How to construct a payoff table in excel

Quantitative And Qualitative Decision Making

Week 6, Lecture 6: Decision Analysis and Support in Organizations

Bb Discussion W6: Quantitative Analysis and Decision Making in an Organization

Preparation for Assignment 2 (Due Monday Oct-28 by 11:59pm) – Q&A

Individual Exercise: Working with the Tutorial for AD715 “Decision Trees in TreePlan”

AD 715: Quantitative and Qualitative Decision-Making

Week 6, Class 6 (10/8/2019)

Boston University MET AD715 © Dr. Zlatev, 2019

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C

D

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A

AGENDA

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Boston University MET AD715 © Dr. Zlatev, 2019 2

Week 6

C D

Decision making and decision analysis – an introduction

Decision making under certainty and uncertainty

Decision making under risk  Q/A: Costs minimization - an example

Decision trees  Q/A: Using software for payoff table and decision tree problems

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The Six Steps in Decision Making: Decision Analysis Prospective

1. Clearly define the problem at hand

2. List the possible alternatives

3. Identify the possible outcomes or states of nature

4. List the payoff (typically profit) of each combination of alternatives and outcomes

5. Select one of the mathematical decision theory models

6. Apply the model and make your decision

Step 1: Recognize the Need of a Decision

Step 2: Generate Alternative

Step 3: Assess Alternative

Step 4: Choose Among Alternatives

Step 5: Implement the Chosen Alternative

Step 6: Learn from Feedback

Decision Making

Process

The Steps in the Managerial Decision Making Process

Decision Making and Decision Analysis – An Introduction

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B 1

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Demonstration of the Decision Making Process as a Step-By-Step Analytical Approach

Step 3 – Identify possible outcomes or states of nature

• The market could be favorable or unfavorable

Step 5 – Select the decision model

• Depends on the environment and amount of risk and uncertainty

Decision Making and Decision Analysis – An Introduction

Business Running Case: Thompson Lumber Company

Step 1 – Define the problem

• Consider expanding by manufacturing and marketing a new product – backyard storage sheds

Step 2 – List possible alternatives

• Construct a large new plant

• Construct a small new plant

• Do not develop the new product line

Step 4 – List the payoffs

• Identify conditional values for the profits for large plant, small plant, and no development for the two possible market conditions

Step 6 – Apply the model to the data

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B 1

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STATE OF NATURE

ALTERNATIVE FAVORABLE MARKET ($)

UNFAVORABLE MARKET ($)

Construct a large plant 200,000 –180,000

Construct a small plant 100,000 –20,000

Do nothing 0 0

Decision Making and Decision Analysis – An Introduction

Business Running Case: Thompson Lumber Company

Step 3 – Identify possible outcomes or states of nature

• The market could be favorable or unfavorable

Step 2 – List possible alternatives

• Construct a large new plant

• Construct a small new plant

• Do not develop the new product line

States of Nature: Outcomes over which the decision makers has little or no control

Decision Table (Payoff Table) with Conditional Values

The easiest way to present the combination of decision alternatives, possible states of nature, and conditional values for each one of the possible decision alternatives and states of nature is called decision table or payoff table.

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B 1

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STATE OF NATURE

ALTERNATIVE FAVORABLE MARKET ($)

UNFAVORABLE MARKET ($)

Construct a large plant 200,000 –180,000

Construct a small plant 100,000 –20,000

Do nothing 0 0

Decision Table (Payoff Table) with Conditional Values

Decision Making and Decision Analysis – An Introduction

Business Running Case: Thompson Lumber Company

Conditional Values: Possible combination of alternatives and outcomes, also called payoffs. Payoffs can be based on money or any appropriate means of measuring benefits.

