A-1 Operations Management Decision-Making Tools Module A

A-1

Operations Operations ManagementManagement

Decision-Making ToolsDecision-Making ToolsModule AModule A

A-2

OutlineOutline Decision Making & Models.

Decision Tables. Decision making under uncertainty. Decision making under risk. Expected value of perfect information (EVPI).

Decision Trees.

A-3

The Decision-Making ProcessThe Decision-Making Process

Problem Decision

Quantitative Analysis

LogicHistorical DataMarketing ResearchScientific AnalysisModeling

Qualitative Analysis

EmotionsIntuitionPersonal Experience and MotivationRumors

A-4

Models and Scientific ManagementModels and Scientific Management

Can Help Managers toCan Help Managers to:

Gain deeper insights into the business.

Make better decisions! Better assess alternative plans and actions.

Quantify, reduce and understand the uncertainty surrounding business plans and actions.

A-5

Steps to Good DecisionsSteps to Good Decisions

Define problem and influencing factors. Establish decision criteria. Select decision-making tool (model). Identify and evaluate alternatives using

decision-making tool (model). Select best alternative. Implement decision. Evaluate the outcome.

A-6

Benefits of ModelsBenefits of Models Allow better and faster decisions.

Less expensive and disruptive than experimenting with the real world system.

Allow managers to ask “What if…?” questions.

Force a consistent and systematic approach to the analysis of problems. Require managers to be specific about constraints and

goals.

A-7

Limitations of ModelsLimitations of Models

May be expensive and time-consuming to develop and test.

May be unused, misused or misunderstood (and feared!). Due to mathematical and logical complexity.

May downplay the value of qualitative information.

May use assumptions that oversimplify the real world.

A-8

Decision TheoryDecision Theory

Terms:

Alternative: Course of action or choice.

Decision-maker chooses among alternatives.

State of nature: An occurrence over which the decision maker has no control.

A-9

Decision TableDecision Table

States of Nature

State 1 State 2

Alternative 1 Outcome 1 Outcome 2

Alternative 2 Outcome 3 Outcome 4

A-10

A firm has two options for expanding production of a product: (1) construct a large plant; or (2) construct a small plant. Whether or not the firm expands, the future market for the product will be either favorable or unfavorable.

If a large plant is constructed and the market is favorable, then the result is a profit of $200,000. If a large plant is constructed and the market is unfavorable, then the result is a loss of $180,000.

If a small plant is constructed and the market is favorable, then the result is a profit of $100,000. If a small plant is constructed and the market is unfavorable, then the result is a loss of $20,000. Of course, the firm may also choose to “do nothing”, which produces no profit or loss.

Example - Decision Making Under Example - Decision Making Under UncertaintyUncertainty

A-11

Example - Decision Making Under Example - Decision Making Under UncertaintyUncertainty

States of NatureAlternatives Favorable

MarketUnfavorable

MarketConstructlarge plant

$200,000 -$180,000

Constructsmall plant

$100,000 -$20,000

$0 $0Do nothing

A-12

Decision Making Under Decision Making Under Uncertainty - CriteriaUncertainty - Criteria

Maximax - Choose alternative that maximizes the maximum outcome for every alternative (Optimistic criterion).

Maximin - Choose alternative that maximizes the minimum outcome for every alternative (Pessimistic criterion).

Expected Value - Choose alternative with the highest expected value.

A-13

Example - MaximaxExample - Maximax


MarketUnfavorable


$200,000 -$180,000


$100,000 -$20,000

$0 $0Do nothing

Maximax decision is to construct large plant.

A-14

Example - MaximinExample - Maximin

Minimumin Row

-$180,000

-$20,000

$0

Maximin decision is to do nothing.

(Maximum of minimums for each alternative)


MarketUnfavorable


$200,000 -$180,000


$100,000 -$20,000

$0 $0Do nothing

A-15

Probabilistic decision situation.

States of nature have probabilities of occurrence.

Select alternative with largest expected value (EV). EV = Average return for alternative if decision were

repeated many times.

Decision Making Under RiskDecision Making Under Risk

A-16

Expected Value EquationExpected Value Equation

Probability of payoffEV A V P V

V P V V P V V P V

i ii

i

N N

( ( )

( ) ( ) ( )

) == *

= * + * + + *

1

1 1 2 2

Number of states of nature

Value of Payoff

Alternative i

...

