Decision Making

Car Design

Objectives1. The Car should be safe2. The Car should be economical to use3. The car should be easy to manufacture4. The Car should cause little pollution

Constraints1. The Car should not weight more than 700 lbs2. The Car should resist a 5 MPH bumper impact

without damage3. The Car should cost less than $15,000

CAR

Engine Brakes EnergySource

Gasoline Electric Disc Regenerative Batteries Fuel Cells

Gasoline

Concept Fan

Gasoline

Enrgy Source

Gasoline

Electric

Disc

Regenerative

Batteries

Fuel Cells

Engine Brakes

Concept Combination Table

Gasoline

Enrgy Source

Gasoline

Electric

Disc

Regenerative

Batteries

Fuel Cells

Engine Brakes

Concept Combination Table

Gasoline

Enrgy Source

Gasoline

Electric

Disc

Regenerative

Batteries

Fuel Cells

Engine Brakes

Concept Combination Table

Safe Economical to Use Easy to Manufacture Low PollutionSafe 1 5 3 3

Economical to Use 1/5 1 1 1/3Easy to Manufacture 1/3 1 1 1/3

Low Pollution 1/3 3 3 1

1 = equal 3 = moderate 5 = strong 7 = very strong 9 = extreme

Safe Economical to Use Easy to Manufacture Low Pollution G. Mean WeightSafe 1.00 5.00 3.00 3.00 2.59002 0.52

Economical to Use 0.20 1.00 1.00 0.33 0.508133 0.10Easy to Manufacture 0.33 1.00 1.00 0.33 0.57735 0.12

Low Pollution 0.33 3.00 3.00 1.00 1.316074 0.26Total 4.9916

totalMeanGw

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Concept Selection

If a contraint is NoConstraints That Option must be DiscardedLess than 700 lbs5 MPH Crash Select option with Highest ScoreLess than $15,000

Objectives w Score W.Score Score W.Score Score W.ScoreSafe 0.52 5.00 2.6 4 2.08 4 2.08 5 is MaximumEconomical to Use 0.10 3.00 0.3 2 0.20 5 0.50Easy to Manufacture 0.12 5.00 0.6 4 0.48 3 0.36Low Pollution 0.26 5.00 1.3 1 0.26 5 1.30

4.8 3.02 4.24

Option 1

YesYesNo Yes Yes

Option 3

YesYes

Option 2

YesYes

Concept Selection

Decisions Based on Objectives: Major Selection

• Satisfy Personal Interest• Maximize Job Possibilities• Maximize Starting Salary• Rapid Growth• Work Indoors• Work Outdoors• Maximize Job Stability• Avoid Complex Courses• Start a Business with little money• Incorporate to Family Business• Grow Family Business to next level• Possibility of Travel

Decisions Based on Objectives: Major Selection

Objectives1. Satisfy Personal Interest2. Maximize Starting Salary3. Maximize Job Possibilities4. Rapid Growth

Constraints1. Find a Job in your Home City2. Minimum Starting Salary $4,000

Objective 1 Objective 2 Objective 3 Objective 4Objective 1 1 1 1 1Objective 2 1 1 1 1Objective 3 1 1 1 1Objective 4 1 1 1 1

1 = equal 3 = moderate 5 = strong 7 = very strong 9 = extreme

Objective 1 Objective 2 Objective 3 Objective 4 G. Mean WeightObjective 1 1.00 1.00 1.00 1.00 1.0000 0.25Objective 2 1.00 1.00 1.00 1.00 1.0000 0.25Objective 3 1.00 1.00 1.00 1.00 1.0000 0.25Objective 4 1.00 1.00 1.00 1.00 1.0000 0.25

Total 4.0000

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Major Selection / Class Work

ConstraintsConstraint 1Constraint 2

Objectives w Score W.Score Score W.ScoreObjective 1 0.25 5.00 1.25 5 1.25Objective 2 0.25 5.00 1.25 5 1.25Objective 3 0.25 5.00 1.25 5 1.25Objective 4 0.25 5.00 1.25 5 1.25

5 5.00

Major 1

??

Major 2

??

