operation management Homework

Topics: Critical path method, Harshad number, Project management Pages: 14 (508 words) Published: October 12, 2013
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
24
24
24

BDEH
6700

BDEH,BDFH
E
150
6850

BDEH,BDFH
D
100
6950

BDEH,BDFH
F,E
200+150
7300

 When project completed in 24 months, activity E, D, F will be crashed 2, 1, 1 separately, and total incremental cost is 600$

Problem2
a) The pre-triage system process flow diagram
A flow unit = a patient

Sign-in
Numbered sheet

Waiting
Retrieve record and
send to the clinic

Waiting area

Receptionist

Bring the record to
the medical desk
Receptionist

Check to ensure
information

Evaluation by NP

Clerk

Place the medical
record in a pile
for the physicians

Nurse

Nurse

Place the record
and the numbered
sheet in a pile
Clerk

Treatment by NP
Nurse

Treatment by MD
Physician

The post-triage system process flow diagram
A flow unit = a patient
Review AVF form
Receptionist

Notify a triage to assess

Notify a physician to assess

Retrieve
record
Receptionist
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