chapter 5: decision-making concepts quantitative decision making with spreadsheet applications 7 th...

Chapter 5: Decision-making Chapter 5: Decision-making ConceptsConcepts

Quantitative Decision Making with Quantitative Decision Making with Spreadsheet Applications 7Spreadsheet Applications 7thth ed. ed.

By Lapin and WhislerBy Lapin and Whisler

Sec 5.5 : Other Decision CriteriaSec 5.5 : Other Decision Criteria

Sec 5.6: Opportunity Loss and the Sec 5.6: Opportunity Loss and the Expected Value of Perfect Expected Value of Perfect

InformationInformation

The Maximin Payoff The Maximin Payoff CriterionCriterion

The maximin payoff criterion is a The maximin payoff criterion is a procedure that guarantees that the procedure that guarantees that the decision maker can do no worse than decision maker can do no worse than achieve the best of the poorest achieve the best of the poorest outcomes.outcomes.

Example: Tippi-Toes Payoff Example: Tippi-Toes Payoff TableTable

EventEvent

(level of (level of demand)demand)

ActAct (choice of movement) (choice of movement)

Gears and Gears and LeversLevers

Spring Spring ActionAction

Weights and Weights and PulleysPulleys

LightLight $25,000$25,000 -$10,000-$10,000 -$125,000-$125,000

ModerateModerate $400,000$400,000 $440,000$440,000 $400,000$400,000

HeavyHeavy $650,000$650,000 $740,000$740,000 $750,000$750,000

ExampleExample

Goal: Ensure a favorable outcome no Goal: Ensure a favorable outcome no matter what happens.matter what happens.

Determine the worst outcome for each act Determine the worst outcome for each act regardless of the event.regardless of the event.

Gears Gears and and LeversLevers

Light Light demanddemand

$25,000$25,000



-$10,000-$10,000

Weights Weights and and PulleysPulleys


--$125,00$125,0000

ExampleExample

Choose an act with the largest lowest Choose an act with the largest lowest payoff. This guarantees a minimum payoff. This guarantees a minimum return that is the best of the poorest return that is the best of the poorest outcomes possible.outcomes possible.

Gears and Levers will guarantee the Gears and Levers will guarantee the toy manufacturer a payoff of at least toy manufacturer a payoff of at least $25,000.$25,000.

Gears and Levers is the maximin Gears and Levers is the maximin payoff act.payoff act.

Example: Tippi-Toes Payoff Example: Tippi-Toes Payoff TableTable

EventEvent


ActAct (choice of movement) (choice of movement)

Gears and Gears and LeversLevers


Weights and Weights and PulleysPulleys

LightLight $25,000$25,000 -$10,000-$10,000 -$125,000-$125,000

ModerateModerate $400,000$400,000 $440,000$440,000 $400,000$400,000

HeavyHeavy $650,000$650,000 $740,000$740,000 $750,000$750,000

Column Column MinimumMinimum

ss

$25,000$25,000 -$10,000-$10,000 -$125,000-$125,000

Risk vs. RewardRisk vs. Reward

EventEvent ActAct

AA11 AA22

EE11 $0$0 -$1-$1

EE22 11 10,0010,0000

Column Column MinimumsMinimums

$0$0 -$1-$1

EventEvent ActAct

BB11 BB22

EE11 $1$1 $10,00$10,0000

EE22 -1-1 --10,00010,000

Column Column MinimumsMinimums

-$1-$1 -$10,000-$10,000

Deficiencies of Maximin Payoff Deficiencies of Maximin Payoff CriterionCriterion

It is an extremely conservative It is an extremely conservative decision criterion and may lead to decision criterion and may lead to some bad decisions.some bad decisions.

It is primarily suited to decision It is primarily suited to decision problems with unknown probabilities problems with unknown probabilities that cannot be reasonably assessed.that cannot be reasonably assessed.

