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. Decision alternatives Declining Same Improving Kentucky 22.00 19.00 15.00 Maryland 19.00 18.50 18.00 North carolina 19.50 17.00 15.50 Tennesee 23.00 17.00 14.00 Virginia 25.00 21.00 13.00 The first part should be done as cost and the second part should be done as profits. (a) Which alternative should the firm choose under the maximax criterion? (b) Which option should the firm choose under the maximin criterion? (c) Which option should the firm choose under the LaPlace criterion? (d) Which option should the firm choose with the Hurwicz criterion with α = 0.4? (e) Using a minimax regret approach, what alternative should the firm choose? (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? (g) What is the most that the firm should be willing to pay for additional information? Use Expected Regret (h) Use the alternative method to verify EVPI Question 1B Assume now that the payoffs are profits answer the following: (a) Using an optimistic approach (maximax), which option would you choose? (b) Using a pessimistic approach (maximin), which option would you choose? (c) If you are a LaPlace decision maker, which option would you choose?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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Question

Question 1A

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.

Decision alternatives	Declining	Same	Improving
Kentucky	22.00	19.00	15.00
Maryland	19.00	18.50	18.00
North carolina	19.50	17.00	15.50
Tennesee	23.00	17.00	14.00
Virginia	25.00	21.00	13.00

The first part should be done as cost and the second part should be done as profits.

(a) Which alternative should the firm choose under the maximax criterion?
(b) Which option should the firm choose under the maximin criterion?
(c) Which option should the firm choose under the LaPlace criterion?
(d) Which option should the firm choose with the Hurwicz criterion with α = 0.4?
(e) Using a minimax regret approach, what alternative should the firm choose?

(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?
(g) What is the most that the firm should be willing to pay for additional information? Use Expected Regret
(h) Use the alternative method to verify EVPI

Question 1B
Assume now that the payoffs are profits answer the following:

(a) Using an optimistic approach (maximax), which option would you choose?
(b) Using a pessimistic approach (maximin), which option would you choose?
(c) If you are a LaPlace decision maker, which option would you choose?
(d) If you are a Hurwicz decision maker, which option would you choose with α = 0.4?
(e) Using a minimax regret approach, which option would you choose?
(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?