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ISE 195 Introduction to Industrial Engineering

Lecture 4 Decision Analysis

Decision Analysis

- What is the hardest decision you have ever had to

make? - Since we all have to make decisions, we are all

Decision Makers of a sort and can benefit from

the study of decision making. - Have you ever had to make a decision and then

later have to explain or defend that decision?

Decision Domains

- Personal domain
- Where to live college to attend car to buy etc
- Business domain
- Introduce the new product bid on a contract

hire - Government domain
- How to allocate money where to get involved

Decision Roles

- Those who study decisions will be referred to as

decision analysts while those that make the

decisions will be referred to as the decision

makers. - Why do you think we would want to separate the

roles of the decision analyst and the decision

maker? - Proper decision making requires collaboration

among the decision makers and the decision

analysts in order to find the best solution based

on insights versus position

Why Decisions Are Hard

- Decisions are hard for a number of structural,

emotional, and organizational reasons - Structural uncertainty, trade-offs, complexity
- Emotional anxiety, multiple objectives,

competition - Organizational lack of consensus, differing

perspectives

Why Decisions Are Hard

- Do you think your personal decisions are going to

be easier or harder than the decisions you might

be faced with in business (engineering)? - What might be some of the reasons, both obvious

and less obvious, for this difference in level of

complexity between decisions from the personal

domain and decisions from the business or

government domain?

Why Decisions Are Hard

- There are other reasons decisions are hard
- Consequences
- Uncertainty
- Ambiguity

Why Decisions Are Hard

Consequences

MEDIUM

HIGH

LOW

Uncertainty

Ambiguity

CAU Model, Skinner

Why Decisions Are Hard

Consequences

Uncertainty

Ambiguity

CAU Model, Skinner

What Makes A Good Decision

- What is a good decision?
- What is a good outcome?
- Does a good decision always lead to a good

outcome? - Name some examples. . .
- A good decision emerges as the result of valid

decision making process (of which there are a few

as we will see)

- When you come to a fork in the road, take it
- - Yogi Berra

History

- Operational research, quantitative management,

based on repetitive actions - Focused on optimizing objectives and meeting

constraints - Failed to focus on needs of executive decision

making - In particular their more complex, strategic

problems - Technique needed for logical guidance on complex,

uncertain situations - DA combines systems analysis and statistical

decision theory

History

- Problems typical of DA application are
- Unique
- Important
- Contain uncertainty
- Have long-run implications
- Contain complex preferences
- DA arose in the late 60s, early 70s and balances

the following OR considerations - Mathematical modeling
- Computer implementation
- Quantitative analysis and decision making

History

- DA also incorporated the following aspects of

human decision making - Management experience
- Management judgment
- Management preferences
- The art of DA involves capturing the above from

the managers and decision makers - The techniques used to capture the above are

sometimes controversial within the operational

research / systems engineering field

Terminology

- Decision
- A conscious irrevocable allocation of resources

with the purpose of achieving a desired objective - Uncertainty
- Something that is unknown or not perfectly known
- Outcomes
- Depend on alternative chosen and the

uncertainties impacting it - Value
- Something the decision maker wants and can

tradeoff

Terminology

- Objective
- Something specific the decision maker wants to

achieve - Decision Maker
- Anyone with the authority to allocate the

necessary resources for the decision being made - Subjective Probability
- Classical approach to probability called the

frequentist approach - Subjective approach, the Bayesian, allows that

each of us can provide valid probabilities

- Probabilistic Methods
- (Pay attention is ISE 301!)
- These assume the possible outcomes (states of

nature) can be assigned probabilities that

represent their likelihood of occurrence. - Also referred to as methods for decision making

under risk

Expected Monetary Value

- Selects alternative with the largest expected

monetary value (EMV)

- EMVi is the average payoff we would receive if we

faced the same decision problem numerous times

and always selected alternative i.

Decision Trees

- Graphical means for displaying a decision problem

that shows, in chronological order - the alternatives available to the decision

maker - the futures that could be experienced and
- the consequences of choosing between alternatives
- Trees consist of
- Branches lines representing possible decision

paths - Decision Forks nodes which represent choices

to be made by the decision maker and - Chance Forks nodes which represent possible

futures that are modeled as selected by nature

Decision Trees (continued)

- To evaluate a tree one must
- assign values of an appropriate evaluation

measure to each branch (often summarized at the

end of the branch) and - choose branches appropriately at each decision

node, working from right to left - When making decisions under risk, this entails
- assigning probabilities to each branch emanating

from a chance fork - computing expected values at each chance node

and - finding the branch that maximizes the expected

value from among all branches emanating from a

decision fork.

