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# Class Note for EMSE 388 at GW (8)

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Date Created: 02/07/15

EMSE 388 Quantitative Methods in Cost Engineering USING ANALYTICAL HIERARCHY PROCESS TO SELECT A JOB When multiple objectives are important to a Decision Maker it is often difficult to choose between alternatives Example You are choosing a job One might offer the highest starting salary but rate poorly on your other objectives quality of life closeness to your family Another job offer might rate highly on these latter objectives but has a relatively low starting salary Which one do you choose THOMAS SAATY s ANALYTICAL HIERARCHY PROCESS Provides a powerful tool that can be used to make decisions when multiple objectives are present Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 229 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Four Objectives Objective 1 High Starting Salary Objective 2 Quality of life in city where job is located Objective 3 Interest of Work Objective 4 Nearness ofjob to family 0 The AHP process generates a weight for each objective By convention the weights sum up to 1 Weights For Objectives OBJECTIVE DESCRIPTION Weight Objective 1 Salary 05115 Objective 2 Life quality 00986 Objective 3 Work interest 02433 Objective 4 Near family 01466 TOTAL WEIGHT 10000 Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 230 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering CONCLUSION 0 High Starting Salary HSS is your most important objective 0 H88 is twice as important as the interest of the work 0 H88 is approximately three times as important as nearness to your family 0 H88 is approximately five times as important Quality of Lie in the city where you work YOU HAVE OBTAINED THREE JOB OFFERS The following Table described how each Job scores on the four objectives Determining best job Matrix of scores Salary Life quality Work interest Near family Job 1 05714 01593 00882 00824 Job 2 02857 02519 06687 03151 Job 3 01429 05889 02431 06025 TOTAL WEIGHT10000 10000 10000 10000 Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 231 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering CONCLUSION 0 Job 1 is twice as important in terms of salary as job 2 and three times as important as job 3 0 Job 3 is twice as important in terms of Quality of Life as job 2 and three times as important as job 1 0 Job 2 is more than twice as important in terms of Interesting Work as job 3 and eight times as important as job 1 WHICH ONE DO YOU CHOOSE Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 232 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering CALCULATE COMBINED SCORES Job 1 Score 05115057140098601593 02433008820146600824 03415 Job 2 Score 05115028570098602519 02433066870146603151 03799 Job 3 Score 05115014290098605889 02431 066870146606025 02786 Conclusion Job 2 gets the highest score Hence the analysis above recommends taking job number 2 Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 233 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Note that 0 Combined Score for Jobs is a MatrixVector product that can be easily calculated using the MMULT function in Excel Inputs to the above analysis are 0 Weights for each objective 0 Scores for each Alternative on each of the Objectives OUTPUT OF ANALYTICAL HIERARCHY PROCESS PROVIDES THESE WEIGHTS AND SCORES Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 234 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering PAIRWISE COMPARISON MATRIX OF OBJECTIVES Suppose we have N objectives Then consider the NN Matrix A such that 6111 a1N A 2 aN1 aNN where a Importance of Objective i compared to Objective j gt 1 Objective i is more important than Objective j aid 2 1 Objective i is as Important as Objective j lt 1 Objective i is less Important as Objective j BUT HOW DO WE GET SPECIFIC VALUES FOR a Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 235 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering ANSWER THROUGH EXPERT JUDGEMENT QUESTIONNAIRES INTERMEZZO WHAT IS EXPERT JUDGMENT IT IS NOT A Group of Experts in a Room deciding on Numbers Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 236 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering EXPERT JUDGEMENT ELICITATION PROCEDURE STRUCTURED APPROACH TO CAPTURING AN EXPERTS KNOWLEDGE BASE AND CONVERT HIS KNOWLEDGE BASE INTO QUANTITATIVE ASSESSMENTS I MODELERS SKILLEDIN I DECOMPOSITION I I AND AGGREGATION OF ASSESSMENTS I NORMATIVE EXPERTS SUBSTANTIVE I I v I l KNOWLEDGABLE ABOUT I I THE SUBJECT MATTER AND EXTENSIVE EXPERIENCEI I ELICITATION PROCESS MULTIPLE CYCLES AT LEAST 2 TTDECOMPOSITIONOFI EVENT OF INTEREST I TO A MEANINGFULL LEVEL FOR SU BSTANT IVE EXPE RT r 3927 E39LICITA39TEJN OF39 39I I I SUBSTANTIVE EXPERT I JUDGMENT OF FACI LITATED IBY NORMATIVE EXPERTI I J I 3 AGGREGATION OF JUDGEMENTS I BY NORMATIVE EXPERT Lecture Notes by Instructor Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 20 Page 237 EMSE 388 Quantitative Methods in Cost Engineering EXAMPLE THE DELPHI METHOD 0 Early 1950 Developed by RAND Corporation as spinoff of an Air Force Research Rroject quotProject Delphiquot 0 1963 Wider audience due to 1963 RAND Study quotReport on a longrange Forecasting studyquot Probably best known method to date of Eliciting and synthesizing expert judgment STEP 1 Monitoring Team defines set of issues and selects sets of Respondents who are experts on the issues in question Respondents do not know who other respondents are and the responses