(a) Briefly explainHurwicz’s criterion for decision making. Is this criterion an optimist, conservative, or middle of the road approach? Give a real world example whereHurwicz’s criterion can be useful.
It stipulates that a decision maker’s view may fall somewhere between the extreme pessimism of the maximin principle and the extreme optimism of the maximax principle. This principle provides different levels of optimism or pessimism, by defining the coefficient of optimism, , which ranges from 0 to 1. An indicates extreme pessimism, while indicates extreme optimism. Hurwicz principle suggests that the decision maker must select an alternative that minimizes:
H = × (maximum payoff of strategy) + (1 − ) × (minimum payoff of strategy)
If the decision-maker tends to be optimistic than pessimistic, then he will define the coefficient of optimism between 1 to 0.5. If the decision-maker tends to more pessimistic than optimistic, then he can define the coefficient of optimism between 0.5 to 0.
Thus, the Hurwicz principle is middle of road approach between optimistic and conservative approaches.
(b) 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.
(c) What is a capital budgeting integer programming problem? Briefly describe the typical objective function and constraints present in a capital budgeting problem. Give a real world example of a capital budgeting problem.
(d)Briefly describe different elements of queuing analysis. Give a real world example and identify the different elements in your example.
2. A constructioncompany is considering five projects. The projects, the number of supervisors and the number of workers required for each project, and the expected profits for each project are given below.
1 2 3 4 5
Supervisors Required 5 4 4 6 3
Workers Required 14 18 28 30 24
Profit (in thousands of dollars) 250 275 290 320 200
The objective is to maximize the company’s total expected profit subject to the following constraints:
– Use no more than 18 supervisors
– Use no more than 100workers
– If project 1 is done, then project 3 must be done and vice versa
– At least three projects are to be done.
Formulate a capital budgeting integer programming problemfor 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. A U.S.-based manufacturer of personal computers is planning to build a newmanufacturing and distribution facility in one of the countries: China, the Philippines,or Mexico. The eventual benefit of the facility will differbetween 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:
Country Improvement Same Decline
China 18.2 13.3 13.0
Philippines 20.6 13.5 14.6
Mexico 21.0 17.8 10.8
(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 improvement in economic/political climate is 0.3, the probability of same economic/political climate is 0.4, and the probability of decline in economic/political climate is 0.3. 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?
(c) Calculate and interpret the value of perfect information.
5. A librarian at a college library, on an average, could process 19 students during one hour. On an average, a student arrives to her at every 4 minutes. 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 student will have an empty queue.
(c) Determine the probability that 2students are in the queuing system.
(d) Determine the average number of students in the queue and the average number of students in the system.
(e) Determine the average waiting time in the queue and the average total time in the system for a student.
(f) Find the utilization factor of the librarian.
6. In Question 5, suppose the current librarian can be replaced by a specialist, who must be paid $30 per hour whereas the current librarian is paid $20 per hour. The specialist can process 23students in one hour. If a student’s time is considered to be worth $10 per hour, is it worth to replace the current librarian with the specialist? Calculate the total cost of paying the current librarian and the students’ time and the total cost of paying the specialist and the students’ time to answer this question.