The Maximum Likelihood The Maximum Likelihood CriterionCriterion

The maximum likelihood criterion The maximum likelihood criterion focuses on the most likely event to focuses on the most likely event to the exclusion of all others.the exclusion of all others.

EventEvent (level of (level of demand)demand)

ProbabilitProbabilityy

ActAct (Choice of Movement) (Choice of Movement)

Gears & Gears & LeversLevers

Spring ActionSpring Action Weights & Weights & PulleysPulleys

LightLight .10.10 $25,000$25,000 -$10,000-$10,000 -$125,000-$125,000

ModeratModeratee

.70.70 400,000400,000 440,000440,000 400,000400,000

HeavyHeavy .20.20 650,000650,000 740,000740,000 750,000750,000

Maximum Likelihood Act

Maximum Likelihood Maximum Likelihood CriterionCriterion

Ignores most of other possible Ignores most of other possible outcomes.outcomes.

Prevalent decision-making behavior.Prevalent decision-making behavior.

The Criterion of Insufficient The Criterion of Insufficient ReasonReason

Used when decision maker has no Used when decision maker has no information about the event information about the event probabilities.probabilities.

Assumes each event has a Assumes each event has a probability of 1/(number of events) of probability of 1/(number of events) of occuring.occuring.

Some knowledge of the probability of Some knowledge of the probability of an event is almost always available.an event is almost always available.

The Bayes Decision RuleThe Bayes Decision Rule

The Bayes decision rule chooses the The Bayes decision rule chooses the act maximizing expected payoff.act maximizing expected payoff.

It makes the greatest use of all It makes the greatest use of all available information.available information.

Its major deficiency occurs when Its major deficiency occurs when alternatives involve different alternatives involve different magnitudes of risk.magnitudes of risk.

EventEvent ProbabiliProbabilityty

Act CAct C11 Act CAct C22

PayoffPayoff Payoff Payoff x Probx Prob

PayoffPayoff Payoff Payoff x Probx Prob

EE11 .5.5 --$1,000,00$1,000,00

00

--$500,00$500,00

00

$250,00$250,0000

$125,00$125,0000

EE22 .5.5 2,000,002,000,0000

1,000,001,000,0000

750,000750,000 375,000375,000

Expected Expected PayoffPayoff

$500,00$500,0000

$500,00$500,0000

Opportunity LossOpportunity Loss

Opportunity loss is the amount of Opportunity loss is the amount of payoff that is forgone by not selecting payoff that is forgone by not selecting the act that has the greatest payoff the act that has the greatest payoff for the event that actually occurs.for the event that actually occurs.

To calculate opportunity losses the To calculate opportunity losses the maximum payoff for each row is maximum payoff for each row is determined and it’s then subtracted determined and it’s then subtracted from its respective row maximum.from its respective row maximum.

EventEvent


PayoffPayoff Row Row MaximumMaximumGears & Gears &

LeversLeversSpring Spring ActionAction

Weights & Weights & PulleysPulleys

LightLight $25,000$25,000 -$10,000-$10,000 -$125,000-$125,000 $25,000$25,000

ModerateModerate 400,000400,000 440,000440,000 400,000400,000 440,000440,000

HeavyHeavy 650,000650,000 740,000740,000 750,000750,000 750,000750,000

Row maximum-Payoff = Opportunity Row maximum-Payoff = Opportunity LossLoss

(in thousands of dollars)(in thousands of dollars)

LightLight 25-25=025-25=0 25-(-25-(-10)=3510)=35

25-(-25-(-125)=150125)=150

ModerateModerate 440-440-400=40400=40

440-440=0440-440=0 440-440-400=40400=40

HeavyHeavy 750-750-650=100650=100

750-750-740=10740=10

750-750=0750-750=0

Opportunity Loss TableOpportunity Loss Table

EventEvent


Act (choice of movement)Act (choice of movement)

Gears & Gears & LeversLevers

Spring ActionSpring Action Weights & Weights & PulleysPulleys

LightLight $0$0 $35,000$35,000 150,000150,000

ModerateModerate 40,00040,000 00 40,00040,000

HeavyHeavy 100,000100,000 10,00010,000 00

The Bayes Decision Rule and The Bayes Decision Rule and Opportunity LossOpportunity Loss

The Bayes decision rule is to select The Bayes decision rule is to select the act that has the maximum the act that has the maximum expected payoff or the minimum expected payoff or the minimum expected opportunity loss.expected opportunity loss.

