-D-(6,7) dummy-H-J-K and B-C-E-F-(6, 7)
dummy-H-J-K. Activity B now has the lowest total crashing cost on the critical path at
$750/week. Since we only need to reduce the project by .5 weeks now, crash activity B
by this amount at a cost of $375 ($750*.5 weeks). The project completion target of 18
weeks is now achieved. The final crashed path lengths are as follows:
Path
B-C-G-H-J-K
B-C-D-I-K
B-C-D-(6, 7) dummy-H-J-K
B-C-E-F-(6, 7) dummy-H-J-K
B-C-E-F-I-K
A-(2, 3) dummy-C-G-H-J-K
A-(2, 3) dummy-C-D-I-K
A-(2, 3) dummy-C-D-(6, 7) dummy-H-J-K
A-(2, 3) dummy-C-E-F-(6, 7) dummy, H-J-K
A-(2, 3) dummy-C-E-F-I-K
Length
(weeks)
16
17
18
18
17
14.5
15.5
16.5
16.5
15.5
b) The total cost of crashing the project down to 18 weeks is $2075 ($950 + $750 +
375).
c) The final critical paths are B-C-D-(6,7) dummy-H-J-K and B-C-E-F-(6, 7) dummyH-J-K.