Due Day: Dec 8 (Monday), 2008 (9:00AM) EMGT 501 Fall 2008 Final Exam Due Day: Dec 8 (Monday), 2008 (9:00AM) 1

(c) Answer on a series of PPS. 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. 2

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day, and a is 2 per day, then 3 units of stock arrive each day for days 1 to 20, 31 to 50, and so on, whereas units are withdrawn at the rate of 2 per day every day.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 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. 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 Construct the rate diagram for this queuing system. 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. Compute the priorities for each pair-wise comparison matrix. Determine an overall priority for each system. Which stereo system is preferred?

Question 3 Cont’d Criterion Price Reception Sound Price Sound 1 3 4 1/3 1/4 Price A B C 1 4 2 1/4 1/3 1/2 3 Reception A B C 1 4 2 1/4 1/2 Sound A B C 1 1/2 1/4 2 1/3 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 Decision Alternative Reject, s1 1 Year, s2 2 Years, s3 Produce pilot, d1 -100 50 150 Sell to competitor, d2 100 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 Construct a decision tree for this problem. What is the recommended decision if the agency opinion is not used? What is the expected value? What is the expected value of perfect information? What is Hale’s optimal decision strategy assuming the agency’s information is used? What is the expected value of the agency’s information? Is the agency’s information worth the $5000 fee? What is the maximum that Hale should be willing to pay for the information? What is the recommended decision?

Number of Defective Parts Found 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 Speed Number of Defective Parts Found 10 20 35 30 60 40 50 85 100

Question 5 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. 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 15