Civil Systems Planning Benefit/Cost Analysis Paulina Jaramillo/Joe Marriott 12-706/19-702 / 73-359 Lecture 10

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

Structuring Decisions (2) Can use: Fundamental objective hierarchy. Influence diagrams. Decision Trees Risk Profiles 12-706 and 73-359

Fundamental Objectives Hierarchy Increase Lifetime Earnings Increase Current Salary Marry Rich Go to School Undergrad Grad School Find New Job Get a Raise Update Resume Network Do a Better Job 12-706 and 73-359

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

Influence Diagram Marry Rich Undergrad Go to School Grad School Lifetime Earnings Grad School High Salary Find a Better Job Work Get a Raise 12-706 and 73-359

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

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

Texaco vs. Pennzoil 12-706 and 73-359 Settlement Amount ($ Billion) Accept $2 Billion 2 Texaco Accept $5 Billion 5 (0.17) (0.5) (0.33) (0.2) (0.3) Counteroffer $5 Billion Final Court Decision 10.3 5 Texaco Refuses Counteroffer Texaco Counteroffer $3 Billion Final Court Decision 10.3 5 Refuse Accept $3 Billion 3 12-706 and 73-359

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

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

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) How many decision strategies are there in general for a tree? Count based on the number of decision nodes! In this case, we have 2 nodes. Thus 3 strategy options. 12-706 and 73-359

Texaco vs. Penzoil, Again Risk profile for “Accept $2 Billion” is obvious - get $2B with 100% chance. 12-706 and 73-359

Risk Profile Texaco Counteroffer, accept $3 billion Below is just the part of original tree to consider when calculating the risk profile: Counteroffer $5 Billion Texaco $3 Billion Texaco Accept $5 Billion 5 Texaco Refuses Final Court Decision 10.3 Accept $3 Billion 3 (0.17) (0.5) (0.33) (0.2) (0.3) 12-706 and 73-359

Texaco vs. Pennzoil, continued 12-706 and 73-359

Cumulative Risk Profiles Graphs of cumulative distributions Percent chance that “payoff is less than x” 12-706 and 73-359

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

Dominance Example CRP below for 2 strategies shows “Accept $2 Billion” is dominated by the other. If there is a value x such that the chance of the payoff being less than x is 100% in alternative B and the chance of payoff being less than x in alternative A is 0%, then B is dominated by A. Graphically: Continue the the vertical line where alternative A laves 0%. If that vertical lines meets with 100% for Alternative B, then A dominates B. 12-706 and 73-359

Next Class Multi-Attribute Decision Making. Multi-Objective Programming. Value of Information. Homework Due. 12-706 and 73-359