Decision analysis: part 1

BSAD 30

Dave Novak

Source: Anderson et al., 2013 Quantitative Methods for Business 12th edition – some slides are directly from J. Loucks © 2013 Cengage Learning

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Overview

What is decision analysis? Problem Formulation

Decision alternativeStates of naturePayoff

Decision Making without ProbabilitiesOptimistic (maximax)Conservative (maximin)Minimum regret (minimax)

2

Overview

Decision Making with ProbabilitiesDecision tressCalculating the expected value OF perfect

information

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Decision analysis

Decision analysis can be used to develop an optimal strategy when a decision maker is faced with a number of alternatives and an uncertain or risk-filled pattern of future events

Even when a careful decision analysis has been conducted, the uncertain future events make the final consequence uncertain

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Decision analysis

The risk (exposure to some type of negative outcome) associated with any decision alternative is a direct result of the uncertainty associated with the final consequence

Good decision analysis includes risk analysis that provides probability information about the favorable as well as the unfavorable consequences that may occur

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Problem formulation

A decision problem is characterized by:1. decision alternatives

2. states of nature

3. resulting payoffs

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Problem formulation

The decision alternatives are the different possible strategies the decision maker can employ

The states of nature refer to future events, not under the control of the decision maker, which may occurStates of nature should be defined so that

they are mutually exclusive and collectively exhaustive

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Development corp. example

Pittsburgh Development Corporation (PDC) purchased land that will be the site of a new luxury condominium complex. PDC commissioned preliminary architectural drawings for three different project alternatives: 1) 30 condos, 2) 60 condos, and 3) 90 condos

The financial success of the project depends upon the size of the condominium complex and the uncertainty concerning the demand for the condominiums

The PDC decision problem is to select the project alternative that will lead to the largest profit given the uncertainty concerning the demand for the condominiums

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Influence diagram

An influence diagram is a graphical device showing the relationships among the decisions, the chance events, and the consequences Squares or rectangles depict decision

nodesCircles or ovals depict chance nodesDiamonds depict consequence nodesLines connecting the nodes show the

direction of influence9

Influence diagram

ComplexSize

Profit

Demand for theCondominiums

DecisionChanceConsequence

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Payoff table

The consequence resulting from a specific combination of a decision alternative and a state of nature is a payoff

A table showing payoffs for all combinations of decision alternatives and states of nature is a payoff table

Payoffs can be expressed in terms of profit, cost, time, distance or any other appropriate quantifiable measure

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Development corp. example Consider the following problem with: 3 decision

alternatives and 2 states of nature with the following payoff table representing profits (in millions):

PAYOFF TABLE States of Nature

Strong Demand Weak Demand Decision Alternative s1 s2

Small complex, d1 8 7

Medium complex, d2 14 5

Large complex, d3 20 -9

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Decision making without probabilities Three commonly used criteria for decision

making when probability information regarding the likelihood of the states of nature is unavailable are: 1. The optimistic approach

2. The conservative approach

3. The minimax regret approach

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Optimistic approach

The decision with the largest possible payoff is chosen

If the payoff table was in terms of costs, the decision with the lowest cost would be chosen

If the payoff table was in terms of profit, the decision with the greatest profit would be chosen

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Optimistic approach

Also referred to as maximax approach Choose the decision that has the largest

profit value in the entire payoff table (largest profit of strong demand scenarios)

Maximum Decision Payoff

d1 8 d2 14 d3 20

Maximaxpayoff

Maximaxdecision

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Conservative approach

For each decision the minimum payoff is listed and then the decision corresponding to the maximum of the minimum payoffs is selected

If the payoff was in terms of costs, the maximum cost would be determined for each decision and then the decision corresponding to the smallest of the maximum costs is selected (the maximum possible cost is minimized

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Conservative approach

Also referred to as maximin approach Choose the decision with the maximum of

the minimum payoffs (largest profit of the weak demand scenarios)

Minimum Decision Payoff

d1 7 d2 5 d3 -9

MaximinpayoffMaximin

decision

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Minimum regret approach

The minimax regret approach requires the construction of a regret table or an opportunity loss table

Calculate the difference between each payoff and the largest payoff for each state of nature

Then, using the regret table, the maximum regret for each possible decision is listed

Select decision corresponding to the minimum of the maximum regrets

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Minimum regret approach

Also referred to as minimax approach Subtract each payoff in a column from the

largest payoff in the column

REGRET TABLE States of Nature

Strong Demand Weak Demand

Decision Alternative s1 s2

Small complex, d1 12 0 Medium complex, d2 6 2 Large complex, d3 0 16

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Minimum regret approach

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Minimum regret approach

Also referred to as minimax approach For each decision list the maximum regret

and choose the decision with the minimum of these values

Maximum Decision Regret

d1 12 d2 6 d3 16

MinimaxregretMinimax

decision

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Incorporating probabilities

Expected Value Approach If probabilistic information regarding the

states of nature is available, we can use the expected value (EV) approach

The expected return for each decision is calculated by summing the products of the payoff under each state of nature and the probability of the respective state of nature

The decision yielding the best expected return is chosen

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Expected value approach

The expected value of a decision alternative is the sum of weighted payoffs for the decision alternative:

EV( ) ( )d P s Vi j ijj

N

1

EV( ) ( )d P s Vi j ijj

N

1

where: N = the number of states of nature

P(sj ) = the probability of state of nature sj

Vij = the payoff corresponding to decision alternative di and state of

nature sj23

Expected value approach

Calculate the expected value for each decision using the decision tree on slide 27 d1, d2, and d3 represent the decision

alternatives of building a small, medium, and large condo complex

s1 and s2 represent the states of nature for strong demand and weak demand

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Decision trees

A decision tree can help with the representation of the problem and the solution for the problem

A decision tree is a chronological representation of the decision problem

Each decision tree has two types of nodes:round nodes correspond to the states of

nature square nodes correspond to the decision

alternatives 25

Decision trees

The branches leaving each round node represent the different states of nature

The branches leaving each square node represent the different decision

At the end of each limb of a tree are the payoffs attained from the series of branches making up that limb

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Decision trees

1

.8

.2

.8

.2

.8

.2

d1

d2

d3

s1

s1

s1

s2

s2

s2

Payoffs

$8 mil

$7 mil

$14 mil

$5 mil

$20 mil

-$9 mil

2

3

4

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Decision trees

1

small d1

medium d2

large d3

2

3

4

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Expected value of perfect information Often information is available which can

improve the probability estimates for the states of nature

The expected value of perfect information (EVPI) is the increase in the expected profit that would result if one knew with certainty which state of nature would occur

The EVPI provides an upper bound (or maximum) on the expected value of any sample or survey information

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Expected value of perfect information EVPI calculation

1. Determine the optimal return corresponding to each state of nature

2. Compute the expected value of the optimal returns

3. Subtract the EV of the optimal decision from the amount determined in Step 2

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Expected value of perfect information Expected value with perfect information

(EVwPI)

Expected value without perfect information (EVwoPI)

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Expected value of perfect information Expected value OF perfect information

(EVPI)

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Summary

What is decision analysis? Problem Formulation

Decision alternativeStates of naturePayoff

Decision Making without ProbabilitiesOptimistic (maximax)Conservative (maximin)Minimum regret (minimax)

33

Summary

Decision Making with ProbabilitiesDecision tressCalculating the expected value OF perfect

information

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