1 / 12

Decision Models

Decision Models. Decision Trees. Situations In Which Decision Trees Can Be Useful. Payoff Tables are fine when a single decision is to be made Sometimes a sequence of decisions must be made Decisions “along the way” will be influenced by events that have occurred to that point

victoria-cooley
Download Presentation

Decision Models

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Decision Models Decision Trees

  2. Situations In Which Decision Trees Can Be Useful • Payoff Tables are fine when a single decision is to be made • Sometimes a sequence of decisions must be made • Decisions “along the way” will be influenced by events that have occurred to that point • Decision Trees can help structure the model so that a series of optimal “what if” decisions can be made.

  3. Structure of A Decision Tree • A decision tree consists of nodes and arcs • Nodes consist of • Start Node • Decision Nodes • States of Nature Nodes • Terminal Nodes • Arcs consist of • Decision Arcs • give a possible decision and the resulting cost (or profit) of making that decision • States of Nature Arcs • give a possible state of nature and the (Bayesian) probability that the state of nature will occur

  4. Example -- BGD Developoment • Interested in Purchasing Land -- (300,000) • To Build/Sell a Shopping Center -- $450,000 • A variance must be obtained before building center -- ($30,000) • Variance Approved -- Center Built • Variance Denied -- Center Not Built • Can purchase 3-month option to buy before applying for variance -- ($20,000) • Can sell the undeveloped land -- $260,000 • Can hire variance consultant -- ($5,000)

  5. BGD Development Probabilities • Probability that a variance is approved = .4 • Prob variance not approved = .6 • Consultant’s Assistance-- • P(Consultant Predicts Approval| Approval) = .7 • P(Consultant Predicts Denial| Approval) = .3 • P(Consultant Predicts Denial| Denial) = .8 • P(Consultant Predicts Approval| Denial) = .2

  6. Bayesian Probabilities Based on Consultant’s Prediction • P(Approval|Predict Approval) = P(Pred. Appr.|Approval)P(Approval)/P(Pred. Appr.) = (.7)(.4)/[(.7)(.4)+(.2)(.6)] = .7 • P(Denial|Predict Approval) = 1 - .7 = .3 • Note that P(Predict Approval) = (.7)(.4)+(.2)(.6) = .4 • P(Denial|Predict Denial) = P(Pred. Deny|Deny)P(Deny)/P(Pred. Deny) = (.8)(.6)/[(.8)(.6)+(.3)(.4)] = .8 • P(Approval|Predict Denial)= 1 - .8= .2 • Note that P(Predict Denial) (.8)(.6)+ (.3)(.4) = .6

  7. The Decision Tree Do nothing $0 Build/Sell Center Approved Buy Land & Variance .4 $450,000 ($330,000) Denied Sell Land .6 $260,000 No Consultant Approved Buy Land/Build/Sell Buy Option & Variance $0 .4 $150,000 ($50,000) Denied Do nothing .6 $0 ($5,000) Consultant See Next Screen $0 $120,000 ($70,000) $100,000 ($50,000) Start

  8. Decision Tree (Cont’d) Do nothing $0 Build/Sell Center Approved Buy Land & Variance .7 $450,000 ($330,000) Denied Sell Land .3 $260,000 ($5,000) Consultant Approved Buy Land/Build/Sell Pred. Approve Buy Option & Variance .7 $150,000 .4 ($50,000) Denied Do nothing .3 $0 Do nothing $0 Build/Sell Center Approved .6 Pred. Deny Buy Land & Variance .2 $450,000 ($330,000) Denied Sell Land .8 $260,000 Buy Land/Build/Sell Approved Buy Option & Variance .2 $150,000 ($50,000) Denied Do nothing .8 $0 ($5,000) $115,000 Start ($75,000) $95,000 ($55,000) ($5,000) $115,000 ($75,000) $95,000 ($55,000)

  9. Decision Tree Analysis Do nothing $0 $10,000 Option/Variance $0 $0 $6,000 (.4)(120,000)+.6(-70,000) Build/Sell Center Approved $120,000 Buy Land & Variance .4 $450,000 ($330,000) Denied Sell Land ($70,000) .6 $260,000 $10,000 (.4)(100,00)+.6(-50,000) No Consultant Approved Buy Land/Build/Sell $100,000 Buy Option & Variance $0 .4 $150,000 ($50,000) Denied Do nothing ($50,000) .6 $0 Start ($5,000) Consultant See Next Screen

  10. Decision Tree Analysis (Cont’d) ($5,000) Do nothing ($5,000) $58,000 Land/Variance $0 (.7)(115,00)+.3(-75,000) $58,000 Build/Sell Center Approved $115,000 Start Buy Land & Variance .7 $450,000 ($330,000) Denied Sell Land ($75,000) .3 $260,000 $50,000 (.7)(95,000)+.3(-55,000) ($5,000) Consultant $95,000 Approved Buy Land/Build/Sell Pred. Approve Buy Option & Variance .7 $150,000 .4 ($50,000) Denied Do nothing ($55,000) .4($58,000)+.6(-$5,000) $20,200 .3 $0 Do nothing ($5,000) ($5,000) $0 (.2)(115,000)+.8(-75,000) ($37,000) Build/Sell Center Approved $115,000 .6 Pred. Deny ($5,000) Do Nothing Buy Land & Variance .2 $450,000 ($330,000) Denied Sell Land ($75,000) .8 $260,000 (.2)(95,000)+.8(-55,000) ($25,000) Buy Land/Build/Sell Approved $95,000 Buy Option & Variance .2 $150,000 ($50,000) Denied Do nothing ($55,000) .8 $0

  11. Summary • Expected Value (No Consultant) = $10,000 • Expected Value (Consultant) = $20,200 • Hire Consultant! • and • If consultant predicts approval • Buy the land and apply for the variance • If consultant predicts denial • Do Nothing

  12. Review • Decision Trees can structure sequences of decisions • Nodes are points in time where a decision is to be made or a state of nature will occur • Arcs give payoffs or (Bayesian) probabilities • Expected Values are calculated for each decision and the best is chosen.

More Related