Note: to use Excel, the data below can be copy/pasted into a spread sheet, saving you the time and irritation of doing it all yourself. Usually (though it can depend on your spread sheet software and computer) you can select a table below, then go to a cell in a spread sheet, and do a "paste special" (or sometimes just "paste" will work). You might have to fiddle around, but you can get it to work and it will eventually save you time over the weeks to come.

5. Telecomp is a US based manufacturer of cellular telephones. It is planning to build a new facility in either South Korea, China, Taiwan, Poland, or Mexico. The cost of the facility will differ between countries and will even vary within countries depending on the economic and political climate, including monetary exchange rates. The company has estimated the facility cost (in $1000000) in each country under three different future economic/political climates (given in the table below).

		Economic/Political Climate
Country	Decline	Same	Improve
South Korea	21.7	19.1	15.2
China	19	18.5	17.6
Taiwan	19.2	17.1	14.9
Poland	22.5	16.8	13.8
Mexico	25	21.2	12.5

Determine the best decision using each (so, you will have possibly a different answer for each criterion) of the following decision criteria (Note: payoff is cost, which one wants to be smallest, so, rather than use the maximax criterion one uses minimin and rather than maximin use minimax):

• Minimin (i.e., for each decision possibility, assume the most optimistic payoff, i.e., least cost, economic climate, then make the decision that has the minimum cost)
• Minimax (i.e., min of the max cost)
• Minimax Regret (i.e., first choose min cost for each climate, get regrets by subtracting those mins from the other decisions in each climate, then max regrets for each decision and make the decision with minimal max regret)
• Hurwicz with = 0.40 (i.e., minimize over decision possibilities * min cost + (1-) * max cost)
• Equal Likelihood (i.e., maximize the equally weighted averages over economic climates)
  • Note: There are all sorts of ways of doing these Hybrid scores (where you calculate a score for each decision option and then pick the best scoring choice) and different explanations of how to do them. Looking at each decision option, there is a best "state of nature" for that decision choice and a worst state of nature. Multiply alpha times the best and (1-alpha) times the worst, add them and that is the score for that decision. Do that same calculation for each decision option (i.e., find best state of nature, worst state of nature, multiply accordingly by alpha or 1-alpha, add them), so as to get a score for each decision option. The option with the greatest score is the Hurwitcz-decision for the given payoff matrix. The confusing thing is that it's likely every time I explain this to someone (or even to myself) I do it slightly differently but basically they are all the same descriptions. Sorry for any confusion.

6. Jillian Smith has come into an inheritance from her grandparents. She is attempting to decide among several investment alternatives. The return after one year is dependent primarily on the interest rate during the next year. The rate is currently 7%, and she anticipates it will stay the same or go up or down by at most 2%. For the various investment alternatives, the returns (in $10000) for each interest rate that might be in effect are shown in the following table.

			Rates
Investments	5%	6%	7%	8%	9%
MMFund	1.7	2.8	3	3.6	4.5
Stock Growth fund	-5	-3	3.5	5	7.5
Bond fund	5	4	3.5	3	2
Government fund	4	3.6	3.2	2.8	2.1
Risk fund	-12	-7	4.2	9.3	16.7
Savings bonds	3	3	3.2	3.4	3.5

Determine the best investment using the following decision criteria (and here you want to maximize payoff).

• Maximax
• Maximin
• Minimax Regret
• Equal Likelihood

Now assume Jillian, after doing some research, has been able to assign probabilities to each of the possible interest rates during the next year as follows:

Interest Rate	5%	6%	7%	8%	9%
Probability	.1	.2	.4	.2	.1

Using expected payoffs determine her best investment decision.

7. The director of career advising at Rider University want to use decision analysis to provide information to help students decide which degree program they should pursue. The director has set up the following payoff table for 6 of the most popular and successful degree programs at RU that shows the estimated (projected) 5-year gross income (in $1000) that an average student graduating with each degree for 4 future economic conditions can expect:

		Economic	Conditions
Degree Program	Recession	Average	Good	Robust
Nursing	115	155	190	180
Law	140	175	200	220
Finance	95	150	180	250
Computer Programming	120	140	150	170
Information Systems	85	120	150	180
Music and Theater	60	80	100	100

Determine the best degree program (a decision under uncertainty) in terms of the projected income, using the following decision criteria:

• Maximax
• Maximin
• Equal Likelihood
• Minimax Regret
• Hurwicz with = .25

If further it has been determined that the probability of each future economic condition is given by:

p(recession)=.45, p(average)=.35, p(good)=.15, p(robust)=.05.

Use expected value to determine the best degree program (a decision under risk presuming equally likely futures) in terms of projected income. If you were the director of career advising which degree program would you recommend (in particular, do you agree with optimizing the expected payoff or some other criteria)?

8. The management of a major US bank was concerned about the potential loss that might occur in the event of a physical catastrophe such as a power failure or a fire. The bank estimated that the loss from one of these incidents could be as much as $100 million, including losses due to interrupted service and customer relations. One project the bank is considering is the installation of an emergency power generator at its operations headquarters. The cost of the emergency generator is $900,000 and if it is installed no losses from this type of incident will be incurred. However, if the generator is not installed, there is a 10% chance that a power outage will occur during the next year. If there is an outage, there is a .04 probability that the resulting losses will be very large, or approximately $90 million in lost earnings. Alternatively, it is estimated that there is a .96 probability of only slight losses of around $2 million. Using decision tree analysis, determine whether the bank should install the new power generator or not.

Hint: One must decide to install a generator or not. If installed, no worries but it does cost $900,000. On the other hand if not installed, there may or may not be a power outage, and then there may or may not be a large loss. Working backward from the losses (large or small), calculate the expected cost of an outage (no outage costs $0), and finally then calculate the expected cost of no installation. Compare to the cost of installation to make the decision. All this works best if you draw the tree of decisions, costs, and probabilities.