Major Selection / Class Work

Satisfy Personal Interest Maximize Starting Salary Maximize Job Possibilities Rapid GrowthSatisfy Personal Interest 1 3 3 3Maximize Starting Salary 1/3 1 1 1/3Maximize Job Possibilities 1/3 1 1 1/3Rapid Growth 1/3 3 3 1

1 = equal 3 = moderate 5 = strong 7 = very strong 9 = extreme

Satisfy Personal Interest Maximize Starting Salary Maximize Job Possibilities Rapid Growth G. Mean WeightSatisfy Personal Interest 1.00 3.00 3.00 3.00 2.2795 0.48Maximize Starting Salary 0.33 1.00 1.00 0.33 0.5774 0.12Maximize Job Possibilities 0.33 1.00 1.00 0.33 0.5774 0.12Rapid Growth 0.33 3.00 3.00 1.00 1.3161 0.28

Total 4.7503

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Major Selection

ConstraintsStay in Home CityMinimum Start 4,000

Objectives w Score W.Score Score W.ScoreSatisfy Personal Interest 0.48 5.00 2.4 4 1.92Maximize Starting Salary 0.12 4.00 0.48 4 0.48Maximize Job Possibilities 0.12 5.00 0.6 4 0.48Rapid Growth 0.28 5.00 1.4 5 1.40

4.88 4.28

Computer E.

YesYes

Civil E.

YesYes

Major Selection

Major Selection 2nd Example

Objectives1. Satisfy Personal Interest2. Maximize Starting Salary3. Incorporate to Family Business4. Avoid Complex Courses5. Grow Family Business to next levelConstraints1. Find a Job in your Home City2. Minimum Starting Salary $4,000

Satisfy Personal Interest Personal Int.Maximize Starting Salary Starting SalaryInc. to Family Business Inc. Family B.Avoid Complex Courses Complex CoursesGrow Family Business to next levelGrow Family B.

1 = equal 3 = moderate 5 = strong 7 = very strong 9 = extreme

Personal Int. Starting Salary Inc. Family B. Complex Courses Grow Family B. G. Mean WeightPersonal Int. 1.00 3.00 3.00 1.00 1.00 1.5518 0.28

Starting Salary 0.33 1.00 0.20 1.00 0.33 0.4670 0.08Inc. Family B. 0.33 5.00 1.00 3.00 1.00 1.3797 0.25

Complex Courses 1.00 1.00 0.33 1.00 0.33 0.6444 0.12Grow Family B. 1.00 3.00 1.00 3.00 1.00 1.5518 0.28

Total 5.5949

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Major Selection

ConstraintsStay in Home CityMinimum Start 4,000

Objectives w Score W.Score Score W.ScoreSatisfy Personal Interest 0.28 5.00 1.4 4 1.12Maximize Starting Salary 0.08 4.00 0.32 5 0.40Inc. to Family Business 0.25 5.00 1.25 5 1.25Avoid Complex Courses 0.12 3.00 0.36 5 0.60Grow Family Business to next level 0.28 5.00 1.4 4 1.12

4.73 4.49

Major 1

YesYes

Major 2

YesYes

Major Selection

Decisions based on Risk

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To buy or not to buy an umbrella?

•You need to attend a meeting in impeccable conditions. Probability of raining is 30% and you need to cross a long uncovered park to get to the meeting. At the park entrance they sell umbrellas for $10 and the end of the park a store sells full clothing starting at $200

To buy or not to buy an umbrella?

a1 buy umbrella

a2 do nothing

w1 It won't rain

w2 It will rain

R(ai) L(ai|w1) P(w1) L(ai|w2) P(w2)

a1 10 10 0.7 10 0.3

a2 60 0 0.7 200 0.3

Buying a Generator

•You have a business in a city where blackouts happen no more than once in a year with probability of 1%. Every time there is a blackout you loose $10,000. Should you pay $500 a month for backup power service?

a1 buy service

a2 do nothingw1 There is no power failurew2 There is a power failure

R(ai) L(ai|w1) P(w1) L(ai|w2) P(w2)

a1 6,000 6,000 0.99 6,000 0.01

a2 100 0 0.99 10,000 0.01

To buy or not to buy an insurance

•You live in a country that may be hit by hurricanes. The cost of insurance is $ 3,000, it will cover all repairs but has a deductible of $4,000. It is Friday and in 5 minutes everybody will retire until Monday for the weekend. There is a forecast that with probability of 5% a hurricane will strike your city. Should you protect your $500,000?