N

A-17

Example - Expected ValueExample - Expected ValueSuppose: Probability of favorable market = 0.5 Probability of unfavorable market = 0.5


MarketUnfavorable


$200,000 -$180,000


$100,000 -$20,000

$0 $0Do nothing

Expected Value

$10,000

$40,000

$0

Decision is to “Construct small plant”.

A-18

Example - Expected ValueExample - Expected ValueSuppose: Probability of favorable market = 0.7 Probability of unfavorable market = 0.3


MarketUnfavorable


$200,000 -$180,000


$100,000 -$20,000

$0 $0Do nothing

Expected Value

$86,000

$64,000

$0

Now, decision is to “Construct large plant”.

A-19

Example - Expected ValueExample - Expected ValueOver what range of values for probability of favorable market is “Construct large plant” preferred?

Solve for x: 380000x-180000 > 120000x-20000


MarketUnfavorable


$200,000 -$180,000


$100,000 -$20,000

$0 $0Do nothing

Expected Value

380,000x - 180,000

120,000x - 20,000

A-20

Solve for x: 380000x - 180000 > 120000x - 20000

x > 0.6154

So, as long as probability of a favorable market exceeds 0.6154, then “Construct large plant”.

Example - Expected ValueExample - Expected ValueOver what range of values for probability of favorable market is “Construct large plant” preferred?

A-21

Expected Value of Perfect Expected Value of Perfect Information (Information (EVPI))

EVPIEVPI places an upper bound on what one would pay for additional information. EVPI is the maximum you should pay to learn the

future.

EVPIEVPI is the expected value under certainty (EVUC) minus the maximum EV.

EVPI = EVUC - maximum EV

A-22

Expected Value Under Certainty Expected Value Under Certainty (EVUC)(EVUC)

)P(S* j

EVUCn

j

where:

P(Sj ) = The probability of state of nature j.

n = Number of states of nature.

(Best outcome for the state of nature j)

A-23

Example - EVUCExample - EVUC

Best outcome for Favorable Market = $200,000

Best outcome for Unfavorable Market = $0


MarketUnfavorable


$200,000 -$180,000


$100,000 -$20,000

$0 $0Do nothing

A-24

Expected Value of Perfect Expected Value of Perfect InformationInformation

EVPIEVPI = EVUC - max(EVEV)

= ($200,000*0.50 + 0*0.50) - $40,000

= $60,000

Thus, you should be willing to pay up to $60,000 to learn whether the market will be favorable or not.

Suppose: Probability of favorable market = 0.5 Probability of unfavorable market = 0.5

A-25

Expected Value of Perfect Expected Value of Perfect InformationInformation

EVPIEVPI = EVUC - max(EVEV)

= ($200,000*0.70 + 0*0.30) - $86,000

= $54,000

Now, you should be willing to pay up to $54,000 to learn whether the market will be favorable or not.

Now suppose: Probability of favorable market = 0.7 Probability of unfavorable market = 0.3

A-26

Graphical display of decision process.

Used for solving problems with several sets of alternatives and states of nature (sequential decisions). Decision tables can not be used for more than one

decision.

Expected Value criterion is used.

Decision TreesDecision Trees

A-27

Using Decision TreesUsing Decision Trees Define the problem. Draw the decision tree. Assign probabilities to all states of nature. Estimate payoffs for each combination of

alternatives and states of nature. Solve the problem:

Compute expected values for each state-of-nature node moving right to left.

Select decisions that maximize expected value.

A-28

Decision TheoryDecision Theory

Terms: Alternative: Course of action or choice. State of nature: An occurrence over which the

decision maker has no control.

Symbols used in decision tree: A decision node from which one of several

alternatives may be selected. A state of nature node out of which one state of

nature will occur.