Step 4 – List the payoffs

• Identify conditional values for the profits for large plant, small plant, and no development for the two possible market conditions

Net profit of $200,000 is a conditional value because receiving the money is conditional upon both building a large factory and having a good (favorable) market

Net loss of $180,000 is a conditional value because receiving the money is conditional upon both building a large factory and having a unfavorable market

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B 1

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Types of Decision-Making Environments

• Decision making under certainty

– The decision maker knows with certainty the consequences of every alternative or decision choice

• Decision making under uncertainty

– The decision maker does not know the probabilities of the various outcomes

• Decision making under risk

– The decision maker knows the probabilities of the various outcomes

Decision Making and Decision Analysis – An Introduction

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B 1

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Decision Making Under Certainty

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Example:

You have $10,000 to invest for a one year period

Existing alternatives to invest in two equally secure and guaranteed investments: Consequences

(Return after 1 year in interest) • Alternative #1 is to open a saving account paying 4% interest $400 • Alternative #2 is to invest in a government Treasury bond paying 6% interest $600

Decision Choice: Select Alternative #2 ($600 > $400)

The decision makers know with certainty the

consequence of every alternative or decision choice

B 2

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Decision Making Under Uncertainty

Criteria for making decisions under uncertainty

1. Maximax (optimistic)

2. Maximin (pessimistic)

3. Criterion of realism (Hurwicz)

4. Equally likely (Laplace)

5. Minimax regret

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B 2

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Optimistic Used to find the alternative that maximizes the maximum payoff – maximax criterion

– Locate the maximum payoff for each alternative

– Select the alternative with the maximum number

STATE OF NATURE

ALTERNATIVE FAVORABLE MARKET ($)

UNFAVORABLE MARKET ($)

MAXIMUM IN A ROW ($)

Construct a large plant

200,000 –180,000 200,000

Construct a small plant

100,000 –20,000 100,000

Do nothing 0 0 0

Maximax Decision

Maximax

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STATE OF NATURE

ALTERNATIVE FAVORABLE MARKET ($)

UNFAVORABLE MARKET ($)

MINIMUM IN A ROW ($)

Construct a large plant

200,000 –180,000 -180,000

Construct a small plant

100,000 –20,000 -20,000

Do nothing 0 0 0

Maximin

Business Running Case: Thompson Lumber Company

Maximin Decision

Used to find the alternative that maximizes the minimum payoff – maximin criterion

– Locate the minimum payoff for each alternative

– Select the alternative with the maximum number

Pessimistic

Decision Making Under Uncertainty Maximax Decision Maximin Decision

B 2

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Criterion of Realism (Hurwicz)

Often called weighted average

– Compromise between optimism and pessimism

– Select a coefficient of realism ɑ, with 0 ≤ a ≤ 1

a = 1 is perfectly optimistic

a = 0 is perfectly pessimistic

– Compute the weighted averages for each alternative

– Select the alternative with the highest value

Weighted average = (best in row) + (1 – )(worst in row)

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 For the large plant alternative using ɑ = 0.8

(0.8)(200,000) + (1 – 0.8)(–180,000) = 124,000

 For the small plant alternative using ɑ = 0.8

(0.8)(100,000) + (1 – 0.8)(–20,000) = 76,000

STATE OF NATURE

ALTERNATIVE FAVORABLE MARKET ($)

UNFAVORABLE MARKET ($)

CRITERION OF REALISM

(a = 0.8) $

Construct a large plant

200,000 –180,000 124,000

Construct a small plant

100,000 –20,000 76,000

Do nothing 0 0 0

Criterion of Realism Decision

Realism

Business Running Case: Thompson Lumber Company

Decision Making Under Uncertainty  Criterion of Realism Decision B 2

Boston University MET AD715 © Dr. Zlatev, 2019

STATE OF NATURE

ALTERNATIVE FAVORABLE MARKET ($)

UNFAVORABLE MARKET ($)

ROW AVERAGE ($)

Construct a large plant

200,000 –180,000 10,000

Construct a small plant

100,000 –20,000 40,000

Do nothing 0 0 0

Equally Likely (Laplace)

Considers all the payoffs for each alternative

– Find the average payoff for each alternative

– Select the alternative with the highest average

Equally Likely Decision

Equally likely

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Decision Making Under Uncertainty

Business Running Case: Thompson Lumber Company

 Equally Likely DecisionB 2

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Minimax Regret

Based on opportunity loss or regret  The difference between the optimal profit and actual payoff for a decision

1. Create an opportunity loss table by determining the opportunity loss from not choosing the best alternative

2. Calculate opportunity loss by subtracting each payoff in the column from the best payoff in the column

3. Find the maximum opportunity loss for each alternative and pick the alternative with the minimum number

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Decision Making Under Uncertainty

