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A - 1© 2011 Pearson Education, Inc. publishing as Prentice Hall
A Decision-Making Tools
PowerPoint presentation to accompany PowerPoint presentation to accompany Heizer and Render Heizer and Render Operations Management, 10e Operations Management, 10e Principles of Operations Management, 8ePrinciples of Operations Management, 8e
PowerPoint slides by Jeff Heyl
A - 2© 2011 Pearson Education, Inc. publishing as Prentice Hall
ExampleExample
Table A.1
State of NatureAlternatives Favorable Market Unfavorable Market
Construct large plant $200,000 –$180,000Construct small plant $100,000 –$ 20,000Do nothing $ 0 $ 0
A - 3© 2011 Pearson Education, Inc. publishing as Prentice Hall
DM under UncertaintyDM under Uncertainty
1. If Optimistic (F), choice is a large plant2. If Pessimistic (UF), choice is to do nothing
Maximax Maximin Equally likely
States of NatureFavorable Unfavorable Maximum Minimum Row
Alternatives Market Market in Row in Row AverageConstruct
large plant $200,000 -$180,000 $200,000 -$180,000 $10,000Construct
small plant $100,000 -$20,000 $100,000 -$20,000 $40,000Do nothing $0 $0 $0 $0 $0
Not a sound business decision!
A - 4© 2011 Pearson Education, Inc. publishing as Prentice Hall
DM Under Risk (Probability)?DM Under Risk (Probability)?
Each possible state of nature has an assumed probability
Probabilities must sum to 1 Determine the expected monetary value
(EMV) for each alternative
A - 5© 2011 Pearson Education, Inc. publishing as Prentice Hall
DM Under RiskDM Under Risk
1. EMV(A1) = (.5)($200,000) + (.5)(-$180,000) = $10,000
Table A.3
States of NatureFavorable Unfavorable
Alternatives Market MarketConstruct large plant (A1) $200,000 -$180,000
Construct small plant (A2) $100,000 -$20,000
Do nothing (A3) $0 $0
Probabilities .50 .50
Best Option
2. EMV(A2) = (.5)($100,000) + (.5)(-$20,000) = $40,0003. EMV(A3) = (.5)($0) + (.5)($0) = $0
A - 6© 2011 Pearson Education, Inc. publishing as Prentice Hall
EVwPI ExampleEVwPI Example
1. The best outcome for the state of nature “favorable market” is “build a large facility” with a payoff of $200,000. The best outcome for “unfavorable” is “do nothing” with a payoff of $0.
Expected value with perfect information
= ($200,000)(.50) + ($0)(.50) = $100,000
A - 7© 2011 Pearson Education, Inc. publishing as Prentice Hall
DM under CertaintyDM under Certainty More certain about the payoff for each
market Is the cost of perfect information worth it? Determine the expected value of perfect
information (EVPI)
EVPI is the difference between the payoff under certainty and the payoff under risk
EVPI = –Expected value
with perfect information
Maximum EMV
A - 8© 2011 Pearson Education, Inc. publishing as Prentice Hall
Expected Value of Expected Value of Perfect InformationPerfect Information
Expected value with perfect information (EVwPI)
= (Best outcome or consequence for 1st state of nature) x (Probability of 1st state of nature)
+ Best outcome for 2nd state of nature) x (Probability of 2nd state of nature)
+ … + Best outcome for last state of nature) x (Probability of last state of nature)
A - 9© 2011 Pearson Education, Inc. publishing as Prentice Hall
EVPI ExampleEVPI Example
2. The maximum EMV is $40,000, which is the expected outcome without perfect information. Thus:
= $100,000 – $40,000 = $60,000
EVPI = EVwPI – Maximum EMV
The most the company should pay for perfect information is $60,000
A - 10© 2011 Pearson Education, Inc. publishing as Prentice Hall
Decision Tree ExampleDecision Tree Example
Favorable market
Unfavorable market
Favorable market
Unfavorable market
Construct small plant
Do nothing
A decision node A state of nature node
Construct
large plant
Figure A.1
A - 11© 2011 Pearson Education, Inc. publishing as Prentice Hall
Decision Tree ExampleDecision Tree Example= (.5)($200,000) + (.5)(-$180,000)EMV for node 1
= $10,000
EMV for node 2= $40,000 = (.5)($100,000) + (.5)(-$20,000)
Payoffs
$200,000
-$180,000
$100,000
-$20,000
$0
Construct large plant
Construct small plant
Do nothing
Favorable market (.5)
Unfavorable market (.5)1
Favorable market (.5)
Unfavorable market (.5)2
Figure A.2
A - 12© 2011 Pearson Education, Inc. publishing as Prentice Hall
Complex Decision Tree Complex Decision Tree Example (Example 7)Example (Example 7)
Figure A.3
A - 13© 2011 Pearson Education, Inc. publishing as Prentice Hall
Complex ExampleComplex Example
1. Given favorable survey results
EMV(2) = (.78)($190,000) + (.22)(-$190,000) = $106,400EMV(3) = (.78)($90,000) + (.22)(-$30,000) = $63,600
The EMV for no plant = -$10,000 so, if the survey results are favorable, build the large plant
A - 14© 2011 Pearson Education, Inc. publishing as Prentice Hall
Complex ExampleComplex Example
2. Given negative survey results
EMV(4) = (.27)($190,000) + (.73)(-$190,000) = -$87,400EMV(5) = (.27)($90,000) + (.73)(-$30,000) = $2,400
The EMV for no plant = -$10,000 so, if the survey results are negative, build the small plant
A - 15© 2011 Pearson Education, Inc. publishing as Prentice Hall
Complex ExampleComplex Example3. Compute the expected value of the
market survey
EMV(1) = (.45)($106,400) + (.55)($2,400) = $49,200
The EMV for no plant = $0 so, given no survey, build the small plant
4. If the market survey is not conducted
EMV(6) = (.5)($200,000) + (.5)(-$180,000) = $10,000EMV(7) = (.5)($100,000) + (.5)(-$20,000) = $40,000
A - 16© 2011 Pearson Education, Inc. publishing as Prentice Hall
Decision TreesDecision Trees Information in decision tables can be
displayed as decision trees A decision tree is a graphic display of the
decision process that indicates decision alternatives, states of nature and their respective probabilities, and payoffs for each combination of decision alternative and state of nature
Appropriate for showing sequential decisions
A - 17© 2011 Pearson Education, Inc. publishing as Prentice Hall
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.