Multi-Attribute Decision Making

Transcription

1 GSBA 509 Multiple Attribute Decisions Multi-Attribute Decision Making Some choice problems need more than one measure to evaluate different outcomes Multiple attributes = multiple criteria to consider when making decisions Yandell GSBA 509 Yandell GSBA Example: Buy a home Decision Approaches You want to buy a house and have narrowed down to 2: Attribute House House 2 Cost 455, , Size br, ba 4 br, 2 ba Neighborhood average nice Distance to work 5 mi 5 mi Condition good average (etc ) To make a choice, a method is needed to either Consider all attributes at the same time Decompose the problem and treat attributes sequentially (Note: Tradeoffs may be difficult to make) Yandell GSBA 509 Yandell GSBA Three Decision Methods Dominance. Dominance: if alternative A has outcomes at least as good as those for alternative B for each attribute, choose A Example: if you want a smaller, inexpensive house close to work and in good condition, and don t care about the neighborhood, choose house This doesn t happen often, especially if the number of criteria is large If it does happen, decision problem becomes trivial Yandell GSBA Yandell GSBA 509 6

2 Three Decision Methods 2. Satisficing: set minimum requirements for each attribute If not satisfactory on one or more attribute, discard the alternative Example: if you decide you need 4 bedrooms, discard all houses with or fewer bedrooms Satisficing Solution may not be unique, or a solution may not exist Attributes must be independent (since they get treated separately) One slightly bad attribute can eliminate an otherwise good choice Examples: -- need: 4 br, good neighborhood, less than $470,000..no solution -- need: at least br, no more than 20 miles from job..nothing eliminated Yandell GSBA Yandell GSBA Three Decision Methods Lexicographic procedure. Lexicographic procedure (ordering): Rank attributes from most important to least important Compare alternatives on most important attribute chose the best one. If still tied, use the next most important attribute.continue until decision is made This may only use one or two attributes and ignore the others (doesn t allow bad performance on one to be made up by good outcomes on others) Yandell GSBA Yandell GSBA Trade-off Methods Idea: create alternatives that are different only on one attribute (the surviving attribute) Trade-off Methods Method:. Choose the surviving attribute 2. Choose a base level for the remaining attributes. Adjust each alternative s outcomes change all but the surviving attribute to base level, then adjust the measure of the surviving attribute so the new outcome is equivalent to the old outcome 4. Choose preferred alternative by comparing surviving attribute values Yandell GSBA 509 Yandell GSBA

3 Example Steps Example: houses, criteria: Criteria House House 2 House Cost: 495,000 80, ,000 Size: br, 2ba br, ba 4br, 2ba Nbrhd: good excellent average. Let surviving attribute = cost ($ values are easiest to adjust) 2. Choose base level for size and nbrhd: Let size base level = br br, 2ba Let neighborhood base level = good. Adjust Cost to account for differences from base Yandell GSBA 509 Yandell GSBA Adjustments Adjustments House : no adjustment needed, base levels exist House 2: What would you accept to settle for only bath (i.e., what is the marginal value of extra bathroom from to 2?) $5,000 (example) What would you pay for an excellent neighborhood? (i.e., what is the marginal value of good to excellent neighborhood?) $20,000 (example) i.e., 80, ,000 20,000 = 95,000 cost + size adj. nbrhd adj. = adjusted cost House : What would you pay for the extra bedroom? $0,000 (example) What would you accept to settle for only an average neighborhood? $50, (example) i.e., 560,000 0, ,000 = 580,000 cost size adj. + nbrhd adj. = adjusted cost Yandell GSBA Yandell GSBA After Adjustment After Adjustment Example: houses, criteria: Criteria House House 2 House Cost: 495,000 80, ,000 Size: br, 2ba br, ba 4br, 2ba Nbrhd: good excellent average Now these are easier to compare. If these really represent your preferences and values, you should pick House #2 95, ,000 br, 2 ba br, 2 ba good good Yandell GSBA Yandell GSBA 509 8

4 Another Scaling Technique Apply weights to individual criteria, then compute a weighted score for each alternative MUST Criteria: No scaling necessary since these are absolutely necessary WANT Criteria: Scaling is necessary since these are not equal in desirability IGNORABLE Criteria: No scaling necessary since these are not part of the decision problem Yandell GSBA Yandell GSBA MUST Criteria: No scaling necessary WANT Criteria: 0 Very Important Important Somewhat Important 2 Somewhat Unimportant IGNORABLE Criteria: No scaling necessary MUST Criteria: No scaling necessary WANT Criteria: Example Weights: 0 Very Important 9 Monthly Payment = Important 6 5 Quality of schools = 5 4 Somewhat Important 2 Somewhat Unimportant Air conditioning = 2 IGNORABLE Criteria: No scaling necessary Yandell GSBA Yandell GSBA Example MUST criteria A couple with two children must buy a new home and move in within 0 days after arriving in a city to start new jobs. Apartments have been ruled out. First, the couple lists their MUST criteria: or more bedrooms 2 or more bathrooms Available within 0 days Not downtown Not more than 0 minutes driving time to jobs Monthly payment, including taxes, not more than $2500 Down payment not more than $20,000 Must not have a swimming pool Yandell GSBA Yandell GSBA

5 WANT criteria IGNORE criteria Weight Monthly payment 0 Distance to jobs 9 Distance to kid s school 7 Size of garage 7 Condition of home 6 Extra bedroom 5 Traffic and noise 4 View 2 Age of home Brick or wood exterior Attached or separate garage Fireplace Yandell GSBA Yandell GSBA Compare Alternatives Compare weighted scores Σ(weight x score) House House 2 House Criterion Attribute Score Attribute Score Attribute Score Monthly payment Distance to jobs 0 mi 7 5 mi 4 6 mi 9 Distance to school 4 blocks 6 2 blocks 8 blocks 7 Size of garage 2 car 7 2 car 7 car 0 Condition of home good 6 good 6 average Extra bedroom no 0 no 0 yes 0 Traffic and noise fair average 5 good 8 View no 0 partial 4 no 0 House : (0x8)+(9x7)+(7x6)+(7x7)+(6x6)+(5x0)+(4x)+(2x0) = 282 House 2: (0x5)+(9x4)+(7x8)+(7x7)+(6x6)+(5x0)+(4x5)+(2x4) = 255 House : (0x)+(9x9)+(7x7)+(7x0)+(6x)+(5x0)+(4x8)+(2x0) = 0 Best Choice (Note: the 0-0 scale used to score individual attributes is arbitrary, but consistent across houses) Yandell GSBA Yandell GSBA Summary Multi-Attribute Decision Models Descriptive procedures Dominance Satisficing Lexicographic Trade-off procedures Surviving attribute Weighted scores Yandell GSBA