STATE OF NATURE

ALTERNATIVE FAVORABLE MARKET ($)

UNFAVORABLE MARKET ($)

Construct a large plant

200,000 - 200,000 0 – (–180,000)

Construct a small plant

200,000 - 100,000 0 – (–20,000)

Do nothing 200,000 - 0 0 - 0

STATE OF NATURE

ALTERNATIVE FAVORABLE MARKET ($)

UNFAVORABLE MARKET ($)

Construct a large plant

0 180,000

Construct a small plant

100,000 20,000

Do nothing 200,000 0

Business Running Case: Thompson Lumber Company Determining Opportunity Losses Opportunity Loss Table

STATE OF NATURE

ALTERNATIVE FAVORABLE MARKET ($)

UNFAVORABLE MARKET ($)

MAXIMUM IN A ROW

($)

Construct a large plant

0 180,000 180,000

Construct a small plant

100,000 20,000 100,000

Do nothing 200,000 0 200,000

Minimax Decision Using Opportunity Loss

Minimax

Minimax Regret Decision (Opportunity Loss)

B 2

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Decision Making Under Risk

Expected Monetary Value (EMV)

When there are several possible states of nature and the probabilities associated with each possible state are known

– Most popular method – choose the alternative with the highest expected monetary value (EMV)

EMV(alternative) = X iP(X i )å where

Xi = payoff for the alternative in state of nature i

P(Xi) =probability of achieving payoff Xi (i.e., probability of state of nature i)

∑ = summation symbol

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Expanding the equation

EMV (alternative i) = (payoff of first state of nature) x (probability of first state of nature) + (payoff of second state of nature) x (probability of second state of nature) + … + (payoff of last state of nature) x (probability of last state of nature)

 EMVB 3

Boston University MET AD715 © Dr. Zlatev, 2019

• Each market outcome has a probability of occurrence of 0.50

• Which alternative would give the highest EMV?

EMV (large plant) = ($200,000)(0.5) + (–$180,000)(0.5)

= $10,000

EMV (small plant) = ($100,000)(0.5) + (–$20,000)(0.5)

= $40,000

EMV (do nothing) = ($0)(0.5) + ($0)(0.5)

= $0

Business Running Case: Thompson Lumber Company (EMV)

STATE OF NATURE

ALTERNATIVE FAVORABLE MARKET ($)

UNFAVORABLE MARKET ($) EMV ($)

Construct a large plant

200,000 –180,000 10,000

Construct a small plant

100,000 –20,000 40,000

Do nothing 0 0 0

Probabilities 0.5 0.5

Decision Table with Probabilities and EMVs

Best EMV

Decision Making Under Risk

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 EMVB 3

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Expected Value of Perfect Information (EVPI)

EVPI places an upper bound on what you should pay for additional information

EVwPI is the long run average return if we have perfect information before a decision is made

EVwPI = ∑(best payoff in state of nature i) (probability of state of nature i)

Decision Making Under Risk

Expanded EVwPI becomes EVwPI = (best payoff for first state of nature) x (probability of first state of nature) + (best payoff for second state of nature) x (probability of second state of nature) + … + (best payoff for last state of nature) x (probability of last state of nature)

EVPI = EVwPI – Best EMV and

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 EVPIB 3

Boston University MET AD715 © Dr. Zlatev, 2019

• Scientific Marketing, Inc. offers analysis that will provide certainty about market conditions (favorable)

• Additional information will cost $65,000

Business Running Case: Thompson Lumber Company (EVPI)

STATE OF NATURE

ALTERNATIVE FAVORABLE MARKET ($)

UNFAVORABLE MARKET ($) EMV ($)

Construct a large plant

200,000 –180,000 10,000

Construct a small plant

100,000 –20,000 40,000

Do nothing 0 0 0

Probabilities 0.5 0.5 With Perfect Information 200,000 0 100,000

Decision Table with Perfect Information

Best EVwPI

Best EMV The maximum EMV without additional information is $40,000

EVwPI = $200,000 x 0.5 + $0 x 0.5 = $100,000

where $200,000 is best payoff for first state of nature

$0 is the best payoff for second state of nature

EVPI = EVwPI – Best EMV = $100,000 - $40,000 = $60,000

Therefore, the maximum Thompson should pay for the additional information is $60,000

SOLUTION: Thompson should not pay $65,000 for this information

Should Thompson Lumber purchase the information?

