Civil systems planning benefit cost analysis
This presentation is the property of its rightful owner.
Sponsored Links
1 / 20

Civil Systems Planning Benefit/Cost Analysis PowerPoint PPT Presentation


  • 58 Views
  • Uploaded on
  • Presentation posted in: General

Civil Systems Planning Benefit/Cost Analysis. Scott Matthews Courses: 12-706 / 19-702/ 73-359 Lecture 16. Admin. Project 1 - avg 85 (high 100) Mid sem grades today - how done?. Recall: Choosing a Car Example. CarFuel Eff (mpg) Comfort

Download Presentation

Civil Systems Planning Benefit/Cost Analysis

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Civil systems planning benefit cost analysis

Civil Systems PlanningBenefit/Cost Analysis

Scott Matthews

Courses: 12-706 / 19-702/ 73-359

Lecture 16


Admin

Admin

  • Project 1 - avg 85 (high 100)

  • Mid sem grades today - how done?

12-706 and 73-359


Recall choosing a car example

Recall: Choosing a Car Example

  • CarFuel Eff (mpg) Comfort

  • Index

  • Mercedes25 10

  • Chevrolet283

  • Toyota356

  • Volvo309

12-706 and 73-359


Pricing out

“Pricing out”

  • Book uses $ / unit tradeoff

  • Our example has no $ - but same idea

  • “Pricing out” simply means knowing your willingness to make tradeoffs

  • Assume you’ve thought hard about the car tradeoff and would trade 2 units of C for a unit of F (maybe because you’re a student and need to save money)

12-706 and 73-359


With these weights

With these weights..

  • U(M) = 0.26*1 + 0.74*0 = 0.26

  • U(V) = 0.26*(6/7) + 0.74*0.5 = 0.593

  • U(T) = 0.26*(3/7) + 0.74*1 = 0.851

  • U(H) = 0.26*(4/7) + 0.74*0.6 = 0.593

    • Note H isnt really an option - just “checking” that we get same U as for Volvo (as expected)

12-706 and 73-359


Mcdm swing weights

MCDM - Swing Weights

  • Use hypothetical combinations to determine weights

  • Base option = worst on all attributes

  • Other options - “swings” one of the attributes from worst to best

  • Determine your rank preference, find weights

12-706 and 73-359


Add 1 attribute to car cost

Add 1 attribute to car (cost)

  • M = $50,000 V = $40,000 T = $20,000 C=$15,000

  • Swing weight table:

  • Benchmark 25mpg, $50k, 3 Comf

12-706 and 73-359


Stochastic dominance defined

Stochastic Dominance “Defined”

  • A is better than B if:

  • Pr(Profit > $z |A) ≥ Pr(Profit > $z |B), for all possible values of $z.

  • Or (complementarity..)

  • Pr(Profit ≤ $z |A) ≤ Pr(Profit ≤ $z |B), for all possible values of $z.

  • A FOSD B iff FA(z) ≤ FB(z) for all z

12-706 and 73-359


Stochastic dominance example 1

Stochastic Dominance:Example #1

  • CRP below for 2 strategies shows “Accept $2 Billion” is dominated by the other.

12-706 and 73-359


Stochastic dominance again

Stochastic Dominance (again)

  • Chapter 4 (Risk Profiles) introduced deterministic and stochastic dominance

    • We looked at discrete, but similar for continuous

    • How do we compare payoff distributions?

    • Two concepts:

    • A is better than B because A provides unambiguously higher returns than B

    • A is better than B because A is unambiguously less risky than B

    • If an option Stochastically dominates another, it must have a higher expected value

12-706 and 73-359


First order stochastic dominance fosd

First-Order Stochastic Dominance (FOSD)

  • Case 1: A is better than B because A provides unambiguously higher returns than B

    • Every expected utility maximizer prefers A to B

    • (prefers more to less)

    • For every x, the probability of getting at least x is higher under A than under B.

  • Say A “first order stochastic dominates B” if:

    • Notation: FA(x) is cdf of A, FB(x) is cdf of B.

    • FB(x) ≥ FA(x) for all x, with one strict inequality

    • or .. for any non-decr. U(x), ∫U(x)dFA(x) ≥ ∫U(x)dFB(x)

    • Expected value of A is higher than B

12-706 and 73-359


Civil systems planning benefit cost analysis

FOSD

12-706 and 73-359

Source: http://www.nes.ru/~agoriaev/IT05notes.pdf


Fosd example

Option A

Option B

FOSD Example

12-706 and 73-359


Civil systems planning benefit cost analysis

12-706 and 73-359


Second order stochastic dominance sosd

Second-Order Stochastic Dominance (SOSD)

  • How to compare 2 lotteries based on risk

    • Given lotteries/distributions w/ same mean

  • So we’re looking for a rule by which we can say “B is riskier than A because every risk averse person prefers A to B”

  • A ‘SOSD’ B if

    • For every non-decreasing (concave) U(x)..

12-706 and 73-359


Sosd example

Option A

Option B

SOSD Example

12-706 and 73-359


Civil systems planning benefit cost analysis

Area 2

Area 1

12-706 and 73-359


Civil systems planning benefit cost analysis

SOSD

12-706 and 73-359


Sd and mcdm

SD and MCDM

  • As long as criteria are independent (e.g., fun and salary) then

    • Then if one alternative SD another on each individual attribute, then it will SD the other when weights/attribute scores combined

    • (e.g., marginal and joint prob distributions)

12-706 and 73-359


Reading pdf cdf graphs

Reading pdf/cdf graphs

  • What information can we see from just looking at a randomly selected pdf or cdf?

12-706 and 73-359


  • Login