Question

Telecomp is a U.S.-based manufacturer of cellular telephones. It is planning to build a new manufacturing and distribution 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 $ millions) in each country under three different future economic/political climates as follows.Economic/Political Climate Country Decline Same Improve South Korea 21.7 19.1 15.2 China 19.0 18.5 17.6 Taiwan 19.2 17.1 14.9 Poland 22.5 16.8 13.8 Mexico 25.0 21.2 12.5 Determine the best decision using the following decision criteria. (Note that since the payoff is cost, the maximax criteria becomes minimax and maximin becomes minimax.)
a. Maximin
b. Minimax
c. Hurwicz ( 0.40)
d. Equal likelihood

Answer 1

Answer:

a. Maximin =  19.0

b. Minimax  = 17.6

c. Hurwicz ( 0.40)  = Taiwan

d. Equal likelihood = Taiwan

Explanation:

Remember, we are told to: Note that since the payoff is cost, the maximax criteria becomes minimax and maximin becomes minimax

a) Maximin: Since the payoff is cost, we begin by determining the maximum cost for each alternative and then selecting the one which gives the minimum of these maximums. (minimax)

b) Minimax: Since the payoff is cost, we begin by determining the minimum cost for each alternative and then selecting the one which gives the maximum of these minimums. (maximin).

c) Hurwicz (0.40): In this method, we add and multiply each payoff value by alpha (0.4).

South Korea = 15.2 (0.4) + 21.7 (0.6) = 19.1 ( remember, in $ millions)

China = 17.6 (0.4) + 19.0 (0.6) = 18.44

Taiwan = 14.9 (0.4) + 19.2 (0.6) = 17.48

Poland = 13.8 (0.4) + 22.5 (0.6) = 19.02

Mexico = 12.5 (0.4) + 25.0 (0.6) = 20

From the values above we select the minimum outcome since the company is looking at saving cost. Which is Taiwan; having the lowest cost of $17.48 million.

d) Using the formula $\frac{P_{1} +P_{2}+P_{3}...P_{n} }{n}$ where P = payoffs value, n = number of events.

South Korea =  15.2 + 21.7 + 19.1 /3 = 18.66

China = 17.6 + 19.0 + 18.5 /3 = 18.36

Taiwan = 14.9 + 19.2 +17.1 /3 = 17.06

Poland = 13.8 + 22.5 + 16.8 /3 = 17.7

Mexico = 12.5 + 25.0 + 21.2 /3 = 19.56

Taiwan should be selected since it has the lowest cost of $17.06 million.