Decision Making Under Risk

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 EVPIB 3

Boston University MET AD715 © Dr. Zlatev, 2019

Expected Opportunity Loss

Expected opportunity loss (EOL) is the cost of not picking the best solution

– Construct an opportunity loss table

– For each alternative, multiply the opportunity loss by the probability of that loss for each possible outcome and add these together

– Minimum EOL will always result in the same decision as maximum EMV

– Minimum EOL will always equal EVPI

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Decision Making Under Risk

Business Running Case: Thompson Lumber Company

EOL (large plant) = (0.50)($0) + (0.50)($180,000) = $90,000

EOL (small plant) = (0.50)($100,000) + (0.50)($20,000) = $60,000

EOL (do nothing) = (0.50)($200,000) + (0.50)($0) = $100,000

STATE OF NATURE

ALTERNATIVE FAVORABLE MARKET ($)

UNFAVORABLE MARKET ($)

EOL

($)

Construct a large plant

0 180,000 90,000

Construct a small plant

100,000 20,000 60,000

Do nothing 200,000 0 100,000 Opportunity Loss Table

Probabilities 0.5 0.5

Best EOL

EOL Table

 EOL (Expected Opportunity Loss)

B 3

Boston University MET AD715 © Dr. Zlatev, 2019

EMV & Sensitivity Analysis

EMV(large plant) = $200,000P – $180,000)(1 – P)

= $200,000P – $180,000 + $180,000P

= $380,000P – $180,000

If P = 1 then EMV = $380,000x1 - $180,000 = $200,000

If P = 0 then EMV = $380,000x0 - $180,000 = -$180,000

EMV(small plant) = $100,000P – $20,000)(1 – P)

= $100,000P – $20,000 + $20,000P

= $120,000P – $20,000

If P = 1 then EMV = $120,000x1 - $20,000 = $100,000

If P = 0 then EMV = $120,000x0 - $20,000 = -$20,000

EMV(do nothing) = $0P + 0(1 – P)

= $0 20

Decision Making Under Risk  EMV & Sensitivity Analysis

$300,000

$200,000

$100,000

0

–$100,000

–$200,000

EMV Values

EMV (large plant)

EMV (small plant)

EMV (do nothing)

Point 1

Point 2

.167 .615 1

Values of P

Business Running Case: Thompson Lumber Company

B 3

Boston University MET AD715 © Dr. Zlatev, 2019

Probabilities P (1-P)

EMV & Sensitivity Analysis

EMV(large plant) = $200,000P – $180,000)(1 – P)

= $200,000P – $180,000 + $180,000P

= $380,000P – $180,000

EMV(small plant) = $100,000P – $20,000)(1 – P)

= $100,000P – $20,000 + $20,000P

= $120,000P – $20,000

EMV(do nothing) = $0P + 0(1 – P)

= $0

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Decision Making Under Risk  EMV & Sensitivity Analysis

$300,000

$200,000

$100,000

0

–$100,000

–$200,000

EMV Values

EMV (large plant)

EMV (small plant)

EMV (do nothing)

Point 1

Point 2

.167 .615 1

Values of P

Point 1: EMV(do nothing) = EMV(small plant) Point 2: EMV(small plant) = EMV(large plant)

0 = $120,000P - $20,000

20,000 P = ------------- = 0.167

120,000

$120,000P - $20,000 = $380,000P - $180,000

160,000 P = ------------- = 0.615

260,000

Business Running Case: Thompson Lumber Company

B 3

Boston University MET

AD715 © Dr. Zlatev, 2019

EMV & Sensitivity Analysis

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Decision Making Under Risk  EMV & Sensitivity Analysis

$300,000

$200,000

$100,000

0

–$100,000

–$200,000

EMV Values

EMV (large plant)

EMV (small plant)

EMV (do nothing)

Point 1

Point 2

.167 .615 1

Values of P

Business Running Case: Thompson Lumber Company

BEST ALTERNATIVE RANGE OF P VALUES

Do nothing Less than 0.167

Construct a small plant 0.167 – 0.615

Construct a large plant Greater than 0.615

CONCLUSIONS:

B 3

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Problem (Text, p.p.75 - 77):

A department will be signing three year lease for a new copy machine and three different machines are being considered

• For each of the machines, there is a monthly fee (incl. monthly fee & charge per each copy)

• The department has estimated that the number of copies/Mo could be 10,000 or 20,000 or 30,000

• The monthly cost for each machine based on the offers and the three levels of activities is shown in the table below

Which machine should be selected?

