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You can use a calculator to do numerical calculations. No graphing calculator is allowed. Please DO NOT USE ANY COMPUTER SOFTWARE to solve the problems.

All six questions are required.

Question 1: 24 Points

Questions 3 and 5: 20 Points each

Questions 2, 4, and 6: 12 Points each

1. (a) Explain the concept of value of perfect information in decision analysis. Give a real world example where the value of perfect information will be useful to a decision maker.

(b) Briefly describe different elements of queuing analysis. Give a real world example and identify different elements in your example.

(c) What are the zero-one integer programming problems? Why are they so useful in real world situations? Briefly describe a real world example of a zero-one integer programming problem.

(d) How is the simulation process used in Decision Sciences models? What are the advantages of using simulation? What are its limitations? How can a simulation model be verified? Give a real world example where using simulation is appropriate.

2. An undergraduate business major is attempting to determine her course schedule for the fall semester. She is considering six courses, which are shown in the following table. Also included are the number of hours she expects to have to devote to each course each week and her expected grade in each course:

Course Hours per Week Expected Grade

Management I 6 3.2

Principles of Accounting 12 4

Corporate Finance 8.5 2.7

Marketing Management 7.4 3.3

Introduction to Computers 10 2.8

Entrepreneurship 7 3.2

She does not want to work more than 32 hours each week. Principles of Accounting, Corporate Finance, and Introduction to Computers all require a lot of computing or mathematics, and she would like to take no more than two of these courses. To remain on schedule and meet prerequisites, she needs to take at least two of the following courses: Management I, Principles of Accounting and Introduction to Computers. To remain a full time student, she must take at least 4 courses. The student wants to develop a course schedule that will maximize the total expected grade.

Formulate a capital budgeting problem for the above situation by determining

(a) The decision variables.

(b) The objective function.

Note: Do NOT solve the problem after formulating.

3. A U.S.-based manufacturer of personal computers is planning to build a new manufacturing and distribution facility in one of the countries: China, the Philippines, or Mexico. The eventual benefit of the facility will differ between countries and will even vary within countries depending on the economic and political climate. The company has estimated the expected total profit (in millions of dollars) for the facility in each country under three different future economic/political climates, as follows:

Economic/Political Climate

Country Improvement Same Decline

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China 21.4 17.5 16.2

Philippines 23.8 16.5 17.8

Mexico 24.2 21.0 14.0

(a) What is the best decision using the maximax criterion? What is the payoff for it?

(b) What is the best decision using the maximin criterion? What is the payoff for it?

(d) What is the best decision using the Hurwicz’s criterion if α = 0.6? What is the payoff for it?

4. For the problem given in Question 3, assume that the probability of improvement in economic/political climate is 0.4, the probability of same economic/political climate is 0.2, and the probability of decline in economic/political climate is 0.4. Answer the following questions using the payoff table given in Question 3.

(a) Calculate the expected value of each decision alternative. What is your recommendation using the expected value criterion?

(b) Calculate the expected opportunity loss value of each decision alternative. What is your recommendation using the expected opportunity loss criterion?

5. The Charm City Manufacturing Company manufactures a product in an assembly line operation. One of the machines on the line is a drill press that has a single assembly line feeding into it. A partially completed unit arrives at the press to be worked on every 8 minutes, on average. The machine operator can process an average of 10.5 units per hour. Assume it is a single-server waiting line model.

(a) Determine the mean arrival rate and the mean service rate.

(b) Determine the probability that a unit will have an empty queue.

(d) Determine the average waiting time in the queue and the average total time in the system for a unit.

(e) Find the utilization factor of the operator.

6. In Question 5, suppose the current operator can be replaced by a more efficient new operator, but the new operator is paid $28 per hour whereas the current operator is paid $22 per hour. The new operator can process 12.2 units per hour. If a unit’s time is considered to be worth $12 per hour, is it worth to replace the current operator with the new operator?