Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.
-
Upload
samson-host -
Category
Documents
-
view
223 -
download
0
Transcript of Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.
![Page 1: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/1.jpg)
Decision Analysis
OPS 370
![Page 2: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/2.jpg)
Decision Theory
• A. • B.
– a.– b.– c.– d.– e.
![Page 3: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/3.jpg)
Decision Theory
• A.
– a.
– b. – c.
![Page 4: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/4.jpg)
Decision Theory
• Steps:– 1.
• A. • B.
– 2. • A.
– 3.
– 4.
– 5.
![Page 5: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/5.jpg)
Payoff Table
• Shows Expected Payoffs for Various States of Nature
Low Moderate HighIndoor 500 1200 2000
Drive-In 700 1500 1250Both -2000 -1000 3000
Demand for Ice Cream
Type of Parlor
* Payoffs in Predicted Profit Per Month
![Page 6: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/6.jpg)
Decision Environments
• A. – a.
• B.– a.
• C. – a.
![Page 7: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/7.jpg)
Decision Making
• A. – a. – b.
Low Moderate HighIndoor 500 1200 2000
Drive-In 700 1500 1250Both -2000 -1000 3000
Demand for Ice Cream
Type of Parlor
* Payoffs in Predicted Profit Per Month
![Page 8: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/8.jpg)
Decision Making
• Under Uncertainty– Four Decision Criteria– 1.
• A.
• B.
– 2. • A.
• B.
![Page 9: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/9.jpg)
Decision Making
• Under Uncertainty– 3.
• A.
• B.
– 4. • A.
• B.
![Page 10: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/10.jpg)
Example
• Maximin– Indoor – Drive-In – Both – Choose “Best of Worst”
Low Moderate HighIndoor 500 1200 2000
Drive-In 700 1500 1250Both -2000 -1000 3000
Demand for Ice Cream
Type of Parlor
* Payoffs in Predicted Profit Per Month
![Page 11: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/11.jpg)
Example
• Maximax– Indoor – Drive-In – Both – Choose “Best of Best”
Low Moderate HighIndoor 500 1200 2000
Drive-In 700 1500 1250Both -2000 -1000 3000
Demand for Ice Cream
Type of Parlor
* Payoffs in Predicted Profit Per Month
![Page 12: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/12.jpg)
Example
• Laplace– Indoor – Drive-In – Both – Choose
Low Moderate HighIndoor 500 1200 2000
Drive-In 700 1500 1250Both -2000 -1000 3000
Demand for Ice Cream
Type of Parlor
* Payoffs in Predicted Profit Per Month
![Page 13: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/13.jpg)
Decision Making
• Minimax Regret– Criterion for Decision Making Under Uncertainty
• A.
• B.
![Page 14: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/14.jpg)
Decision Making
Low Moderate HighIndoor 500 1200 2000
Drive-In 700 1500 1250Both -2000 -1000 3000
Demand for Ice Cream
Type of Parlor
Low Moderate HighIndoor
Drive-InBoth
Demand for Ice Cream
Type of Parlor
![Page 15: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/15.jpg)
Decision Making
• A.– Indoor – Drive-In – Both
• B. – a.
![Page 16: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/16.jpg)
Decision Making
• Under Risk– A.
– B.
• a. • b.
![Page 17: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/17.jpg)
Decision Making
• Under Risk
– Expected Payoffs:• Indoor:• Drive-In: (0.3)(700) + (0.5)(1500) + (0.2)(1250) = • Both: (0.3)(-2000) + (0.5)(-1000) + (0.2)(3000) =
– Select
0.3 0.5 0.2Low Moderate High
Indoor 500 1200 2000Drive-In 700 1500 1250
Both -2000 -1000 3000
Type of Parlor
Demand Probabilities
![Page 18: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/18.jpg)
Expected Value of Perfect Info
• A.
• B.
![Page 19: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/19.jpg)
Expected Value of Perfect Info
• Steps:– 1. – 2. – 3.
• Example– A.
• a.
– B. – C.
![Page 20: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/20.jpg)
Expected Value of Perfect Info
• NOTE:– A.
