(My take on) Class Objectives Learn how to… –think about large, complex problems without much direction –make good assumptions –solve problems using a range of modeling tools –present and explain your solution This last part is the most important –if you do not clearly, concisely and convincingly present your findings, then your reader/TA/professor/boss has no reason to believe that you adequately modeled the problem and no way to understand it if you did

Formatting Your Homework Your reader ought to be able to recreate your solution given minimal information from you –The TA’s need to see… Your assumptions and a defense of them (your reasoning and/or a reference) Your solution and how you got there (ex: equations you used and not your entire excel spreadsheet) –When was the last time you read a published paper with MS Excel cells in it? There are ways to explain your solution without showing all of your cells.

Excel Example from HW 2 Question 2 (15 pts): A benefit-cost study of a proposed dam is conducted. The dam costs $75 million to construct. The study estimates a continuous stream of social benefits of $9.5 million per year (from avoided flood damage, hydroelectric power, etc.) and costs of $4 million ($2 million from operation and $2 million in environmental damages). a) [6 pts] Assuming a social marginal rate of time preference of 4% per year, how many years does it take for the dam to “break even” (i.e., the NPV of benefits just exceed the NPV of costs)? The following equation is used to estimate the continuous net present worth (NPV) of the dam: Where the discount rate, r, equals 4% and n is number of years. Can “hide” spreadsheet rows not needed

Theory Behind Minimal Information (very intelligent people have thought about this before us) Occam’s razor –“Entities should not be multiplied unnecessarily” Einstein’s principle –“Everything should be made as simple as possible, but not simpler” Definition of engineering elegance from Antoine de Saint-Exup'ery (aviator and author of The Little Prince) –"A designer knows he has achieved perfection not when there is nothing left to add, but when there is nothing left to take away" Antoine de Saint-Exup'ery quote from Occam’s razor and Einstein quote from

Grading of the Homework Give just enough information - nothing more, nothing less –Solutions following this theory are tough to master (and to grade) and take practice Points will be taken off for… –Consistently giving too much information –Poor presentation including hard to follow logic, poor spelling, poor writing, or generally messy work Try to format your homework like a project

Mutli-Attribute Decision Making Scott Matthews Courses: /

and 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.

and Dominance Example #1  CRP below for 2 strategies shows “Accept $2 Billion” is dominated by the other.

and But..  Need to be careful of “when” to eliminate dominated alternatives, as we’ll see.

and Multi-objective Methods  Multiobjective programming  Mult. criteria decision making (MCDM)  Is both an analytical philosophy and a set of specific analytical techniques  Deals explicitly with multi-criteria DM  Provides mechanism incorporating values  Promotes inclusive DM processes  Encourages interdisciplinary approaches

and Decision Making  Real decision making problems are MC in nature  Most decisions require tradeoffs  E.g. college-selection problem  BCA does not handle MC decisions well  It needs dollar values for everything  Assumes all B/C quantifiable  BCA still important : economic efficiency

and Structuring Objectives Choose a college Max. ReputationMin. CostMax Atmosphere AcademicSocial TuitionLivingTrans.  Making this tree is useful for  Communication (for DM process)  Creation of alternatives  Evaluation of alternatives

and Desirable Properties of Obj’s  Completeness (reflects overall objs)  Operational (supports choice)  Decomposable (preference for one is not a function of another)  Non-redundant (avoid double count)  Minimize size

and MCDM Terminology  Non-dominance (aka Pareto Optimal)  Alternative is non-dominated if there is no other feasible alternative that would improve one criterion without making at least one other criterion worse  Non-dominated set: set of all alternatives of non-dominance

and More Defs  Measures (or attributes)  Indicate degree to which objective is achieved or advanced  Of course its ideal when these are in the same order of magnitude. If not, should adjust them to do so.  Goal: level of achievement of an objective to strive for  Note objectives often have sub-objectives, etc.

and Choosing a Car  CarFuel Eff (mpg) Comfort  Index  Mercedes2510  Chevrolet283  Toyota356  Volvo309  Which dominated, non-dominated?  Dominated can be removed from decision  BUT we’ll need to maintain their values for ranking

and Conflicting Criteria  Two criteria ‘conflict’ if the alternative which is best in one criteria is not the best in the other  Do fuel eff and comfort conflict? Usual.  Typically have lots of conflicts.  Tradeoff: the amount of one criterion which must be given up to attain an increase of one unit in another criteria

and Tradeoff of Car Problem Fuel Eff Comfort M V T C 1) What is tradeoff between Mercedes and Volvo? 2) What can we see graphically about dominated alternatives?