10,000 COPIES PER MONTH

20,000 COPIES PER MONTH

30,000 COPIES PER MONTH

Machine A 950 1,050 1,150

Machine B 850 1,100 1,350

Machine C 700 1,000 1,300

TABLE 3.12 – Payoff Table

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Q/A: Costs Minimization - An ExampleB 3

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10,000 COPIES PER

MONTH

20,000 COPIES PER

MONTH

30,000 COPIES PER

MONTH

BEST PAYOFF (MINIMUM)

WORST PAYOFF

(MAXIMUM)

Machine A 950 1,050 1,150 950 1,150

Machine B 850 1,100 1,350 850 1,350

Machine C 700 1,000 1,300 700 1,300

TABLE 3.13 – Best and Worst Payoffs

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Q/A: Costs Minimization - An Example

Using Best Payoff (Minimum) vs Worst Payoff (Maximum)

Using Hurwicz criteria with 70% coefficient

For each machine

Machine A: 0.7(950) + 0.3(1,150) = 1,010

Machine B: 0.7(850) + 0.3(1,350) = 1,000

Machine C: 0.7(700) + 0.3(1,300) = 880

Weighted average =

= 0.7(best payoff) + (1 – 0.7)(worst payoff)

Decision: to select machine C based on this criterion (it has the lowest weighted average costs)

DECISIONS  Criterion of Realism

B 3

Boston University MET AD715 © Dr. Zlatev, 2019

Using equally likely criteria

For each machine

Machine A: (950 + 1,050 + 1,150)/3 = 1,050

Machine B: (850 + 1,100 + 1,350)/3 = 1,100

Machine C: (700 + 1,000 + 1,300)/3 = 1,000

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Q/A: Costs Minimization - An Example DECISIONS  Equally Likely Criterion

10,000 COPIES PER MONTH

20,000 COPIES PER MONTH

30,000 COPIES PER MONTH

Machine A 950 1,050 1,150

Machine B 850 1,100 1,350

Machine C 700 1,000 1,300

Decision: to select machine C based on this criterion (it has the lowest average costs)

B 3

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Using EMV Criterion USAGE PROBABILITY

10,000 0.40

20,000 0.30

30,000 0.30

Q/A: Costs Minimization - An Example DECISIONS  EMV Criterion

Assumptions for probability

for the three states of nature

(based on past records)

10,000 COPIES PER

MONTH

20,000 COPIES PER

MONTH

30,000 COPIES PER

MONTH EMV

Machine A 950 1,050 1,150 1,040

Machine B 850 1,100 1,350 1,075

Machine C 700 1,000 1,300 970

With perfect information 700 1,000 1,150 925

Probability 0.4 0.3 0.3

TABLE 3.14 Expected Monetary Values and Expected Value with Perfect Information

Decision: to select machine C based on this criterion (it has the lowest EMV)

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B 3

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Using EVPI & Expected Opportunity Loss Criterion

Q/A: Costs Minimization - An Example DECISIONS  EOL Criterion

10,000 COPIES PER

MONTH

20,000 COPIES PER

MONTH

30,000 COPIES PER

MONTH EMV

Machine A 950 1,050 1,150 1,040

Machine B 850 1,100 1,350 1,075

Machine C 700 1,000 1,300 970

With perfect information 700 1,000 1,150 925

Probability 0.4 0.3 0.3

TABLE 3.14 Expected Monetary Values and Expected Value with Perfect Information

EVwPI = $925

Best EMV without perfect information= $970

EVPI = 970 – 925 = $45

Decision: to select machine C based on the minimax regret criterion (it has the minimum of the maximum)