•Model used to guide an investment decision

a1 buy insurance

a2 do nothingw1 There is no hurricanew2 There is a hurricane

R(ai) L(ai|w1) P(w1) L(ai|w2) P(w2)

a1 3,200 3,000 0.95 7,000 0.05

a2 25,000 0 0.95 500,000 0.05

•You have $400,000 to invest. You can invest in a CD with no interest or in stocks. Investing in stocks has 80% probability of gaining $300,00 and 20% probability of loosing $100,000. Should you invest?

a1 buy $400,000 in stocks

a2 buy $400,000 in CDw1 There is a stock price increasew2 There is no stock price increase

E(ai) L/G(ai|w1) P(w1) L/G(ai|w2) P(w2)

a1 700,000 800,000 0.8 300,000 0.2

a2 400,000 400,000 0.8 400,000 0.2

•A student is undecided about selecting Major A or Major B. The following information is anticipated.▫Major A Salary 5,000 monthly▫Major B Salary 4,000 monthly▫Major A probability of losing 1 semester .2▫Major B probability of losing 1 semester .1

•Make a decision based in one year loses

a1 Select Major A

a2 Select Major Bw1 You don't lose one semesterw2 You lose one semester

E(ai) L/G(ai|w1) P(w1) L/G(ai|w2) P(w2)

a1 4,367 0 0.8 21,834 0.2

a2 12,587 12,000 0.9 17,868 0.1

•A student is undecided about selecting Major A or Major B. The following information is anticipated.▫Major A Salary 5,000 monthly▫Major B Salary 4,500 monthly▫Major A probability of losing 1 semester .3▫Major B probability of losing 1

semester .05•Make a decision based in one year loses

a2 Select Major Bw1 You don't lose one semesterw2 You lose one semester

E(ai) L/G(ai|w1) P(w1) L/G(ai|w2) P(w2)

a1 6,550 0 0.7 21,834 0.3

a2 6,693 6,000 0.95 19,851 0.05

•A student is undecided about selecting Major A or Major B. The following information is anticipated.▫Major A Salary 5,000 monthly▫Major B Salary 5,000 monthly▫Major A probability of losing 1 semester .3▫Major B probability of losing 1

semester .05•Make a decision based in one year loses

a1 Select Major Aa2 Select Major Bw1 You don't lose one semesterw2 You lose one semester

E(ai) L/G(ai|w1) P(w1) L/G(ai|w2) P(w2)

a1 6,550 0 0.7 21,834 0.3

a2 1,092 0 0.95 21,834 0.05

Pay great attention to this video

Probability

•Probabilities are associated with experiments where the outcome is not known in advance or cannot be predicted

•The sample space S is the set of all possible outcomes in an experiment.

•An element in S is called a sample point.•Each outcome of an experiment

corresponds to a sample point•Any subset of S is called an event.

Probability

•Sample space of rolling a die:▫S = {1,2,3,4,5,6}

•The event “even”:▫E = {2,4,6}

•The event Greater than 3:▫E = {4,5,6}

•Sample space of tossing two coins▫S = {HH,HT,TH,TT}

Probability

Probability

•The complement of “even” is “odd”:▫E = {1,3,5}

•The union of Greater than 3 and “odd”:▫E = {1,3,4,5,6}

•The intersection of Greater than 3 and “odd”:▫E = {5}

Receiver Operating Curve

Receiver Operating Curve

Receiver Operating Curve

• The ROC curve was first used during World War II for the analysis of radar signals before it was employed in signal detection theory.

• Following the attack on Pearl Harbor in 1941, the United States army began new research to increase the prediction of correctly detected Japanese aircraft from their radar signals.

• In medicine, ROC analysis has been extensively used in the evaluation of diagnostic tests

• ROC curves are also used extensively in epidemiology and medical research and are frequently mentioned in conjunction with evidence-based medicine.

• In radiology, ROC analysis is a common technique to evaluate new radiology techniques.

• In the social sciences, ROC analysis is often called the ROC Accuracy Ratio, a common technique for judging the accuracy of default probability models.

• ROC curves also proved useful for the evaluation of machine learning techniques.