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Civil Systems Planning Benefit/Cost Analysis Paulina Jaramillo/Joe Marriott 12-706/19-702 / 73-359 Lecture 10 1 Structuring Decisions All about the objectives (what you want to achieve) Decision context: setting for the decision Decision: choice between options (there is always an option, including status quo) Waiting for more information also an option Uncertainty: as we’ve seen, always exists Outcomes: possible results of uncertain events Many uncertain events lead to complexity 12-706 and 73-359 2 Structuring Decisions (2) Can use: Fundamental objective hierarchy. Influence diagrams. Decision Trees Risk Profiles 12-706 and 73-359 3 Fundamental Objectives Hierarchy Increase Lifetime Earnings Increase Current Salary Find New Job Update Resume Marry Rich Undergrad Get a Raise Network Go to School Grad School Do a Better Job 12-706 and 73-359 4 Influence Diagram/Decision Trees Probably cause confusion. If one confuses you, do the other. Important parts: Decisions Calculation/constant Chance Events Consequence/payoff 12-706 and 73-359 5 Influence Diagram Marry Rich Undergrad Go to School Grad School High Salary Lifetime Earnings Find a Better Job Work Get a Raise 12-706 and 73-359 6 Other Notes Chance node branches need to be mutually exclusive/exhaustive Only one can happen, all covered “One and only one can occur” Timing of decisions along the way influences how trees are drawn (left to right) As with NPV, sensitivity analysis, etc, should be able to do these by hand before resorting to software tools. 12-706 and 73-359 7 Solving Decision Trees We read/write them left to right, but “solve” them right to left. Because we need to know expected values of options before choosing. Calculate values for chance nodes Picking best option at decision nodes We typically make trees with “expected value” or NPV or profit as our consequence Thus, as with BCA, we choose highest value. 12-706 and 73-359 8 Texaco vs. Pennzoil Settlement Amount ($ Billion) Accept $2 Billion 2 Texaco Accept $5 Billion 5 (0.17) (0.2) Counteroffer $5 Billion Texaco Refuses Final Court Counteroffer (0.5) Decision (0.5) (0.3) 10.3 5 0 Texaco (0.2) Counteroffer $3 Billion Final Court (0.33) Decision Refuse Accept $3 Billion 12-706 and 73-359 (0.5) (0.3) 10.3 5 0 3 9 To Solve the Tree Solve from right to left: At chance node multiply monetary value to probability and add them. At choice node choose highest value. EMV for Simple Texaco vs. Pennzoil Tree: $4.63 Billion 12-706 and 73-359 10 Risk Profiles Risk profile shows a distribution of possible payoffs associated with particular strategies. A strategy is what you plan to do going in to the decision. Holds your plans constant, allows chances to occur Only eliminate things YOU wouldn’t do, not things “they” might not do. Its not just finding the NPV of a branch. 12-706 and 73-359 11 Risk Profiles (cont.) Let’s think about the “subset” of the Texaco decision tree where we are only curious about the uncertainty/risk profile associated with various strategies to consider. These represent the riskiness of each option There are only 3 “decision strategies” in the base Texaco case: Accept the $2 billion offer (topmost branch of 1st dec. node) Counteroffer $5 Billion, but plan to refuse counteroffer (lower branch of 1st node, upper branch of second) Counteroffer $5B, but plan to accept counteroffer (lower branch of both decision nodes) 12-706 and 73-359 12 Texaco vs. Penzoil, Again Risk profile for “Accept $2 Billion” is obvious - get $2B with 100% chance. Risk Profile for "Accept to $2 Billion" Chance that Settlement Equals X 120% 100% 100% 80% 60% 40% 20% 0% 0% 0 1 2 0% 0% 3 4 0% 0% 0% 0% 0% 0% 0% 5 6 7 8 9 10 11 x ($ Billion) 12-706 and 73-359 13 Risk Profile Texaco Counteroffer, accept $3 billion Below is just the part of original tree to consider when calculating the risk profile: Texaco Accept $5 Billion 5 (0.17) (0.2) Counteroffer $5 Billion Texaco Refuses Final Court Counteroffer (0.5) Decision (0.5) (0.3) 10.3 5 0 Texaco Counteroffer $3 Billion (0.33) Accept $3 Billion 12-706 and 73-359 3 14 Texaco vs. Pennzoil, continued Risk Profile for "Counteroffer $5 Billion, Accept Texaco's $3 Billion Counteroffer" 42% 40% 33% 35% 30% 25% 20% 15% 15% 10% 10% Risk Profile for "Counteroffer $5 Billion, Reject Texaco's $3 Billion Counteroffer" 5% 0% 0% 0 1 2 0% 3 4 5 0% 0% 0% 0% 6 7 8 9 x ($ Billion) 0% 10 70% 11 Chance that Settlement Equals x Chance that Settlement Equals x 45% 59% 60% 50% 40% 30% 25% 20% 17% 10% 0% 0 0% 0% 0% 0% 1 2 3 4 5 0% 0% 0% 0% 6 7 8 9 0% 10 11 x ($ Billion) 12-706 and 73-359 15 Cumulative Risk Profiles Graphs of cumulative distributions Percent chance that “payoff is less than x” Chance that payoff is less or equal to x Cumulative Risk Profile for 3 Options in Texaco Case 120% 100% 80% 60% Counteroffer $5 Billion, Accept Texaco's $3 Billion Counteroffer Accept $2 Billion 40% Counteroffer $5 Billion, Refuse Texaco's $3 Billion Counteroffeer 20% 0% 0 2 4 6 8 10 12 x ($billion) 12-706 and 73-359 16 Dominance To pick between strategies, it is useful to have rules by which to eliminate options Let’s construct an example - assume minimum “court award” expected is $2.5B (instead of $0). Now there are no “zero endpoints” in the decision tree. 12-706 and 73-359 17 Dominance Example Chance that payoff is less or equal to x CRP below for 2 strategies shows “Accept $2 Billion” is dominated by the other. 120% 100% 80% 60% 40% 20% 0% 0 2 4 6 8 10 12 x ($billion) 12-706 and 73-359 18 Next Class Multi-Attribute Decision Making. Multi-Objective Programming. Value of Information. Homework Due. 12-706 and 73-359 19