10,000 COPIES PER

MONTH

20,000 COPIES PER

MONTH

30,000 COPIES PER

MONTH MAXIMUM EOL

Machine A 250 50 0 250 115

Machine B 150 100 200 200 150

Machine C 0 0 150 150 45

Probability 0.4 0.3 0.3

TABLE 3.15 – Opportunity Loss Table Decision: to select machine C based on the EOL criterion (it has the lowest expected opportunity loss)

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B 3

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Decision Trees

Any problem that can be presented in a decision table can be graphically represented in a decision tree

– Most beneficial when a sequence of decisions must be made

– All decision trees contain decision points/nodes and state-of-nature points/nodes

– At decision nodes one of several alternatives may be chosen

– At state-of-nature nodes one state of nature will occur

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1. Define the problem

2. Structure or draw the decision tree

3. Assign probabilities to the states of nature

4. Estimate payoffs for each possible combination of alternatives and states of nature

5. Solve the problem by computing expected monetary values (EMVs) for each state of nature node

Five Steps of Decision Tree Analysis

B 4

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Structure of Decision Trees

• Trees start from left to right

• Trees represent decisions and outcomes in sequential order

• Squares represent decision nodes

• Circles represent states of nature nodes

• Lines or branches connect the decisions nodes and the states of nature

Decision Trees

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B 4

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Thompson’s Decision Tree

Favorable Market

Unfavorable Market

Favorable Market

Unfavorable Market

1

Construct

Small Plant 2

FIGURE 3.2

A Decision Node

A State-of-Nature Node

Decision Trees

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STATE OF NATURE

ALTERNATIVE FAVORABLE MARKET ($)

UNFAVORABLE MARKET ($)

Construct a large plant 200,000 –180,000

Construct a small plant 100,000 –20,000

Do nothing 0 0

Decision Table (Payoff Table) with Conditional Values

Business Running Case: Thompson Lumber Company

B 4

Boston University MET AD715 © Dr. Zlatev, 2019

Favorable Market

Unfavorable Market

Favorable Market

Unfavorable Market

1

Construct

Small Plant 2

Alternative with best EMV is selected

FIGURE 3.3

EMV for Node 1 = $10,000

= (0.5)($200,000) + (0.5)(–$180,000)

EMV for Node 2 = $40,000

= (0.5)($100,000) + (0.5)(–$20,000)

Payoffs

$200,000

–$180,000

$100,000

–$20,000

$0

(0.5)

(0.5)

(0.5)

(0.5)

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Thompson’s Decision Tree

Decision Trees

Business Running Case: Thompson Lumber Company

B 4

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Thompson’s Complex Decision Tree

First Decision Point

Second Decision Point

Favorable Market (0.78)

Unfavorable Market (0.22)

Favorable Market (0.78)

Unfavorable Market (0.22)

Favorable Market (0.27)

Unfavorable Market (0.73)

Favorable Market (0.27)

Unfavorable Market (0.73)

Favorable Market (0.50)

Unfavorable Market (0.50)

Favorable Market (0.50)

Unfavorable Market (0.50) Small

Plant

No Plant

6

7

Small

Plant

No Plant

2

3

Small

Plant

No Plant

4

5

1

Payoffs

–$190,000

$190,000

$90,000

–$30,000

–$10,000

–$180,000

$200,000

$100,000

–$20,000

$0

–$190,000

$190,000

$90,000

–$30,000

–$10,000

FIGURE 3.4

32

Decision Trees

Business Running Case: Thompson Lumber Company

Thompson’s Complex Decision Tree

B 4

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1. Given favorable survey results EMV(node 2) = EMV(large plant | positive survey)

= (0.78)($190,000) + (0.22)(– $190,000) = $106,400

EMV(node 3) = EMV(small plant | positive survey)

= (0.78)($90,000) + (0.22)(– $30,000) = $63,600

EMV for no plant = – $10,000

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Decision Trees

Business Running Case: Thompson Lumber Company

2. Given negative survey results EMV(node 4) = EMV(large plant | negative survey) = (0.27)($190,000) + (0.73)(– $190,000) = – $87,400

EMV(node 5) = EMV(small plant | negative survey)

= (0.27)($90,000) + (0.73)(– $30,000) = $2,400

EMV for no plant = – $10,000

Thompson’s Complex Decision Tree

B 4

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3. Expected value of the market survey EMV(node 1) = EMV(conduct survey) = (0.45)($106,400) + (0.55)($2,400)