are anonymous Preliminary questionnaire is sent for comments which are then used to establish a definitive questionnaire Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 238 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering STEP 2 Questionnaire is sent to respondents Monitoring Team analyses the answers STEP 3 The set of responses is sent back together with 25 lower and 25 upper responses The respondents are asked if they wish to revise the initial predictions Those who answered outside of the above range are asked to give arguments STEP 4 The revised predictions are analyzed by the monitoring team and the outliers for arguments are summarized GOTO STEP 2 TYPICALLY THREE ROUNDS Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 239 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering EXAMPLE OF DELPHI QUESTIONNAIRE 1 Questionnaire 1 This is the first in a series of four questionnaires intended to demonstrate the use of the Delphi Technique in obtaining reasoned opinions from a group of respondents Each of the following six questions is concerned with developments in the United States with the next few decades In addition to giving your answerto each question you are also being asked to rank the questions from 1 to 7 Here 1 means that in comparing your ability to answerthis question with what you expect the ability of the other participants to be you feel that you have the relatively best chance of coming closer to the truth than most of the others while a 7 means that you regard that chance as relative least Source Helmer 1968 Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 240 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Rank D EDD EDD 1 In your opinion in what year will the median familiy income in 1967 dollars reach twice its present amount 2 In what year will the percentage of electric automobiles along all automobile in use reach 50 percent 3 In what year will the percentage ofhouseholds that are equipped with computer consoles tied to a central computer and databank reach 50 percent 4 By what year will the percapita anlount of personal cash transactions in 1967 dollars be reduced to oneetenth ofwhat it is now 5 In what year will power generation be thermonuclear fusion become comercially competitive with hydroelectric power 6 By what year will it be possible by commercial carriers to get from New York39s Time Square to San Fransisco39s Union Suare in half the time that is now required to make that trip 7 In what year will a man for the rst time travel to the Moon stay for at least 1 month and return to earth HNeverH is alson an acceptable answer An sw erquot HUM HUU Please also answer the following question and give your nan1e this is for identi cation purposes during the exercise only no opinions will be attributed to a particular person Check One I would like III III E I would prefer not I am willing but no anxious participate in the three remaining qustionnaires Name block letter please Lecture Notes by Instructor Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 20 Page 241 EMSE 388 Quantitative Methods in Cost Engineering CRITIQUE ON DELPHI METHOD Sackman39s Delphi Critique 1975 Methodological 0 Questions are vague are often so vague that it would be impossible to determine when if ever they occurred 0 Furthermore the respondents are not treated equally 0 Many dropouts No Explanation for of dropouts given or researched nor are effects assessed on eventual assessment Does Delphi convergence because of boredom in stead of consensus o Sackman argues that experts and non experts produce comparable results Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 242 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Comparison to other Methods Delbecq Van de Ven and Gusstafson 1975 0 Method 1 quotnominal group techniquequot participants confront each other directly in a controlled environment 0 Method 2 quotno interaction model initial assessments are simply aggregated mathematically Results 0 Nominal group technique superior to the others 0 Delphi worst of the three Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 243 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering EXPERT JUDGMENT ELICITATION PRINCIPLES Source Experts in Uncertainty Roger M Cooke 1 Reproducibility It must be possible for scientific peers to review and if necessary reproduce all calculations This entails that the calculation model must be fully specified and the ingredient data must be made available 2 Accountability The source of Expert Judgment must be identified 3 Empirical Control Expert probability assessment must in principle be susceptible to empirical control Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 244 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering 4 Neutrality The method for combiningevaluating expertjudgements should encourage experts to state true opinions 5 Fairness All Experts are treated equally prior to processing the results of observations PRACTICAL EXPERT JUDGMENT ELICITATION GUIDELINES 1 The questions must be clear 2 Prepare an attractive format for the questions and graphic format for the answers Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 245 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering 3 Perform a dry run 4 An Analyst must be present during the elicitation 5 Prepare a brief explanation of the elicitation format and of the model for processing the responses 6Avoid Coaching 7 The elicitation session should not exceed 1 hour Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 