Example Electronics Firm

- An electronics firm makes components that are

sold and shipped to an automobile manufacturer. - Five percent of all components produced are

defective due to poor solder connections. - Cant tell if defective until after it is

installed on a car. - Auto maker will charge the electronics firm 800

per defective component to cover the cost of

repair. - A proposal double-solder each component before

before it is shipped to the automobile maker. - Will cost 50 per component to double-solder but

is sure to eliminate this cause of defective

components - i.e., no double-soldered components will be

defective.

Example Electronics Firm (Continued)

- Is the proposal worthwhile?
- Assume electronics firm seeks to minimize its

expected cost and consider using our structure - Actions 1 -- double solder before shipping 2

-- do not double solder - Outcomes 1 -- component is defective 2 --

component is good - Prior Probabilities P1 0.05 P2 0.95
- Note that these probabilities apply only if the

component is not double-soldered! - Value Function E11 -50 E12 -50

E21 -800 E22 0

Values are negative costs here

Electronics Firm Decision Tree

- Expected Values --

Double-Solder E(V)1 -50 Do Not E(V)2

-800(0.05) 0(0.95) -40 - No, it would not be worthwhile to double-solder

every component since the maximum expected value

(minimum expected cost) is obtained for action 2

(do not double-solder). - Decision Tree

Double Solder

-50

X

-40

Defective (0.05)

-40

-800

Do Not

Good (0.95)

0

Example Doing Better?

- To this point, we have assumed that the firm is

unable to tell if a component is defective until

after it is installed on a car. - Obviously, if the firm were to know in advance

that a component was defective, it would

double-solder that component. - A reasonable strategy, then, might be to attempt

to determine whether or not a component is

defective before the decision to double-solder or

not is made. - How much should the firm be willing to pay to for

this sort of information?

Example Paying for More Information

- Without any advance info about components, the

firms best strategy is to not double-solder any

components - This has an expected cost of 40 per component.
- With advance info, however, the firm should
- double-solder all defective components at a cost

of 50 each, and - not double-solder the rest (the good components).
- Since 5 of all components are defective, the

expected cost of this strategy would be - 50(0.05) 0(0.95) 2.50 per component.
- Thus, the most the firm should be willing to pay

for this advance info is the difference between

these, or - 40 - 2.50 37.50 per component.

Getting Advance Information

- Advance information can often be obtained by

performing some sort of test before making a

decision - If so, then the initial choice we must make is

whether or not to do the testing - The ideal situation would be one in which the

testing enables us to correctly predict the

future - In our example, this would mean that the test is

100 accurate in classifying components as good

or defective - e.g., if the test classifies a component as

defective, then that component is indeed

defective.

Decision Tree w/ Perfect Testing

Double Solder

-40

-50

X

Do Not Test

Defective (0.05)

-40

-800

No Action

Good (0.95)

0

Classify as Defective (0.05)

Double Solder

-50

-50

Perform Test (Get Advance Info)

Defective (1.00)

-800

-800

X

No Action

-2.5

Good (0.00)

0

Classify as Good (0.95)

Double Solder

-50

0

X

Defective (0.00)

0

-800

No Action

Good (1.00)

0

- We assume here that testing is perfect, so

that all components will be correctly classified

and, thus, 95 will be classified as good while

5 will be classified as defective

Bayesian Decision Making

- A method for accounting for the effects of

advance testing in decision making - Based on Bayes Theorem which provides us a way

to revise our initial prior probabilities for

the occurrence of each possible future given the

results of testing

Example Revisited

- Suppose now that the firm can choose to test each

component, at a cost of 20 apiece, to see if the

component might be defective before the decision

to double-solder or not is made. - The test is not perfect, but they have a track

record - Based on the results of testing known good and

known defective components, it is determined

that - the test will incorrectly classify 15 of all

defective components as good, and - incorrectly classify 10 of all good components

as defective. - Is it worthwhile for the firm to perform this

test?

Decision Tree w/ Testing

Double Solder

-40

-50

X

Do Not Test

Defective (0.05)

-40

-800

No Action

Good (0.95)

0

Double Solder

Classify as Defective (???)

-50

-20

Defective (???)

Perform Test

-800

No Action

Good (???)

0

Classify as Good (???)

Double Solder

-50

Defective (???)

-800

No Action

Good (???)

0

- To evaluate this tree and decide what to do, we

need to fill in appropriate probabilities at all

chance forks.

Example Description of Test

- Note that there are two possible results when a

component is subjected to the proposed test - Result 1 The component is classified as

defective - Result 2 The component is classified as good
- The particular result to be obtained will depend

on both - the state of nature (the condition of the

component being tested), and, - since the experiment is not perfect, also on

chance. - What we know about the accuracy of the test is

captured by the conditional probabilities of

obtaining a particular result given a particular

state of nature . . .

