Decision Making Under Uncertainty - Final 5t4i2i

STEPS TO GOOD DECISION-MAKING 1. Define problem and influencing factor. 2. Establish decision criteria. 3. Select decision making tool (model)

4. Identify and Evaluate alternatives using decision-making tool (model). 5. Select best alternative.

6. Implement decision. 7. Evaluate outcome.

Decision Making Under Uncertainty The outcome of a decision alternative is not known, and even its probability is not known. Parameters are estimated with certainty. Outcome – known Termed as DETERMINISTIC ANALYSIS Few criteria (approaches) are available for the decision makers to select according their preferences.

SOURCES OF UNCERTAINTIES DEMAND STRUCTURE

COMPETITORS

EXTERNALITIES

UNCERTAINTY

INTERNAL FORCES

SUPPLY STRUCTURE

TIME

METHODS: Decision-Making Under UNCERTAINTY 1.

Maximax Criterion

2.

Maximin Criterion

3.

Hurwicz alpha Criterion (Rationality or Realism)

4.

Laplace Criterion (Equally Likelihood)

5.

Minimax Criterion

CRITERION 1: MAXIMAX (Optimistic) • An adventurous and aggressive decision maker may choose to act that would result in the maximum payoff possible. Step 1. Pick maximum payoff of each alternative.

Step 2. Pick the maximum of those maximums in Step 1; its corresponding alternative is the decision. This is viewed as an optimistic approach, “Best of best”

CRITERION 1: MAXIMAX Maximizes the maximum payoff “Best of Best” State of Nature or Outcomes

Payoff Table: Alternatives

ECONOMY Growing

Stable

Declining

Bonds

41

46

5

Stocks

72

29

-12

72

Mutual Funds

54

50

-8

54

Best 46

Decision Alternatives *Payoffs in PROFIT

CRITERION 2: MAXIMIN (Pessimistic) • This is called Waldian Criterion. This criterion of decision making stands for choice between alternative courses of action assuming pessimistic view of nature. Step 1. Pick minimum payoff of each alternative. Step 2. Pick the maximum of those minimums in Step 1; its corresponding alternative is the decision. This is viewed as an pessimistic approach, “Best of the worst”

CRITERION 2: MAXIMIN Maximizes the minimum payoff “Best of Worst” Payoff Table: ECONOMY Alternatives

GROWING

STABLE

DECLINING

Bonds

41

46

5

Stocks

72

29

-12

-12

Mutual Funds

54

50

-8

-8

Worst 5

*Payoff is in PROFIT

CRITERION 3: HURWICZ (Realism) • This method is the combination of Maximum and Minimax criterion. Also known as criterion of rationality. This is neither too optimistic or too pessimistic. Step 1. Calculate Hurwicz value for each alternative. Step 2. Pick the alternative of largest Hurwicz value as the decision.

CRITERION 3: HURWICZ (Realism) Choose the best weighted average payoff based on a 𝛼coefficient Close to of1 realism = OPTIMISM 𝛼, 0 ≤ 𝛼 ≤ 1

𝛼 Close to 0 = PESSIMISM Alternatives

GROWING

STABLE

DECLINING

Bonds

41

46

5

Stocks

72

29

-12

Mutual Funds

54

50

-8

𝛼 (best payoff)

+

(1- 𝛼) (worst payoff)

CRITERION 3: HURWICZ (Realism) 𝛼 = 0.3

1- 𝛼 = 0.7

Alternatives GROWING

Bonds

41

STABLE

DECLINING

Weighted Average

46

5

.3(46) + .7(5) = 17.3

BEST

Stocks

72

29

BEST

Mutual Funds

𝛼 (best payoff)

54 BEST

+

WORST

-12 WORST

50

-8 WORST

(1- 𝛼) (worst payoff)

.3(72) + .7(-12) = 13.2 .3(54) + .7(-8) = 10.6

CRITERION 4: Equally Likely • The decision maker makes a simple assumption that each state of nature is equally likely to occur and compute average payoff for each. Choose decision with the average payoff. • Also known as LAPLACE Criterion.

Step 1. Calculate the average payoff of each alternative. Step 2. The alternative with the highest average is the decision.

CRITERION 4: Equally Likely (LAPLACE) Maximizes the average payoff “Best of Average” Payoff Table:

ECONOMY

Alternatives GROWING

Bonds

41

STABLE 46

DECLINING

Average Payoff

5

Stocks

72

29

-12

Mutual Funds

54

50

-8

=

Payoff1 + Payoff2 + Payoff3 3

*Payoff is in PROFIT

CRITERION 4: Equally Likely (LAPLACE) Maximizes the average payoff “Best of Average” ECONOMY GROWING

STABLE

DECLINING

Average

Bonds

41

46

5

(41+46+5) /3 = 30.7

Stocks

72

29

-12

(72+29-12)/3 = 29.7

Mutual Funds

54

50

-8

(54+45-8) /3 = 32

Alternatives

CRITERION 5: Minimax Regret • Application of Minimax criterion requires a table of losses or table of regret instead of gains. • Regret = Opportunity Cost = Opportunity Loss

Step 1. Construct a “regret table” Step 2. Pick a maximum regret of each row in regret table.

Step 3. Pick minimum of those maximums in Step 2, its corresponding alternative is the decision.

CRITERION 5: Regret Approach Regret Table: Alternatives

ECONOMY GROWING

STABLE

DECLINING

Bonds

50

55

5

Stocks

80

40

-18

Mutual Funds

63

45

-10

Regret = Opportunity Loss *Payoff in PROFIT

CRITERION 5: Regret Approach Regret Table: Alternatives

ECONOMY GROWING

STABLE

DECLINING

Bonds

50

55

5

Stocks

80

40

-18

Mutual Funds

63

45

-10

Regret = Best of Payoff – Payoff Received *Payoff in PROFIT

CRITERION 5: Regret Approach Regret Table:

ECONOMY GROWING

STABLE

80 – 50 = 30

55 – 55 = 0

50

55

80 – 80 = 0

55 – 40 = 15

80

40

80 – 63 = 17

55 – 45 = 10

63

45

DECLINING

Alternatives

Bonds Stocks Mutual Funds

5–5=0

5 5 – (-18) = 23

-18 5 – (-10) = 15

-10

CRITERION 5: Regret Approach

Regret Table Alternatives

ECONOMY

GROWING

STABLE

DECLINING

Maximum

Bonds

50

55

5

30

Stocks

80

40

-18

23

Mutual Funds

63

45

-10

17

*Payoff in PROFIT