A CEO of a multihospital system is planning to expand operations into various st
ID: 3054681 • Letter: A
Question
A CEO of a multihospital system is planning to expand operations into various states. It will take several years to get certificate of need (CON) approvals so that the new facilities can be constructed. The eventual cost (in millions of dollars) of building a facility will differ among states, depending upon finances, labor, and the economic and political climate. An outside consulting firm estimated the costs for the new facilities as based on declining, similar, or improving economies, and the associated probabilities as shown in the Table below:
(a) Which alternative should the firm choose under the maximax criterion? (1 mark)
(b) Which option should the firm choose under the maximin criterion? (1 mark)
(c) Which option should the firm choose under the LaPlace criterion? (2 marks)
(d) Which option should the firm choose with the Hurwicz criterion with ? = 0.4? (2 marks)
(e) Using a minimax regret approach, what alternative should the firm choose? (4 marks)
(f) Economists have assigned probabilities of 0.25, 0.40, and 0.35 to the possible economic climate of
declining, same and improving respectively. Using expected monetary values, what option should be
chosen and what is that optimal expected value? (4 marks)
(g) What is the most that the firm should be willing to pay for additional information? Use Expected Regret
(3 marks)
(h) Use the alternative method to verify EVPI (3 marks)
Question 1B
Assume now that the pay offs are profits answer the following:
(a) Using an optimistic approach (maximax), which option would you choose? 1 mark
(b) Using a pessimistic approach (maximin), which option would you choose?1 mark
(c) If you are a LaPlace decision maker, which option would you choose? 2 marks
(d) If you are a Hurwicz decision maker, which option would you choose with ? = 0.4?1 mark
(e) Using a minimax regret approach, which option would you choose? 4 marks
(f) Using the same probabilities of 0.25, 0.4, and 0.35 for possible economic climates respectively, which decision alternative will maximise the expected profit? What is the expected annual profit associated with that recommendation? 4 marks
g) What is the most the firm should be willing to pay to obtain further (perfect) information (EVPI)? 3 marks
h) Use the alternative method to verify EVPI (3 marks
Explanation / Answer
(a)
The payoff is eventual cost (in millions of dollars) of building a facility. The best payoff will be the minimum payoff.
The best payoff for Kentucky is 15.00.
The best payoff for Maryland is 18.00.
The best payoff for North Carolina is 15.50.
The best payoff for Tennesee is 14.00.
The best payoff for Virginia is 13.00.
The best of these best payoffs of each state is 13.00 for Virginia. So, by maximax criterion, Virginia state would be chosen.
(b)
Maximin is best of worst approach.
The worst payoff for Kentucky is 22.00.
The worst payoff for Maryland is 19.00.
The worst payoff for North Carolina is 19.50.
The best payoff for Tennesee is 23.00.
The worst payoff for Virginia is 25.00.
The best of these best payoffs of each state is 19.00 for Maryland. So, by maximin criterion, Maryland state would be chosen.
(c)
LaPlace criterion maximizes the average payoffs.
The average payoff for Kentucky is (22+19+15)/3 = 18.67.
The average payoff for Maryland is (19 + 18.5 + 18)/ 3 = 18.5.
The average payoff for North Carolina is (19.50 + 17 + 15.5)/3 = 17.33 .
The average payoff for Tennesee is (23 + 17 + 14)/3 = 18 .
The average payoff for Virginia is (25 + 21 + 13)/3 = 19.67.
The best of these average payoffs of each state is 17.33 for North Carolina. So, by LaPlace criterion, North Carolina state would be chosen.
(d)
Hurwicz criterion maximizes the weighted average payoffs.
weighted average payoff = 0.4 * best payoff + (1-0.4) * worst payoff = 0.4 * best payoff + 0.6 * worst payoff
The weighted average payoff for Kentucky is 0.4 * 15+ 0.6 * 22 = 19.2
The weighted average payoff for Maryland is 0.4 * 18 + 0.6 * 19 = 18.6
The weighted average payoff for North Carolina is 0.4 * 15.5 + 0.6 * 19.5 = 17.9
The weighted average payoff for Tennesee is 0.4 * 14 + 0.6 * 23 = 19.4
The weighted average payoff for Virginia is 0.4 * 13 + 0.6 * 25 = 20.2
The best of these weighted average payoffs of each state is 17.9 for North Carolina. So, by Hurwicz criterion, North Carolina state would be chosen.
(e)
Minimax regret approach minimizes the maximum regret.
Regret = Payoff received - Best Payoff
The regret table is,
The maximum regret for Kentucky is 3.
The maximum regret for Maryland is 5.
The maximum regret for North Carolina is 2.5.
The maximum regret for Tennesee is 4.
The maximum regret for Virginia is 6.
The minimum of maximum regret is 2.5 for North Carolina. So, by minimax regret criterion, North Carolina state would be chosen.
Decision Alternatives Declining Same Improving Kentucky 3 2 2 Maryland 0 1.5 5 North Carolina 0.5 0 2.5 Tennesee 4 0 1 Virginia 6 4 0Related Questions
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