A-29

Decision TreeDecision Tree

1

2

State 1

State 2

State 1

State 2

Alternative 1

Alternative 2

Decision Decision NodeNode

Outcome 1Outcome 1Outcome 1Outcome 1




State of Nature NodeState of Nature Node

A-30

Decision Tree for ExampleDecision Tree for Example

Favorable Mkt (0.7)

Build Large

Build Small

Unfavorable Mkt (0.3)

$200,000

Favorable Mkt (0.7)


-$180,000

$100,000

-$20,000

$0

Do nothing

A-31

Decision Tree for Example - Decision Tree for Example - SolutionSolution

Favorable Mkt (0.7)

Build Large

Build Small


$200,000

Favorable Mkt (0.7)


-$180,000

$100,000

-$20,000

$0

Do nothing

$86,000

$64,000

$0

A-32

Decision Tree ExampleDecision Tree ExampleA firm can build a large plant or small plant initially (for a new product). Demand for the new product will be high or low initially. The probability of high demand is 0.6. (The probability of low demand is 0.4.)

If they build “small” and demand is “low”, the payoff is $40 million. If they build “small” and demand is “high”, they can do nothing and payoff is $45 million, or they can expand. If they expand, there is a 30% chance the demand drops off and the payoff will be $35 million, and a 70% chance the demand grows and the payoff is $48 million.

If they build “large” and demand is “high”, the payoff is $60 million. If they build “large” and demand is “low”, they can do nothing and payoff is -$10 million, or they can reduce prices and payoff is $20 million. Determine the best decision(s) using a decision tree.

A-33

Decision Tree ExampleDecision Tree ExampleThree decisions: 1. Build “Large” or “Small” plant initially. 2. If build “Small” and demand is “High”, then “Expand”

or “Do nothing”. 3. If build “Large” and demand is “Low”, then decide to

“Reduce prices” or “Do nothing”.

Two states of nature: 1. Demand is “High” (0.6) or “Low” (0.4) initially. 2. If build “Small”, demand is “High”, and decision is

“Expand”, then demand “Grows” (0.7) or demand “Drops” (0.3).

A-34


Build small

Build large High (0.6)

Low (0.4)

High (0.6)

Low (0.4)

Expand

Do nothing

Do nothing

Reduce prices

Demand grows (0.7)

Demand drops (0.3)

$48

$35

$45

$40

$60

$20

-$10

1

3

2

A-35

Decision Tree SolutionDecision Tree Solution

Work right to left (from end back to beginning).

Start with Decision 3:“Reduce prices” or “Do nothing”.

Choose “Reduce prices” (20 > -10).

A-36


Build small


Low (0.4)

High (0.6)

Low (0.4)

Expand

Do nothing

Do nothing

Reduce prices

Demand grows (0.7)

Demand drops (0.3)

$48

$35

$45

$40

$60

$20

-$10

1

3

2

$20

A-37

Decision Tree SolutionDecision Tree Solution

Consider Decision 2: “Expand” or “Do nothing”.

To compare outcomes we need expected value if we “Expand”: (48*0.7) + (35*0.3) = 44.1

Choose “Do nothing” (45 > 44.1).

A-38


Build small


Low (0.4)

High (0.6)

Low (0.4)

Expand

Do nothing

Do nothing

Reduce prices

Demand grows (0.7)

Demand drops (0.3)

$48

$35

$45

$40

$60

$20

-$10

1

3

2

$44.1

$45

$20

$45

A-39


Build small


Low (0.4)

High (0.6)

Low (0.4)

Expand

Do nothing

Do nothing

Reduce prices

Demand grows (0.7)

Demand drops (0.3)

$48

$35

$45

$40

$60

$20

-$10

1

3

2

$44.1

$45

$20

$45

$44

$43

A-40

Decision Tree Final SolutionDecision Tree Final Solution

Decisions:

1. Build “Large”.

2. If demand is “Low”, then “Reduce prices”.

Expected payoff = $44 million.

A-41

Larger Decision TreeLarger Decision Tree

0.4

$10

$ 8

$12

$11

$ 6

$ 8

$ 9

1

3

2

0.3

0.3

0.6

0.4

0.5

0.3

0.20.6

0.4

$ 9

$12

$ 8

A-42

Larger Decision Tree - SolutionLarger Decision Tree - Solution

0.4

$10

$ 8

$12

$11

$ 6

$ 8

$ 9

1

3

2

0.3

0.3

0.6

0.4

0.5

0.3

0.20.6

0.4

$ 9

$12

$ 8

$10.28

$9.6

$9.6

$8.3

$10.4$10.4

Documents

A-1 Operations Management Decision-Making Tools Module A