= $47,880 + $1,320 = $49,200

4. Expected value no market survey EMV(node 6) = EMV(large plant) = (0.50)($200,000) + (0.50)(– $180,000) = $10,000

EMV(node 7) = EMV(small plant)

= (0.50)($100,000) + (0.50)(– $20,000) = $40,000

EMV for no plant = $0

The best choice is to seek marketing information

Decision Trees Thompson’s Complex Decision Tree

34

Business Running Case: Thompson Lumber Company

B 4

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FIGURE 3.5 First Decision Point

Second Decision Point

Favorable Market (0.78)

Unfavorable Market (0.22)

Favorable Market (0.78)

Unfavorable Market (0.22)

Favorable Market (0.27)

Unfavorable Market (0.73)

Favorable Market (0.27)

Unfavorable Market (0.73)

Favorable Market (0.50)

Unfavorable Market (0.50)

Favorable Market (0.50)

Unfavorable Market (0.50) Small

Plant

No Plant

6

7

Small

Plant

No Plant

2

3

Small

Plant

No Plant

4

5

1

Payoffs

–$190,000

$190,000

$90,000

–$30,000

–$10,000

–$180,000

$200,000

$100,000

–$20,000

$0

–$190,000

$190,000

$90,000

–$30,000

–$10,000

$ 4

0 ,0

0 0

$ 2

,4 0

0 $

1 0

6 ,4

0 0

$ 4

9 ,2

0 0

$106,400

$63,600

–$87,400

$2,400

$10,000

$40,000

Decision Trees Thompson’s Complex Decision Tree

35

Business Running Case: Thompson Lumber Company

B 4

Boston University MET AD715 © Dr. Zlatev, 2019

Expected Value of Sample Information

Thompson wants to know the actual value of doing the survey

= (EV with SI + cost) – (EV without SI)

EVSI = ($49,200 + $10,000) – $40,000 = $19,200

EVSI = – Expected value

with sample information

Expected value of best decision without sample

information

Decision Trees

36

Business Running Case: Thompson Lumber Company

B 4

Boston University MET AD715 © Dr. Zlatev, 2019

Efficiency of Sample Information

• Possibly many types of sample information available

• Different sources can be evaluated

Efficiency of sample information = EVSI

EVPI 100%

Efficiency of sample information = 19,200

60,000 100% = 32%

Market survey is only 32% as efficient as perfect information

Decision Trees

Business Running Case: Thompson Lumber Company

37

B 4

Boston University MET AD715 © Dr. Zlatev, 2019

Sensitivity Analysis • How sensitive are the decisions to changes in the probabilities? • How sensitive is our decision to the probability of a favorable survey result?

• If the probability of a favorable result (p = .45) where to change, would we make the same decision?

• How much could it change before we would make a different decision?

Decision Trees

p = probability of a favorable survey result

(1 – p) = probability of a negative survey result

EMV(node 1) = ($106,400)p +($2,400)(1 – p)

= $104,000p + $2,400

Business Running Case: Thompson Lumber Company

We are indifferent when the EMV of node 1 is the same as the EMV of not conducting the survey

$104,000p + $2,400 = $40,000

$104,000p = $37,600

p = $37,600/$104,000 = 0.36

DECISION: If p < 0.36, do not conduct the survey If p > 0.36, conduct the survey

38

B 4

Boston University MET AD715 © Dr. Zlatev, 2019

39

Q/A: Using Software for Payoff Table and Decision Tree Problems

Other Decision Tree Software (A Short List):

Tutorial ‘Decision Trees in TreePlan’ >>> v-labs (Excel 2016 Add-In ‘TreePlan’)

ASSIGNMENT 2 Task 2-4: Apply TreePlan

B 4

1. Excel Decision Tree Add-Ins

• Risk Solver Pro & Analytic Solver Pro v2016 by FrontlineSolvers, www.solver.com

• Monte Carlo Risk Simulation, Decision Tree and Statistical Excel Analysis Add-In by Lumenaut, www.lumenaut.com

• Decision Tree Suite by Palisade, www.palisade.com • TreePlan by TreePlan Software, www.treeplan.com

