Assignment:
1. (a) In decision analysis models, what do the terms decision alternatives, states of nature, and payoff represent? Give a real world example and identify these terms in your example.
(b) What are the different types of integer programming problems? Briefly describe each type and give one real world example for each type.
(c) How is the simulation process used in the 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.
(d) Briefly describe the different types of queue disciplines. Give one real world example for each type.
2. A company is considering 5 proposals for investment. The table below displays each proposal's net present value (NPV) in millions of dollars and each proposal's requirements for cash (in millions of dollars) for each of the next three years.
Cash Requirements
Proposal NPV Year 1 Year 2 Year 3
1 12.8 4.40 3.30 3.50
2 10.5 4.30 2.50 2.10
3 9.4 4.10 3.40 1.50
4 11.7 4.70 3.90 3.10
5 10.2 5.00 3.40 0.75
The manager wants to maximize the total NPV while meeting the following restrictions:
(i) The total cash requirement cannot exceed 14.2 million dollars in the first year.
(ii) The total cash requirement cannot exceed 12.8 million dollars in the second year.
(iii) The total cash requirement cannot exceed 10 million dollars in the third year.
(iii) At most three of the proposals can be approved.
(iv) If proposal 1 is approved then proposal 3 must also be approved.
Formulate a capital budgeting integer programming problem for this situation by defining
(a) The decision variables.
(b) The objective function. What does it represent?
(c) All the constraints. What does each constraint represent?
Note: Do NOT solve the problem after formulating.
3. The Charming City Consultants Inc. wants to build a new network of computers for its employees. The management of the company is considering three network sizes for the possible purchase: large, medium, or small. The management believes that the demand for their services will be either high level, medium level, or low level. The payoff (profit in dollars) table for the situation is given below:
Demand Level
Decision High Medium Low
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Large Size $200,000 $ 110,000 $ 70,000
Medium Size $150,000 $160,000 $100,000
Small Size $210,000 $120,000 $130,000
(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?
(c) What is the best decision using the minimax regret criterion? What is the regret for it?
(d) What is the best decision using the Hurwicz's criterion if α = 0.3? What is the payoff for it?
4. For the problem given in Question 3, assume that the probability of high demand level is 0.2, the probability of medium demand level is 0.5, and the probability of low demand level is 0.3.
(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?
(c) Calculate and interpret the value of perfect information.
5. Monica works at a cafeteria counter in a food court. Customers arrive at a mean rate of 7 per hour. The mean service rate is 9.5 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 customer will have an empty queue.
(c) Determine the probability that 4 customers are in the queuing system.
(d) Determine the average number of customers in the queue and the average number of customers in the system.
(e) Determine the average waiting time in the queue and the average total time in the system for a customer.
(f) Find the utilization factor of the server.
6. In Question 5, suppose Monica can be replaced by another server, Jodi, who must be paid $14 per hour whereas Monica is paid $10 per hour. Jodi can serve 11 customers per hour. If a customer's time is considered to be worth $10 per hour, is it worth to replace Monica with Jodi? Calculate the total cost of paying Monica and the customers' time and the total cost of paying Jodi and the customers' time to answer this question.
(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?
(c) What is the best decision using the minimax regret criterion? What is the regret for it?
(d) What is the best decision using the Hurwicz's criterion if α = 0.3? What is the payoff for it?