Introduction to management science 10e by bernard taylor chapter 13

■ Components of Decision Making ■ Decision Making without Probabilities ■ Decision Making with Probabilities ■ Decision Analysis with Additional Information ■ Utility Chapter Topics Copy

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Decision Analysis

Chapter 12

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■ Components of Decision Making

■ Decision Making without Probabilities

■ Decision Making with Probabilities

■ Decision Analysis with Additional Information

■ Utility

Chapter Topics

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Table 12.1 Payoff Table

■ A state of nature is an actual event that may

occur in the future

■ A payoff table is a means of organizing a decision

situation, presenting the payoffs from different

decisions given the various states of nature

Components of Decision Making

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Table 12.3 Payoff Table Illustrating a

Maximax Decision

In the maximax criterion the decision maker

selects the decision that will result in the

maximum of maximum payoffs; an optimistic

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Table 12.4 Payoff Table Illustrating a

Maximin Decision

In the maximin criterion the decision maker

selects the decision that will reflect the

maximum of the minimum payoffs; a pessimistic

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minimizes the maximum regret.

Decision Making without

Probabilities

Minimax Regret Criterion

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The Hurwicz criterion multiplies the best payoff

by  and the worst payoff by 1- ., for each

decision, and the best result is selected.

Decision Values Apartment building $50,000(.4) +

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12-The equal likelihood ( or Laplace) criterion

multiplies the decision payoff for each state of nature by an equal weight, thus assuming that the states of nature are equally likely to occur.

Decision Values Apartment building $50,000(.5) +

Equal Likelihood Criterion

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12-■ A dominant decision is one that has a better

payoff than another decision under each state

of nature.

■ The appropriate criterion is dependent on the

“risk” personality and philosophy of the

Equal likelihood Apartment

Probabilities

Summary of Criteria Results

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12-Exhibit 12.1

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Exhibit 12.2

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12-Exhibit 12.3

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12-Expected value is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence.

EV(Apartment) = $50,000(.6) + 30,000(.4) =

42,000

EV(Office) = $100,000(.6) - 40,000(.4) = 44,000 EV(Warehouse) = $30,000(.6) + 10,000(.4) = 22,000

Table 12.7

Decision Making with Probabilities

Expected Value

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■ The expected opportunity loss is the expected

value of the regret for each decision.

■ The expected value and expected opportunity

loss criterion result in the same decision.

EOL(Apartment) = $50,000(.6) + 0(.4) = 30,000

EOL(Office) = $0(.6) + 70,000(.4) = 28,000

EOL(Warehouse) = $70,000(.6) + 20,000(.4) = 50,000

Table 12.8

Expected Opportunity Loss

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12-Exhibit 12.5

Expected Value Problems

Solution with QM for Windows

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Exhibit 12.6

Expected Value Problems

Solution with Excel and Excel QM (1

of 2)

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12-Expected Value Problems

Solution with Excel and Excel QM (2

of 2)

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Exhibit 12.7

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■ The expected value of perfect information

(EVPI) is the maximum amount a decision

maker would pay for additional information.

■ EVPI equals the expected value given perfect

information minus the expected value without perfect information.

■ EVPI equals the expected opportunity loss

(EOL) for the best decision.

Expected Value of Perfect

Information

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■ Decision with perfect information:

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12-Exhibit 12.8

EVPI with QM for Windows

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A decision tree is a diagram consisting of

decision nodes (represented as squares),

probability nodes (circles), and decision

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■ The expected value is computed at each

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Exhibit 12.9

Decision Trees with QM for Windows

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12-Decision Making with Probabilities

Decision Trees with Excel and

TreePlan (1 of 4)

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Exhibit 12.10

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Exhibit 12.11

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12-Exhibit 12.12

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Exhibit 12.13

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Sequential Decision Trees (1 of 4)

■ A sequential decision tree is used to illustrate a

situation requiring a series of decisions.

■ Used where a payoff table, limited to a single

decision, cannot be used.

■ Real estate investment example modified to

encompass a ten-year period in which several decisions must be made:

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Figure 12.4 Sequential Decision Tree

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■ Decision is to purchase land; highest net

expected value ($1,160,000).

■ Payoff of the decision is $1,160,000.