EventEvent(level of (level of demand)demand)

ProbabilitProbabilityy

Act (choice of movement)Act (choice of movement)

Gears & LeversGears & Levers Spring ActionSpring Action Weights & Weights & PulleysPulleys

LossLoss Loss x Loss x ProbProb



LightLight .10.10 $0$0 $0$0 $35,00$35,0000

$3,50$3,5000

$150,00$150,0000

$15,00$15,0000

ModeratModeratee

.70.70 40,0040,0000

28,0028,0000

00 00 40,0040,0000

28,0028,0000

HeavyHeavy .20.20 100,00100,0000

20,0020,0000

10,0010,0000

2,0002,000 00 00

Expected Expected Opportunity LossOpportunity Loss

$48,00$48,0000

$5,50$5,5000

$43,00$43,0000

The Expected Value of Perfect The Expected Value of Perfect InformationInformation

When the decision maker can acquire When the decision maker can acquire perfect information the decision will be perfect information the decision will be made under certainty. Then the decision made under certainty. Then the decision maker can guarantee the best decision.maker can guarantee the best decision.

We want to investigate the worth of such We want to investigate the worth of such information before it is obtained, so we will information before it is obtained, so we will determine the expected payoff once determine the expected payoff once perfect information is obtained. perfect information is obtained.

This quantity is called the This quantity is called the expected payoff expected payoff under certaintyunder certainty..

Calculating Expected Payoff Calculating Expected Payoff Under CertaintyUnder Certainty

1.1. Determine the highest payoff for Determine the highest payoff for each event.each event.

2.2. Multiply the maximum payoffs with Multiply the maximum payoffs with their respective event probabilities. their respective event probabilities. Then sum these amounts. Then sum these amounts.

3.3. Determine the worth of perfect Determine the worth of perfect information to the decision maker.information to the decision maker.

Example: Highest Payoff for Example: Highest Payoff for each Eventeach Event

Event(Event(level level of of demademand)nd)

ProbaProbabilitybility

ActAct Under CertaintyUnder Certainty

Gears Gears & & LeversLevers


WeightWeights & s & PulleysPulleys

MaximMaximum um PayoffPayoff

ChoseChosen Actn Act

Payoff Payoff x Probx Prob

LightLight .10.10 $25,00$25,0000

--$10,000$10,000

--$125,000$125,000

$25,00$25,0000

G&LG&L $2,500$2,500

ModeratModeratee

.70.70 400,00400,0000

440,00440,0000

400,00400,0000

440,00440,0000

SASA 308,00308,0000

HeavyHeavy .20.20 650,00650,0000

740,00740,0000

750,00750,0000

750,00750,0000

W&PW&P 150,00150,0000

Expected Expected Payoff under Payoff under certaintycertainty

460,50460,5000

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

EVPI = Expected payoff under EVPI = Expected payoff under certaintycertainty

- Maximum expected payoff.- Maximum expected payoff. Our example:Our example: EVPI = $460,500-$455,000 = $5,500.EVPI = $460,500-$455,000 = $5,500. This is the greatest amount of money This is the greatest amount of money

the decision maker would be willing to the decision maker would be willing to pay to obtain perfect information pay to obtain perfect information about what demand will be. about what demand will be.

chapter 5: decision-making concepts quantitative decision making with spreadsheet applications 7 th...

Documents