![Page 21: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/21.jpg)
Decision Trees
• Visual tool to represent a decision model• Squares: - Decisions• Circles: - Uncertain Events (Subject to
Probability)• Branches: Potential Actions or Results• Some Branches are Terminal (End) Terminal
Branches Have Payoffs (Payoffs Should Reflect All Costs/Revenues)
![Page 22: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/22.jpg)
Decision Trees
• Simple Example
No
Yes($1 to Buy)
Buy Raffle Ticket? Win (0.01)
Lose (0.99)
Terminal Branches
Decision
Uncertain Event
$0
$49
-$1
![Page 23: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/23.jpg)
Decision Trees
• Build Decision Trees from LEFT to RIGHT• Solve Decision Trees from RIGHT to LEFT• Determine Expected Values at Chance Nodes• Choose “Best” Expected Value at Decision
Nodes• Identify “Best” Path of Decisions
![Page 24: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/24.jpg)
Decision Trees
• Simple Example
No
Yes($1 to Buy)
Buy Raffle Ticket? Win (0.01)
Lose (0.99)
$0
$49
-$1
Expected Value = (0.01)(49) + (0.99)(-1) = 0.49 – 0.99 = -0.5
![Page 25: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/25.jpg)
Decision Trees
• Simple Example
• Should You Buy a Raffle Ticket?• NO! Your Expected Value is Negative
No
Yes
Buy Raffle Ticket?
$0
-$0.5
![Page 26: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/26.jpg)
Decision Trees
• More Complex Example
![Page 27: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/27.jpg)
Decision Trees
Settle?
Settle Now ($?)
Wait
![Page 28: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/28.jpg)
Decision Trees
Settle?
Settle Now ($?)
Wait
Opp Wins (0.5)
Opp Loses (0.5)
$0
![Page 29: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/29.jpg)
Decision Trees
Settle?
Settle Now ($?)
Wait
Opp Wins (0.5)
Opp Loses (0.5)
$0
Opp Sues (0.8)
No Suit(0.2)
![Page 30: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/30.jpg)
Decision Trees
Settle?
Settle Now ($?)
Wait
Opp Wins (0.5)
Opp Loses (0.5)
$0
Opp Sues (0.8)
No Suit(0.2)
$0
Settle ($8)
Contest
ContestSettlement
![Page 31: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/31.jpg)
Decision Trees
Settle?
Settle Now ($?)
Wait
Opp Wins (0.5)
Opp Loses (0.5)
$0
Opp Sues (0.8)
No Suit(0.2)
$0
Settle ($8)
Contest
ContestSettlement
We Win (0.3) ($0)
We Lose (0.7) ($10)
Low (0.4) ($5)
Win (0.6) ($15)
![Page 32: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/32.jpg)
Decision Trees
Settle?
Settle Now ($?)
Wait
Opp Wins (0.5)
Opp Loses (0.5)
$0
Opp Sues (0.8)
No Suit(0.2)
$0
Settle ($8)
Contest
ContestSettlement
We Win (0.3) ($0)
We Lose (0.7) ($10)
Low (0.4) ($5)
Win (0.6) ($15)
EV = (0.3)(0) + (0.7)(10) = 7
EV = (0.4)(5) + (0.6)(15) = 11
![Page 33: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/33.jpg)
Decision Trees
Settle?
Settle Now ($?)
Wait
Opp Wins (0.5)
Opp Loses (0.5)
$0
Opp Sues (0.8)
No Suit(0.2)
$0
Settle ($8)
Contest
ContestSettlement
$7
$11
![Page 34: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/34.jpg)
Decision Trees
Settle?
Settle Now ($?)
Wait
Opp Wins (0.5)
Opp Loses (0.5)
$0
Opp Sues (0.8)
No Suit(0.2)
$0
$7
![Page 35: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/35.jpg)
Decision Trees
Settle?
Settle Now ($?)
Wait
Opp Wins (0.5)
Opp Loses (0.5)
$0
Opp Sues (0.8)
No Suit(0.2)$0
$7
EV = (0.8)(7) + (0.2)(0) = 5.6
![Page 36: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/36.jpg)
Decision Trees
Settle?
Settle Now ($?)
Wait
Opp Wins (0.5)
Opp Loses (0.5)
$0
$5.6
![Page 37: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/37.jpg)
Decision Trees
Settle?
Settle Now ($?)
Wait
Opp Wins (0.5)
Opp Loses (0.5)$0
$5.6
EV = (0.5)(5.6) + (0.5)(0) = 2.8
![Page 38: Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.](https://reader035.fdocuments.us/reader035/viewer/2022062318/551902a35503462f428b45e6/html5/thumbnails/38.jpg)
Decision Trees
Settle?
Settle Now ($?)
Wait$2.8