A poster discussing a possible alternative to  Analytic
Hierarchy Process

Todd, Robert S.

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Ranking Multi-Attribute Entities - A Possible Inexpensive Alternative to AHP

Ranking Multi-attribute Entities: A Possible Inexpensive Alternative To AHP   Robert Todd, School of Business University of Bridgeport, Bridgeport, CT  Purpose :    There are many situations where we wish to compare multi-attribute entities, such as buying a car, choosing a college, evaluating employees and customers, or  even choosing a date.     There is a method for this sort of comparison called the Analytic Hierarchy Process, or AHP.  This method allows for multiple alternatives to a required choice to be evaluated and ranked by multiple criteria.  But when there are many alternatives, simply preparing the input becomes an enormous chore since one must make a pair-wise comparison of each alternative with every other alternative for each criterion.      The proposed method may offer an alternative to AHP that is vastly simpler and–perhaps–equally good.  (Resolving this issue can be done relatively quickly, but not quickly enough for today’s presentation.) 1-Normalizing Data:     After allocating each attribute to one of the five scales, we normalize all the data using scale-specific formulas which are relative rather than absolute.  When the scores are normalized to values between”0” and “100” (where “0”is worst and “100”is the best) we can compare disparate raw values on an equal footing. Dealing with outliers:     A consequence of outliers is that a single outlier will result in all other entities having unfairly low scores.  An example is “salary."  If one person has an unusually large salary, everybody else will have a normalized score of close to zero since normalization is relative. Outliers can be handled in two ways, either ”statistically“ or by “User’s choice.” Weighting:     The user might consider one attribute more important than  another.  We weight normalized scores by pushing above-average attribute scores upward and below-average attribute scores downward.  The lady in this example has chosen income, looks, and IQ to be 1.5 times more important than the other attributes.     Now we have to find the alternative which is the “closest” to the ideal. 2-Ranking Multi-attribute Entities:    After doing all the previous steps we now have the final result which is in the “Total” column in the table below.   This gives the final rank of the alternatives on a scale 0-100 and considering all the lady’s preferences.  As we said before, 100 is the best and 0 is the worst.  In this example Quentin is the best choice.      Ladies – do you agree? Suppose a woman wants to choose a date from among 26 men. She will rate them on the following criteria: income, looks, height, weight, IQ, health, and age.  These particular attributes are chosen because they will, collectively, illustrate all the different scales, as well as the necessity of handling outliers.  This young lady will also indicate her ideal values for each criterion and supply a weight to each.  All data were randomly generated. Here is the original data:         The first line in the table declares the “scale type."  Here are the kinds of scales that could be encountered:  1.High score is good (e.g., test scores, gas mileage). 2. Low score is good (errors, costs). 3. Central Optimum, higher or lower is equally bad (blood pressure). 4. Central Optimum, higher is better than lower ($100 more is better than $100 less). 5. Central Optimum, lower is better than higher (10 lbs underweight is better than 10 lbs overweight).   Ranking Multi-attribute Entities Method: There are two steps involved in comparing multi-attribute entities. The first is to normalize all the data of each attribute for each entity, so that numerically disparate attribute values can be compared on the same 0-100 scale.  The second step is to calculate the “distance” of each entity from a user defined ideal. So let’s start by briefly explaining the steps… scale type 4 1 4 5 3 2 4 how much better 50%   10% 25%     50% Perfect--> $200,000 10 6-2 180 120 0 40 Weight--> 150% 150% 100% 100% 150% 100% 100% Member Income Looks Height Weight IQ Sick Days Age Al $34,600 7 5-6 155 95 4 61 Bill $77,400 7 6-3 282 151 5 53 Curly $45,500 10 5-8 163 116 0 63 Dave $39,400 8 5-11 163 97 3 61 Ed $66,200 7 5-4 195 100 3 31 Frank $85,100 7 5-7 191 95 0 33 George $68,500 1 5-11 175 91 5 43 Hal $52,400 4 5-11 187 125 0 63 Izzy $65,300 7 5-9 188 113 0 30 Jack $32,400 6 6-1 200 143 2 46 Karl $67,900 4 6-0 195 127 0 43 Larry $49,400 6 5-10 169 153 0 37 Mo $67,600 5 5-9 156 103 0 33 Ned $51,400 2 6-2 170 132 0 41 Ozzy $75,400 1 6-4 156 105 3 50 Paul $49,200 6 5-9 177 128 4 42 Quentin $87,600 10 6-0 189 137 0 41 Ron $556,800 2 6-4 185 131 0 61 Sam $42,100 2 5-7 179 120 0 61 Tom $33,900 3 6-1 189 156 0 33 Umberto $35,800 7 6-5 197 114 0 51 Vince $37,300 10 6-0 167 87 0 64 Walt $66,900 2 5-7 153 109 0 54 Xander $85,500 2 6-1 178 130 0 65 Yves $84,300 10 5-7 175 134 4 45 Zachary $648,700 9 5-11 275 98 0 34 Member Income Looks Height Weight IQ Sick Days Age Total Rank Al $34,600 7 5-6 155 95 4 61 1.2 25 Bill $77,400 7 6-3 282 151 5 53 0 26 Curly $45,500 10 5-8 163 116 0 63 67.6 6 Dave $39,400 8 5-11 163 97 3 61 30.6 22 Ed $66,200 7 5-4 195 100 3 31 16.4 23 Frank $85,100 7 5-7 191 95 0 33 50.1 17 George $68,500 1 5-11 175 91 5 43 8.1 24 Hal $52,400 4 5-11 187 125 0 63 54.1 12 Izzy $65,300 7 5-9 188 113 0 30 73.4 5 Jack $32,400 6 6-1 200 143 2 46 50.3 16 Karl $67,900 4 6-0 195 127 0 43 73.6 4 Larry $49,400 6 5-10 169 153 0 37 53.8 13 Mo $67,600 5 5-9 156 103 0 33 51.7 14 Ned $51,400 2 6-2 170 132 0 41 74 3 Ozzy $75,400 1 6-4 156 105 3 50 35 21 Paul $49,200 6 5-9 177 128 4 42 54.6 10 Quentin $87,600 10 6-0 189 137 0 41 100 1 Ron $556,800 2 6-4 185 131 0 61 66.8 7 Sam $42,100 2 5-7 179 120 0 61 41.2 18 Tom $33,900 3 6-1 189 156 0 33 36.6 20 Umberto $35,800 7 6-5 197 114 0 51 78.7 2 Vince $37,300 10 6-0 167 87 0 64 51.2 15 Walt $66,900 2 5-7 153 109 0 54 37.2 19 Xander $85,500 2 6-1 178 130 0 65 57.3 8 Yves $84,300 10 5-7 175 134 4 45 55.8 9 Zachary $648,700 9 5-11 275 98 0 34 54.5 11 # 56-1 :  __  __  __ 

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Ranking Multi-Attribute Entities - A Possible Inexpensive Alternative to AHP

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