EMGT 501
Fall 2008
Final Exam
Due Day: Dec 8 (Monday), 2008
(9:00AM)
Note:
(a) Do not send me after copying your computer
results. See my HW on my HP regarding how to
prepare your answers.
(b) I need your professional preparation. Large
Characters at the level that I can read.
(c) Answer on a series of PPS.
(d) Do not discuss the exam with other students.
(e) Return your answer attached to your e-mail.
Question 1
In the basic EOQ model, suppose the stock is replenished
uniformly (rather than instantaneously) at the rate of b items per
unit time until the order quantity Q is fulfilled. Withdrawals from
the inventory are made at the rate of a items per unit time, where
a < b. Replenishments and withdrawals of the inventory are made
simultaneously. For example, if Q is 60, b is 3 per day, and a is 2
per day, then 3 units of stock arrive each day for days 1 to 20, 31
to 50, and so on, whereas units are withdrawn at the rate of 2 per
day every day. The diagram of inventory level versus time is
given below for this example.
Question 1 Cont’d
Inventory
level
(20, 20)
Point of
maximum
inventory
(0, 0)
M
(30, 0)
Time (days)
Question 1 Cont’d
(a) Find the total cost per unit time in terms of the setup
cost K, production quantity Q, unit cost c, holding
cost h, withdrawal rate a, and replenishment rate b.
(b) Determine the economic order quantity Q*.
Question 2
The reservation office for Central Airlines has two Agents
answering incoming phone calls for flight reservations. In
addition, one caller can be put on hold until one of the agents in
available to take the call. If all three phone lines (both agent lines
and the hold line) are busy, a potential customer gets a busy
signal, in which case the call may go to another airline. The calls
and attempted calls occur randomly (i.e., according to a Poisson
process) at a mean rate of 15 per hour. The length of a telephone
conversation has an exponential distribution with a mean of 4
minutes.
Question 2 Cont’d
(a) Construct the rate diagram for this queuing system.
(b) Find the steady-state probability that
( i ) A caller will get to talk to an agent immediately,
( ii ) The caller will be put on hold, and
( iii ) The caller will get a busy signal.
Question 3
A woman considering the purchase of a custom sound stereo
system for her car looked at three different systems (A, B, and
C), which varied in terms of price, sound quality, and FM radio
reception. The following pair-wise comparison matrixes were
developed.
(a)Compute the priorities for each pair-wise comparison matrix.
(b)Determine an overall priority for each system. Which stereo
system is preferred?
Question 3 Cont’d
Criterion
Price
Price
Sound
Reception
A
B
C
Price
1
3
4
A
1
4
2
Sound
1/3
1
3
B
1/4
1
1/3
Reception
1/4
1/3
1
C
1/2
3
1
Reception
Sound
A
B
C
A
1
4
2
1/3
B
1/4
1
1
1
C
1/2
1
1
A
B
C
A
1
1/2
1/4
B
2
1
C
4
3
Question 4
Hale’s TV Production is considering producing a pilot for a
comedy series in the hope of selling it to a major television
network. The network may decide to reject the series, but it may
also decide to purchase the rights to the series for either one or
two years. At this point in time, Hale may either produce the pilot
and wait for the network’s decision or transfer the rights for the
pilot and series to a competitor for $100,000. Hale’s decision
alternatives and profits (in thousands of dollars) are as follows:
Question 4 Cont’d
State of Nature
Reject, s1
1 Year, s2
2 Years, s3
Produce pilot, d1
-100
50
150
Sell to competitor, d2
100
100
100
Decision Alternative
The probabilities for the states of nature are P(s1) = 0.20, P(s2) =
0.30, and P(s3) = 0.50. For a consulting fee of $5000, an agency
will review the plans for the comedy series and indicate the
overall chances of a favorable network reaction to the series.
Assume that the agency review will result in a favorable (F) or an
unfavorable (U) review and that the following probabilities are
relevant.
P(F) = 0.69
P(s1│F) = 0.09
P(s1│U) = 0.45
P(U) = 0.31
P(s2│F) = 0.26
P(s2│U) = 0.39
P(s3│F) = 0.65
P(s3│U) = 0.16
Question 4 Cont’d
(a) Construct a decision tree for this problem.
(b) What is the recommended decision if the agency opinion is not
used? What is the expected value?
(c) What is the expected value of perfect information?
(d) What is Hale’s optimal decision strategy assuming the agency’s
information is used?
(e) What is the expected value of the agency’s information?
(f) Is the agency’s information worth the $5000 fee? What is the
maximum that Hale should be willing to pay for the
information?
(g) What is the recommended decision?
Question 5
The supervisor of a manufacturing process believed that assemblyline speed (in feet/minute) affected the number of defective parts
found during on-line inspection. To test this theory, management had
the same batch of parts inspected visually at a variety of line speeds.
The following data were collected.
Line Speed
10
20
30
40
50
60
Number of Defective
Parts Found
20
35
60
50
85
100
Question 5
(a) Develop the estimated regression equation that relates
the line speed to the number of defective parts found.
Use both Goal Programming and Least Squares
Method to fit a regression line to the data set.
Compare these results.
(b) Use the equations developed in part (a) to forecast the
number of defective parts found for a line speed of 100
feet per minute. Predict the values based upon the two
methods.
Assessment II
• Please indicate the current level of your knowledge. (1: no
idea, 2: little, 3: considerable, 4: very well).
•
•
•
•
•
•
Topic
Your Assessment
(1) Queuing
(2) Decision Analysis
(3) Multi-Criteria Decision Making
(4) Forecasting
(5) Markov Process
• Return the assessment to toshi@nmt.edu