Description of Test Continued

- That is, we know that our experiment will

incorrectly classify 15 of all defective

components as good and 10 of all good components

as defective. - We denote this using the notation
- Pcomponent classified as defective it is

defective PResult 1 State of nature 1 ?

Q11 0.85 - Pcomponent classified as good it is defective

PResult 2 State of nature 1 ? Q21 0.15 - Pcomponent classified as defective it is good

PResult 1 State of nature 2 ? Q12 0.10 - Pcomponent classified as good it is good

PResult 2 State of nature 2 ? Q22 0.90 - Unfortunately, these are not the probabilities we

need to complete the decision tree!

Bayes Theorem

- To compute the conditional probabilities of

encountering each possible future given the

results of the test, we combine previous results

to obtain - Bayes Theorem If are n

mutually exclusive and exhaustive events defined

over a sample space and E is any other event with

PE gt 0, then - Bottom Line the posterior probability of

encountering state of nature j (j 1, 2, . . .,

m) given that the test produces result k (k 1,

2, . . ., r) can be found via

Bayes Rule

The Law of Total Probability

Example Posterior Probabilities

- For the electronics firm, we can then compute
- P11 Pcomponent is defective classified as

defective - PState of nature 1Result 1
- PResult 1State of nature 1 ? PState of

nature 1 ? PResult 1 - Q11P1/Q1
- (0.85)(0.05)/(0.1375) ? 0.3091
- Likewise
- P21 Pcomponent is good classified as

defective - PState of nature 2Result 1
- Q12P2/Q1
- (0.10)(0.95)/(0.1375) ? 0.6909

Example Posterior Probabilities (Continued)

- Similarly
- P12 Pcomponent is defective classified as

good - Q21P1/Q2
- (0.15)(0.05)/(0.8675) ? 0.0087
- and
- P22 Pcomponent is good classified as good
- Q22P2/Q2
- (0.90)(0.95)/(0.8675) ? 0.9913
- Terminology the quantity QkjPj formed in the

preceding computations is often called the joint

probability of encountering state of nature j and

obtaining result k from the experiment (since it

is the probability of both the two events

occurring).

Example Decision Tree (Revisited)

Double Solder

-40

-50

X

Do Not Test

Defective (0.05)

-40

-800

No Action

X

Good (0.95)

0

Double Solder

-50

Classify as Defective (0.1375)

-32.88

-50

-20

-247.47

Defective (0.3091)

Perform Test

-800

No Action

-12.88

X

Good (0.6909)

0

-6.96

Classify as Good (0.8625)

Double Solder

-50

X

-6.96

Defective (0.0087)

-800

No Action

Good (0.9913)

0

Discrete Probability Assessment

- Three methods for assessing discrete probability
- Direct question
- Assumes familiarity with probability
- Usually means decision maker used to providing

probabilities based on similar experiences - Betting method
- Most people bet in some fashion
- odds provide perception of likelihood of the

outcome - Use the odds to derive the probability
- Reference lottery
- Find probability yielding indifference point

Experts and Assessments

- Reliance on experts important in complex problems
- Important to avoid bias in assessment and

collection - Protocol for expert assessment
- Background
- Identify and recruit experts
- Motivate the experts
- Structure and decompose the problem
- Probability assessment training
- Probability elicitation and verification
- Aggregation of distributions

Theoretical Probability Models

- Subjective probabilities may be difficult to get
- Alternative is to use some theoretical

distribution - Actually making a subjective assessment via your

choice - A variety of distributions apply in a variety of

applications - Binomial
- Normal
- Exponential
- Triangular

Other Decision Factors Risk

- Have not worried about risk
- Decision makers may actually have differing

attitudes toward risk - Would like a model to map outcomes into measures

that incorporate attitudes towards risk - In decision analysis this is accomplished using

utility functions - The corresponding outcomes, not measured in

utilities, may provide different alternative

selections than those not using utilities - Changes due to incorporation of risk

Other Decision Factors Multi-attribute

Decisions

- Have focused on a single attribute
- Most decisions are multi-attribute in nature
- Trade-off between weight and redundancy
- Trade-off between reliability and maintenance
- Some multi-attribute models assume independence
- Assess each attribute
- Develop a weighting scheme for each attribute
- Use weighted sum of scores
- Called an additive model

Multiple Attributes

- Reality in most multi-attribute models requires

some form of interaction - Attributes are not independent
- Need to derive a utility surface
- Techniques for determining the surface are

extensions of independent techniques - Complications come during elicitation as the

expert is asked to specifically consider

dependencies

- ISE 195 Overview of Decision Analysis
- Questions?