2. Top Decision Tree Analysis Software Products 2016 (ranked by Capterra, www.capterra.com ; Filter Results: 1000+ number of users):

• pcFinancials by Performance Canvas Financials, http://www.performancecanvas.com

• Analytica by Lumina Decision Systems, http://www.lumina.com/

• 1000Minds (Multi-Criteria Decision-Making) by 1000minds: www.1000minds.com

• Blaze Advisor by Fico, www.fico.com • D-Sight Collaborative Decision-Making platform by D-Sight,

http://www.d-sight.com • Decision Lens by Decision Lens, www.decisionlens.com • Decision Support Software by Logicnets, www.logicnets.com • DPL 8 Direct by Syncopation, www.syncopation.com • Spotfire by Tibco, www.tibco.com • VisiRule by Logic Programming Associates, www.lpa.co.uk

Boston University MET AD715 © Dr. Zlatev, 2019

http://www.solver.com/
http://www.lumenaut.com/
http://www.palisade.com/
http://www.treeplan.com/
http://www.capterra.com/
http://www.performancecanvas.com/
http://www.lumina.com/
http://www.1000minds.com/
http://www.fico.com/
http://www.d-sight.com/
http://www.decisionlens.com/
http://www.logicnets.com/
http://www.syncopation.com/
http://www.tibco.com/
http://www.lpa.co.uk/
Discussion W6: Quantitative Analysis and Managerial Decisions in an OrganizationC

Boston University MET AD715 © Dr. Zlatev, 2019 39

With the help of one or several of the recommended tutorials for Week 6, discuss your experience and plans for applying analytical methods in your Assignment 2 or in your current (or targeted) profession.

Recommended discussion topics (covered in Lecture 06):

Decision making under certainty and uncertainty

Decision making under risk

Decision trees

Using software for payoff table and decision tree problems

Assignment 2: Prep-Plan

40

D

Boston University MET AD715 © Dr. Zlatev, 2019

In-Class Exercise: Task 2-1

In-Class Exercise: Task 2-2

Assignment 2: Prep-Plan

41

D

Boston University MET AD715 © Dr. Zlatev, 2019

In-Class Exercise: Task 2-3

In-Class Exercise: Task 2-4

42Boston University MET AD715 © Dr. Zlatev, 2019

Individual Exercise W6: Working with the Tutorial for AD715 “Decision Trees in TreePlan”

F

Targeted Outcomes:

1. Learn how to access BU MET VLAB

2. Review the Tutorial for AD15 “Decision Trees in TreePlan”

Bb course website >>> Content >>> Tutorials

1. Review the script “Decision Trees in TreePlan”

2. Go to the VLAB, open Excel 2016, and repeat the steps from the script (task 3)

In this course, students will be using Microsoft Excel software applications for

Windows. As part of the tuition, all BU students can use this software free of charge.

Click here for directions to get free access to Microsoft Excel applications from

MET’s Virtual Labs: http://www.bu.edu/metit/pc-labs/virtual-labs/

You will not be able to download the software using this option, but you will be given

access to it for use during the course.

If you are first-time VLAB user, please synchronize your BU account with the BU

Active Directory by following the recommended

procedures: https://weblogin.bu.edu/accounts/create?_hostname=ad;_conffile=kpw

From the existing two VLAB connection modes, I am recommending to select

Horizon Client: http://www.bu.edu/metit/vlabs-client/

The process of accessing and working within the VLABs is demonstrated and

explained with the help of Video Tutorials (one for Windows, and the other for MAC

users).

Attention: Files saved on the desktop or local drive of the virtual lab will be deleted

after you log off. Hence, before logging off, you must save your work on an external

source, such as Google Drive, Shared Folder, USB drive, or email the files to

yourself. Instructions how to save files in the MET VLABs are accessible from here:

http://www.bu.edu/metit/vlabs-client/

To Get Help, call (617) 358-5401 or send a message to METIT@BU.EDU . Please

indicate that you have a VLAB issue and include your course number.

http://www.bu.edu/metit/pc-labs/virtual-labs/
https://weblogin.bu.edu/accounts/create?_hostname=ad;_conffile=kpw
http://www.bu.edu/metit/vlabs-client/
http://www.bu.edu/metit/vlabs-client/