Decision Analysis OPS 370. Decision Theory A. B. – a. – b. – c. – d. – e.

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Presentation transcript:

Decision Analysis OPS 370

Decision Theory A. B. – a. – b. – c. – d. – e.

Decision Theory A. – a. – b. – c.

Decision Theory Steps: – 1. A. B. – 2. A. – 3. – 4. – 5.

Payoff Table Shows Expected Payoffs for Various States of Nature

Decision Environments A. – a. B. – a. C. – a.

Decision Making A. – a. – b.

Decision Making Under Uncertainty – Four Decision Criteria – 1. A. B. – 2. A. B.

Decision Making Under Uncertainty – 3. A. B. – 4. A. B.

Example Maximin – Indoor – Drive-In – Both – Choose Best of Worst

Example Maximax – Indoor – Drive-In – Both – Choose Best of Best

Example Laplace – Indoor – Drive-In – Both – Choose

Decision Making Minimax Regret – Criterion for Decision Making Under Uncertainty A. B.

Decision Making

A. – Indoor – Drive-In – Both B. – a.

Decision Making Under Risk – A. – B. a. b.

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

Expected Value of Perfect Info A. B.

Expected Value of Perfect Info Steps: – 1. – 2. – 3. Example – A. a. – B. – C.

Expected Value of Perfect Info NOTE: – A.

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)

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

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

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

Decision Trees Simple Example Should You Buy a Raffle Ticket? NO! Your Expected Value is Negative No Yes Buy Raffle Ticket? $0 -$0.5

Decision Trees More Complex Example

Decision Trees Settle? Settle Now ($?) Wait

Decision Trees Settle? Settle Now ($?) Wait Opp Wins (0.5) Opp Loses (0.5) $0

Decision Trees Settle? Settle Now ($?) Wait Opp Wins (0.5) Opp Loses (0.5) $0 Opp Sues (0.8) No Suit(0.2)

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 Settlement

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 Settlement We Win (0.3) ($0) We Lose (0.7) ($10) Low (0.4) ($5) Win (0.6) ($15)

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 Settlement 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

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 Settlement $7 $11

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

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

Decision Trees Settle? Settle Now ($?) Wait Opp Wins (0.5) Opp Loses (0.5) $0 $5.6

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

Decision Trees Settle? Settle Now ($?) Wait $2.8