OPERATION MANAGEMENT EXPERT ONLY

3. (30 points) draw the project network diagram represented by the following situation:

Activity	Immediate Predecessor(s)
A	-
B	-
C	A
D	B
E	B
F	C, E, D
G	D, E
H	F, G
I	G
J	E, H

4. For the following project network, the times for each activity are listed in the table below. There should be circles and arrows connecting some of the circles, in the diagram below. If these are not visible or did not print, please request assistance.

The following diagram is an AOA (Activity on Arrow). The AON (Activity on Node) equivalent of this is below. Continue to the next page to find the critical path method table to fill in. You can use either type of diagram, whichever you feel more comfortable using.

Note that in the diagram below, there should be an arrow from circle 1 to 2 that is labeled activity D. For some reason Word will not allow this to occur. Use the AON for clearer diagram.

F

J

C

A

G N P

2 K

D

start L O

1 H

B

M

E

I

AON:

4.a. (30 points) Fill in the table with the correct ES, EF, LS, LF, and slack.

Activity	Time	ES	EF	LS	LF	Slack
A	9
B	6
C	10
D	4
E	8
F	7
G	8
H	5
I	13
J	4
K	15
L	9
M	10
N	4
O	10
P	3

b. (5 points) Determine the critical path. Use the letters to indicate the critical path.

c. (5 points) Calculate the time to complete the project.

6. A local radio call-in show has about 15 calls arrive each hour, and the radio host spends about 3 minutes per caller, exponentially distributed. Assume no commercials and callers are immediately taken on the air if there is one waiting; all other appropriate assumptions also hold. Also assume that there is an infinite line possible, that is, callers will not get a busy signal but will always be put into a line to go on the air.

a. (5 points) What is the average number of callers waiting to go on the air?

b. (5 points) What is the average time to wait before going on the air?

c. (5 points) What is the utilization?

7. An airline ticket counter has one line feeding into 2 ticket agents. The airline is considering adding a third agent. Arrivals are spaced at an average of 4 minutes, Poisson distribution. An agent spends about 5 minutes per customer, exponentially distributed. All other appropriate assumptions hold.

a. (10 points) What is the average number in line waiting for service?

b. (5 points) What is the average wait time in line waiting for service?

c. (10 points) If a third agent is added, what is the average number in line waiting for service?

d. (5 points) If a third agent is added, what is the average wait time in line waiting for service?

J

P

F

A

K

G

N

C

0 0

Start

0 0 0

End

M

I

D

O

B

L

E

H