Question

Question Set 1. Samsung is considering different R&D paths for the upcoming year’s release. The four strategies (along with changing nothing) under consideration are:

• Decrease Depth: Decrease the depth of the phones without affecting other specs
• More Battery Power: Increase battery capacity of phones by 6%
• Mixed: Combine above two strategies somehow
• No Change: Do not change anything, buyers seem content

                            

The outcomes of the possible strategies (in millions of dollars) depend on how the competitors behave. Samsung considers four different outcomes, which are not shared, say A, B, C and D. Negative values indicate loss for Samsung and positive values indicates possible profits.

	Scenarios
Strategy	A	B	C	D
Decrease Depth	-75	-35	60	90
More Battery Power	-65	-25	50	80
Mixed	-55	-40	35	95
No Change	-40	-25	50	40

For the following questions, you will use Excel to identify the best strategy according to various criteria. You only need to perform the necessary calculations to show which one is best. For example, the first question is for maximax. You need to set up formulas to find the maximum payoff for each strategy and to then find the highest value among them. However, once you have calculated that highest value, you can just type in the corresponding strategy without any further Excel calculations.

1. What would be Samsung’s decision using the maximax criterion? (3pts)

2. What would be Samsung’s decision using the maximin criterion? (3pts)

3. What would be Samsung’s decision using the Laplace criterion? (3pts)

4. What would be Samsung’s decision using the minimax regret criterion? It is helpful to construct a regret table for this problem. (6pts)

Question Set 2. This question set uses the table of outcomes from Question Set 1 for Samsung’s strategies. Assume that the probabilities for scenarios are:

• P(A) = 0.15
• P(B) = 0.20
• P(C) = 0.40
• P(D) = 0.25

1. What decision will maximize Samsung’s expected monetary value? (9pts)

2. What is the expected value of perfect information? (6pts)

Question Set 3. This question set uses the metropolitan model for facility location decisions. Each demand source has a weight indicating the volume of sales it is expected to generate. Using the demand data and five potential locations on the following page:

1. Find the sum of weighted metropolitan model distances for each of the five locations. Be sure the calculations are shown for each location’s sum of distances. (8pts)

2. As evidenced by having the smallest weighted sum of distances, which location is best? (2pts)

Demand Data
Weight	X	Y
2	28	33
4	30	34
5	28	28
1	35	32
3	30	28
2	32	33
3	26	27
2	27	28
1	27	27
6	30	31
3	27	24
5	30	31
3	28	24
3	27	26
4	25	28
1	34	29
7	30	37
2	25	36
2	31	33
2	30	33

Location	X	Y
A	26	32
B	31	29
C	31	33
D	31	31
E	32	29

Answer 1

Question Set – 1:

The Payoff table is:

	Scenario
Strategy	A	B	C	D
Decrease Depth	-75	-35	60	90
More Battery Power	-65	-25	50	80
Mixed	-55	-40	35	95
No Change	-40	-25	50	40

1. Using Maximax:

Maximax maximizes the maximum payoffs.

We choose the best (maximum) pay off among the strategies. Then we choose the Strategy with highest payoff among these maximums.

In excel:

Hence, chosen: Mixed Strategy

2. Maximin:

Maximin maximizes the minimum payoffs.

We choose the worst (minimum) pay off among the strategies. Then we choose the Strategy with highest payoff among these minimums.

In excel:

Hence chosen: No Change

3. Laplace Criterion:

Maximizes the average payoff (Best of Average)

First we have to find the average of all the strategies. And then choose the maximum among the average.

In excel:

Hence chosen decision: Decrease Depth or More Battery Power

4. Minimax Regret Criterion

It minimizes the maximum regret.

Regret for a Scenario = Best payoff of that Scenario – payoff received.

The regret table is created. Then we calculate the maximum regret for each strategy. And then select the lowest among the maximum regrets.

Hence chosen decision: More battery power or Mixed

Question Set – 2:

P(A) = 0.15

P(B) = 0.2

P(C) = 0.4

P(D) = 0.25

1. Expected Monetary Value:

Expected Monetary Value of a strategy = total sum of (payoff of a scenario * probability of that scenario) for all the scenarios.

In excel:

Hence, Decision: Decrease Depth

Maximum EMV = 28.25

2. Expected Value of Perfect Information:

EVPI = EVwPI – EVwoPI

EVwPI: Expected Value with Perfect Information

EVwoPI: Expected Value without Perfect Information

EVwoPI = Maximum EMV = 28.25

EVwPI = total sum of (Maximum payoff of each scenario * probability of that scenario) for all scenarios.

In Excel:

EVwPI = 36.75

EVwoPI = 28.25

Expected Value of Perfect Information = EVwPI – EVwoPI = 36.75 – 28.25 = 8.5

Question Set – 3:

Weighted Distance of Each location from A, B, C, D, E:

Now finding the weighted distance for each location:

From Location A:

From Location B:

From Location C:

From Location D:

From Location E:

1. Location A: 397

Location B: 361

Location C: 387

Location D: 351

Location E: 414

2. With smallest weight, the chosen location is: Location D

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