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Figure 12.5 Sequential Decision Tree with Nodal Expected Values

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12-Exhibit 12.14

Sequential Decision Tree Analysis

Solution with QM for Windows

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Exhibit 12.15

Sequential Decision Tree Analysis

Solution with Excel and TreePlan

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12-■ Bayesian analysis uses additional information to alter the marginal probability of the occurrence

of an event.

■ In real estate investment example, using

expected value criterion, best decision was to

purchase office building with expected value of

$444,000, and EVPI of $28,000.

Table 12.11

Decision Analysis with Additional

Information

Bayesian Analysis (1 of 3)

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■ A conditional probability is the probability that

an event will occur given that another event has already occurred.

■ Economic analyst provides additional

information for real estate investment decision, forming conditional probabilities:

g = good economic conditions

p = poor economic conditions

P = positive economic report

N = negative economic report P(Pg) = 80 P(NG) = 20 P(Pp) = 10 P(Np) = 90

Information

Bayesian Analysis (2 of 3)

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12-■ A posterior probability is the altered marginal

probability of an event based on additional

information.

■ Prior probabilities for good or poor economic

conditions in real estate decision:

P(g) = 60; P(p) = 40

■ Posterior probabilities by Bayes’ rule:

(gP) = P(PG)P(g)/[P(Pg)P(g) + P(Pp)P(p)] = (.80)(.60)/[(.80)(.60) + (.10)(.40)]

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Information

Decision Trees with Posterior

Probabilities (1 of 4)Decision tree with posterior probabilities differ

from earlier versions in that:

■ Two new branches at beginning of tree

represent report outcomes.

■ Probabilities of each state of nature are

posterior probabilities from Bayes’ rule.

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Information

Decision Trees with Posterior

Probabilities (3 of 4)EV (apartment building) = $50,000(.923) +

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Table 12.12 Computation of Posterior Probabilities

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12-Decision Analysis with Additional

Information Computing Posterior

Probabilities with Excel

Exhibit 12.16

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■ The expected value of sample information

(EVSI) is the difference between the expected

value with and without information:

For example problem, EVSI = $63,194 - 44,000 =

$19,194

■ The efficiency of sample information is the ratio

of the expected value of sample information to the expected value of perfect information:

efficiency = EVSI /EVPI = $19,194/ 28,000 = 68

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12-Expected Cost (insurance) = 992($500)

■ Utility is a measure of personal satisfaction

derived from money.

■ Utiles are units of subjective measures of

utility.

■ Risk averters forgo a high expected value to

avoid a low-probability disaster.

■ Risk takers take a chance for a bonanza on a

very low-probability event in lieu of a sure

Information

Utility (2 of 2)

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12-States of Nature Decision Good Foreign Competitive Conditions Poor Foreign Competitive Conditions Expand

Maintain Status Quo

Sell now

$ 800,000 1,300,000 320,000

$ 500,000 -150,000 320,000

Example Problem Solution (1 of 9)

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12-Decision Analysis

a Determine the best decision without

probabilities using the 5 criteria of the

chapter.

b Determine best decision with probabilities

assuming 70 probability of good

conditions, 30 of poor conditions Use

expected value and expected opportunity loss criteria.

c Compute expected value of perfect information.

d Develop a decision tree with expected value at

the nodes.

e Given following, P(Pg) = 70, P(Ng) = 30,

P(Pp) = 20, P(Np) = 80, determine posterior probabilities using Bayes’ rule.

f Perform a decision tree analysis using the

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12-Step 1 (part a): Determine decisions without

probabilities.

Maximax Decision: Maintain status quo

Decisions Maximum Payoffs

Expand $800,000

Status quo 1,300,000 (maximum)

Sell 320,000

Maximin Decision: Expand

Decisions Minimum Payoffs

Expand $500,000 (maximum)

Status quo -150,000

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Minimax Regret Decision: Expand

Decisions Maximum Regrets

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12-Equal Likelihood Decision: Expand

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Expected opportunity loss decision: Maintain

status quo

Expand $500,000(.7) + 0(.3) = $350,000 Status quo 0(.7) + 650,000(.3) =

$195,000

Sell $980,000(.7) + 180,000(.3) =

$740,000

Step 3 (part c): Compute EVPI.

EV given perfect information = 1,300,000(.7) + 500,000(.3) = $1,060,000

EV without perfect information =

$1,300,000(.7) - 150,000(.3) = $865,000

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Step 4 (part d): Develop a decision tree.

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Step 5 (part e): Determine posterior

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12-Step 6 (part f): Decision tree

analysis.

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