246 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering ELICITATION PROCEDURES 0 Direct Procedures Ask for ProbabilitiesMeasures of Central TendencyMeasures of Variability 0 Indirect Procedures Use Betting Strategies Paired Comparisons Example Betting Strategies Indifference when Expected payoffs are the same 1 Betting Stategies Event Lakers winning the NBA title this season Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 247 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering STEP 1 Offer a person to Choose between following the following bets where X100 YO Max Profit La kers Win X Bet for Lakers Lakers Loose Y Lakers Win X Bet against Lakers Lakers Loose Y STEP 2 Offer a person to Choose between following the following bets where XO Y100 Consistency Check Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 248 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering STEP 3 Offer a person to choose between following the following bets where X100 Y50 STEP 4 Offer a person to choose between following the following bets where X50 Y100 Consistency Check Continue until point of indifference has been reached Assumption When a person is indifferent between bets the expected payoffs from the bets must be the same Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 249 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Thus XPrLW YPrLL XPrLW YPrLL ltgt 2XPrLW 2Y1 PrLVV o ltgt Y PrLVV X Y 1 Example x1oo Y50 3 PrLW E e 3333 Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 250 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering 2 Paired Comparisons of Situations Issaquah class ferry on the Bremerton to Seattle route in a crossing situation within 15 minutes no other vessels around good visibility negligible wind I Tr quot i 39 I 51quot Iquot I n I I i nl M39J I II ifth n iquot I 39 a m 539 Guam Other vessel is a navy vessel Other vessel is a product tanker Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 251 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Question 1 89 Situation 1 Attribute Situation 2 Issaquah Ferry Class SEABREA Ferry Route Navy 1st Interacting Vessel Product Tanker Crossing Traffic Scenario 1St Vessel 05 5 miles Traffic Proximity 1st Vessel No Vessel 2nd Interacting Vessel No Vessel Traffic Scenario 2quotd Vessel No Vessel Traffic Proximity 2quotd Vessel gt 05 Miles Visibility Along Ferry Wind Direction 0 Wind Speed Likelihood of Collision Avoidance 98765432123456789 Situation 1 is worse ltXgt Situation 2 is worse 9 VERY MUCH MORE LIKELY to result in a collision 7 MUCH MORE LIKELY to result in a collision 5 MODERATELY LIKELY to result in a collision 3 SOMEWHAT MORE LIKELY to result in a collision 1 EQUALY LIKELY to result in a collision Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 252 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Underlying Model for Paired Comparison Questionnaire Traf c Scenario 1 KIM Traf c Scenario 2 X2 1X 2 Vector including 2 way interactions PrAccident Prop Failure X1 Poe Edggyzo PrAccident Prop Failure X2 POeETWQ l l m 4 mi Prmccident I Prop Failure X5 2 E T n11 ZX2 PrAccident Prop Failure X2 Calibration to Accident Data Calibrate to convert relative probabilities to absolute probabilities by solving for P0 eg fix the total number of expected collisions over a given time period Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 253 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering BACK TO THE ANALYTICAL HIERARCHY PROCESS PAIRWISE COMPARISON MATRIX OF OBJECTIVES TO OBTAIN WEIGHTS FOR OBJECTIVES Suppose we have N objectives Then consider the NN Matrix A such that a1 1 auv a N 1 a N N where a How much more important is objective i compared to Objective j Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 254 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering gt 1 Objective i is more important than Objective j at 1 Objective i is as Important as Objective j lt 1 Objective i is less Important as Objective j ASSUMPTION 0 There exists a set of numbers Wi i1 n such that Wz Relative importance of objective i compared to the other objectives 11 W1 w 1w gt 061 l l l i 1 w Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 255 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Note that w 1 1 i w wt 1 A w BUT HOW DO WE GET SPECIFIC VALUES FOR a STEP 1 Introduce a quantitative scale for measuring importance 1 Equally Important 3 Slightly More Important 5 Strongly More Important 7 Very Strongly More Important 9 Absolutely More Important Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 256 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering CRITIQUE Where does this scale come from Why five categories and why a scale from 1 to 9 Do the analysis result depend one these choices ANSWER There is instability in the final scores that are being calculated and in the RANKINGS of the alternatives as well AHP is not perfect but very practical and widely applied method STEP 2 Develop a questionnaire Use an attractive graphical format for the questions Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 257 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering For example Objective Objective Quality of Life Starting Salary LHS is Preferred RHS is Preferred gt EEEEEE ery Strongly More Importan ery Strongly More Importan c 6 t o D E D L o E 2 CD 3 o in Q Strongly More Important Slightly More Important Equally Important Slightly More Important Strongly More Important bsolutely More Important Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 258 