Federated Electronics, Ltd., manufactures display screens and monitors for compu
ID: 457230 • Letter: F
Question
Federated Electronics, Ltd., manufactures display screens
and monitors for computers and televisions, which it sells
to companies around the world. It wants to construct a new warehouse and distribution center in Asia to serve emerging
markets there. It has identified potential sites in the port
cities of Shanghai, Singapore, Pusan, Kaohsiung, and Hong
Kong and has estimated the possible revenues for each
(minus construction costs which are higher in some cities
like Hong Kong). At each site the projected revenues are
primarily based on these factors, (1) the economic conditions
at the port including the projected traffic, infrastructure,
labor rates and availability; and expansion and
modernization; and (2) the future government situation
which includes the political stability, fees, tariffs, duties,
and trade regulations. Following is a payoff table that
shows the projected revenues (in $ billions) for six years
given the four possible combinations for positive and negative
port and government conditions:
Port Port Port Port
Negative/ Negative/ Positive/ Positive/
Government Government Government Government
Port Negative Positive Negative Positive
Shanghai —$0.271 $0.437 $0.523 $1.08
Singapore —0.164 0.329 0.441 0.873
Pusan 0.119 0.526 0.337 0.732
Kaoshiung —0.235 0.522 0.226 1.116
Hong Kong —0.317 0.256 0.285 1.653
Determine the port city Federated should select for its new
distribution center using the following decision criteria:
a. Maximax
b. Maximin
c. Equal likelihood
d. Hurwicz ( .55)
Explanation / Answer
The Payoff can be summerized as follows:
Possible Events
Location Decision
Port -ve
Govt. -ve
Port -ve
Govt. +ve
Port +ve
Govt. -ve
Port +ve
Govt. +ve
Maximum
Minimum
Equally Likelihood
Shanghai
0.271
0.437
0.523
1.08
1.08
0.271
0.57775
Singapore
0.164
0.329
0.441
0.873
0.873
0.164
0.45175
Pusan
0.119
0.526
0.337
0.732
0.732
0.119
0.4285
Kaoshiung
0.235
0.522
0.226
1.116
1.116
0.226
0.52475
Hong Kong
0.317
0.256
0.285
1.653
1.653
0.256
0.62775
Maximum
1.653
0.271
0.62775
Maximax criterion: choose the decision that will maximize the maximum possible revenue among all events.
Optimal Decision = Max (1.08, 0.873, 0.723, 1.116, 1.653) = 1.653
Locate at Hong Kong according to maximax criterion.
Maximax criterion: choose the decision that will maximize the minimum possible revenue among all events.
Optimal Decision = Max (0.271, 0.164, 0.119, 0.226, 0.256) = 0.271
Locate at Shanghai according to maximin criterion.
Equally Liklihood criterion: Choose the decision that will maximize the average payoff among all events.
Optimal Decision = Max (0.5777, 0.4517, 0.4285, 0.547, 0.6277) = 0.6277
Locate at Hong Kong according to Equally Likelihood criterion.
Hurwicz Principle
Given the coefficient of optimism, = 0.55, the coefficient of pessimism will be 1 – = 0.45. Then select the course of action that will optimize the payoff value ‘H’.
H = × (maximum payoff of action) + (1 – ) × (minimum payoff of action)
For location shanghai, H = 0.55 x 1.08 + 0.45 x 0.271 = 0.71595
Location Decision
Maximum Payoff
Minimum Payoff
H
Shanghai
1.08
0.271
0.71595
Singapore
0.873
0.164
0.55395
Pusan
0.732
0.119
0.45615
Kaoshiung
1.116
0.226
0.7155
Hong Kong
1.653
0.256
1.02435
Maximum H
1.02435
Optimal Decision = Max (0.7159, 0.55395, 0.4561, 0.7155, 1.0245) = 1.0245
Locate at Hong Kong according to Hurwicz criterion.
Possible Events
Location Decision
Port -ve
Govt. -ve
Port -ve
Govt. +ve
Port +ve
Govt. -ve
Port +ve
Govt. +ve
Maximum
Minimum
Equally Likelihood
Shanghai
0.271
0.437
0.523
1.08
1.08
0.271
0.57775
Singapore
0.164
0.329
0.441
0.873
0.873
0.164
0.45175
Pusan
0.119
0.526
0.337
0.732
0.732
0.119
0.4285
Kaoshiung
0.235
0.522
0.226
1.116
1.116
0.226
0.52475
Hong Kong
0.317
0.256
0.285
1.653
1.653
0.256
0.62775
Maximum
1.653
0.271
0.62775
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