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 1In 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to 50, and so on, whereas units are withdrawn at the rate of 2 per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

(0, 0)

(20, 20)

Point of maximum inventory

(30, 0) Time (days)M

(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 1 Cont’d

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 Sound Reception

Price 1 3 4

Sound 1/3 1 3

Reception 1/4 1/3 1

Sound

A B C

A 1 1/2 1/4

B 2 1 1/3

C 4 3 1

Price

A B C

A 1 4 2

B 1/4 1 1/3

C 1/2 3 1

Reception

A B C

A 1 4 2

B 1/4 1 1

C 1/2 1 1

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

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.

State of Nature

Decision Alternative Reject, s1 1 Year, s2 2 Years, s3

Produce pilot, d1 -100 50 150

Sell to competitor, d2 100 100 100

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 assembly-line 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 SpeedNumber of Defective

Parts Found10 2020 3530 6040 5050 8560 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