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Total number of objectives is N What is the number of pairwise comparison you need to ask lNl ANSWER K2 Answers are typically summarized in a Matrix Form 1524 111 2 2 2 l 5 2 l1 2 121 4 2 Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 259 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Back to our Job Selection Example HOW DO WE CALCULATE THE WEIGHT VECTOR W12W2239 oWnT FROM THIS MATRIX Consider the case of 4 Objectives K W1W2W3 Lecture Notes by Instructor Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 20 Page 260 EMSE 388 Quantitative Methods in Cost Engineering STEP 3 Calculate STEP 4 Calculate Normalized matrix ANorm with elements wi a an az 1wjw ij N 11 1 2a 1 i1 W1 W1 Lecture Notes by Instructor Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 20 Page 261 EMSE 388 Quantitative Methods in Cost Engineering AN orm If Subjective Judgment is perfect the top the elements in each row should be the same Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 262 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering ANSWER MATRIX Salary Life quality Work interest Near family Salary 1 5 2 4 Life quality 15 1 12 12 Work interest 12 2 1 2 Near family 14 2 12 1 Sum 195 10 4 75 NORMALIZED MATRIX Salary Life quality Work interest Near family Salary 0513 0500 0500 0533 Life quality 0103 0100 0125 0067 Work interest 0256 0200 0250 0267 Near family 0128 0200 0125 0133 Sum 10000 10000 10000 10000 Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 263 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering CONCLUSION Subjective Judgment is NOT PERFECT STEP 4 Estimate Weight wi for objective i such that Note that Lecture Notes by Instructor Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 20 Page 264 EMSE 388 Quantitative Methods in Cost Engineering Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 265 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Back to our Job Selection Example Normalized matrix Salary Life quality Work interest Near family Weights Salary 0513 0500 0500 0533 05115 Life quality 0103 0100 0125 0067 00986 Work interest 0256 0200 0250 0267 02433 Near family 0128 0200 0125 0133 01466 Sum 10000 10000 10000 10000 1 Lecture Notes by Instructor Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 20 Page 266 EMSE 388 Quantitative Methods in Cost Engineering CHECKING CONSISTENCY IN JUDGMENTS T A W1 WZ W3 W4 KW19W29w3aw4 H EN CE 4w1 4w2 A y 4w3 4w4 Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 267 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering THEREFORE is lg he lgt Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 268 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Back to our Job Selection Example Product Ratios 20774 40611 03958 40161 09894 40672 05933 40459 Cl 00159 Consistency Index C Average Ratio s n n 1 Note That When expertjudgment is perfect CI should be zero Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 269 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering 0 Suppose an Expert would be filling out the questionnaire at random and we would calculate the associated Cl what would that value be The experiment above can be conducted using computerized random answer By conducting this experiment a great number of times one can calculate RI INDEX average Cl index If pairwise comparison matrix is an NN Matrix the following Rl indices have been calculated n 2 3 4 5 6 7 8 9 10 RI 0 058 09 112 124 132 141 145 151 Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 270 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering THOMAS SAATY s suggests C E lt 010 Degree of consistency satisfactory CI E gt 010 Ser10us1ncons1stenc1es Back to our Job Selection Example 0 CI 00159 0 Rl09 o ClRl00176 CONCLUSION JUDGEMENT IS CONSISTENT Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 271 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering PAIRWISE COMPARISON MATRIX OF ALTERNATIVES TO OBTAIN SCORES FOR ALTERNATIVE IN EACH OBJECTIVE Suppose we have N objectives and M alternatives Then consider the N matrices A of size MM such that where a How much more important is alternative i compared to to alternative j in objective i Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 272 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering gt 1 Alternative i is more important than Alterantive j a 1 Atlemative i is as Important as Alternative j lt 1 Alternative i is less Important as Alternative j ASSUMPTION 0 There exists a set of numbers Wi i1 n such that Wz Relative importance of alternative i compared to the other objectives w w 1 w gt0 a l 9 l 9 1 i1 w Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 273 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Note that BUT HOW DO WE GET SPECIFIC VALUES FOR a ANSWER Same as before through Paired Comparison Questionnaire Lecture Notes by Instructor Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 20 Page 274 EMSE 388 Quantitative Methods in Cost Engineering OBJECTIVE STARTING SALARY Objective Objective Job 1 Job 2 LHS is Preferred RHS is Preferred EEEEEE ery Strongly More Importar ery Strongly More Importar 4 C is t o Q E a L o E Z a 4 2 o m 0 lt bsolutely More Important Strongly More Important Slightly More Important Slightly More Important Strongly More Important Equally Important Lecture Notes by Instructor Dr J Rene van Dorp Chapter 20 Page 275 Source Financial Models Using Simulation and Optimization by Wayne Winston

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