and Tradeoff of Car Problem Fuel Eff Comfort M(25,10) V(30,9) T C 5 The slope of the line between M and V is -1/5, i.e., you must trade one unit less of comfort for 5 units more of fuel efficiency.

and Tradeoff of Car Problem Fuel Eff Comfort M(25,10) V(30,9) T (35,6) 5 Would you give up one unit of comfort for 5 more fuel economy? -3 5 THEN Would you give up 3 units of comfort for 5 more fuel economy?

and Multi-attribute utility theory  To solve, we need 2 parts:  Attribute scales for each objective  Weights for each objective  Our weights should respect the “Range of the attribute scales”  This gets to the point of 0-1, 0-100, etc scales  Does not matter whether we have “consistent” scales as long as weights are context-specific (e.g. 100x different if 0-1, 0-100)  However we often use consistent scales to make the weighting assessment process easier

and Additive Utility  We motivated 2-attribute version already  Generally:  U(x 1,..,x m ) = k 1 U 1 (x 1 ) + … + k m U m (x m )

and Recall: Choosing a Car Example  CarFuel Eff (mpg) Comfort  Index  Mercedes25 10  Chevrolet283  Toyota356  Volvo309

and Tradeoff of Car Problem Fuel Eff Comfort M V T C 1) What is tradeoff between Mercedes and Volvo? 2) What can we see graphically about dominated alternatives?

and Proportional Scoring  Called proportional because scales linearly  Comfort Index: Best = 10, Worst = 3  U c (Mercedes) = 1; U c (Chevrolet) = 0  U c (V) = 9-3/10-3 = 6/7; U c (T) = 6-3/10-3 = 3/7  i.e., Volvo is 1/7 away from best to worst

and Prop Scoring (cont.)  Fuel Economy: Best = 35, Worst = 25  U F (Toyota) = 1; U F (Mercedes) = 0  U F (V) = 30-25/35-25 = 5/10  U F (C) = 28-25/35-25 = 3/10  i.e., Volvo is halfway between best/worst  See why we kept “dominated” options?

and Next Step: Weights  Need weights between 2 criteria  Don’t forget they are based on whole scale  e.g., you value “improving salary on scale at 3x what you value fun going from 0-100”. Not just “salary vs. fun”  If choosing a college, 3 choices, all roughly $30k/year, but other amenities different.. Cost should have low weight in that example  In Texaco case, fact that settlement varies across so large a range implies it likely has near 100% weight

and Weights - Car Example  Start with equal weights (0.5, 0.5) for C,F  U(M) = 0.5* *0 = 0.5  U(V) = 0.5*(6/7) + 0.5*0.5 =  U(T) = 0.5*(3/7) + 0.5*1 =  U(C) = 0.5* *0.3 = 0.15  As expected, Chevrolet is worst (dominated)  Given weights, Toyota has highest utility

and What does this tell us?  With equal weights, as before, we’d be in favor of trading 10 units of fuel economy for 7 units of comfort.  Or 1.43 units F per unit of C  Question is: is that right?  If it is, weights are right, else need to change them.

and “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)

and :1 Tradeoff Example  Find an existing point (any) and consider a hypothetical point you would trade for.  You would be indifferent in this trade  E.g., V(30,9) -> H(31,7)  H would get Uf = 6/10 and Uc = 4/7  Since we’re indifferent, U(V) must = U(H)  k C (6/7) + k F (5/10) = k C (4/7) + k F (6/10)  k C (2/7) = k F (1/10) k F = k C (20/7)  But k F + k C =1 k C (20/7) + k C = 1  k C (27/7) = 1 ; k C = 7/27 = 0.26 (so k f =0.74)

and With these weights..  U(M) = 0.26* *0 = 0.26  U(V) = 0.26*(6/7) *0.5 =  U(T) = 0.26*(3/7) *1 =  U(H) = 0.26*(4/7) *0.6 =  Note H isnt really an option - just “checking” that we get same U as for Volvo (as expected)

and Indifference - 2:1 Fuel Eff Comfort M H T C V

and Notes  Make sure you look at tutorial at end of Chapter 4 on how to simplify with plug-ins  Read Chap 15 Eugene library example!

and Next time: Advanced Methods  More ways to combine tradeoffs and weights  Swing weights  Etc.