Multi-Attribute Utility Model (MAUM) Applying Utility Theory To Practical Problems
When is MAUM used? • When there are multiple options and criterion. • When the decision to be made is important enough to warrant the time and expense. • When there is a cost-benefit to doing the analysis. • When the situation has sufficient complexity that it exceeds our mental ability to rationally consider all aspects. (Bounded Rationality is a limitation)
How We Deal With Bounded Rationality • We use Inadequate Models. • We use simple strategies. • Satisficing • Incremental Adjustment • Heuristics • Decomposition:Breaking a problem down into its component parts and dealing with each part separately. (Avoids information overload)
MAUM Decomposes Problems • MAUM decomposes a complex problem into separate parts so that we only have to consider one part of the problem at a time. • Then it brings all the parts together for us. (Due to bounded rationality, we are unable to mentally do this without the model.)
MAUM Elements • ALTERNATIVES: Choices • For example, you might have two job offers. • CRITERION: These are the variables that are used to evaluate each alternative. • Salary / Type of work / Location / Size of company • ATTRIBUTES: The measurable characteristicsof each criterion. • For example, there could be several different ways to measure the size of a company. (market share / number of employees / annual sales / etc.) Each one is an attribute of the size criterion.
Attributes and Criteria for a Job-Offer Example • CRITERIONATTRIBUTES • Salary Dollar amount • Type of work Functional area • Location Geographic area • Company Size # of Employees
UTILS • UTILS are relative measures of preference, worth, or value. -100 0+100 |___________________|_____________________| Liver Clams Ice Cream • You, the Decision-Maker, must quantify each criterion and each attribute by ranking and giving each a relative worth.
STEP ONE • Identify and list the relevant criteria and constraints. • Constraints allow us to eliminate many alternatives before we take the time and expense of fully evaluating them. • EG: Don’t bother to evaluate a job opportunity if the salary is way too low.
STEP TWO • Identify and list the relevant attributes • You should minimize the number of attributes you use for each criterion. • For example the Criterion, “type of work”could have several attributes: • Functional area • Quantitativeness • Degree of interaction with customers • The fewer attributes you use, the more it simplify the analysis.
STEP THREE • Determine your utility (preference) for each of the various attributes. • Two general categories of attributes: • Discrete (qualitative) E.g. Type of work • Continuous(numerical) E.g. Salary
Setting Attribute Utility Criteria = SALARY DOLLARSUTILITY (1-100) 35-40 30 41-45 50 46-50 80 51-55 100 The utility values are your preference ratings for each salary.
Setting Attribute Utility Criteria for Functional Area AREAUTILITY Personnel 80 Retail 40 Production 75 Office 50 Information 100
Setting Attribute Utility Criteria for Geographic Area AREAUTILITY South Jersey 50 Central Jersey 100 North Jersey 40 Out of State 20
Setting Attribute Utility Criteria for Number of employees PEOPLEUTILITY Less than 100 100 101-500 75 Greater than 500 50
STEP FOUR • Determine the relative importance (weight) of each of the criteria. • Making them percentages is easiest. • Decide which criterion is the most important and which is the least important. • You might value salary more than location.
Step 4 continued Here we are ranking the criteria in terms of importance to us, and then determining the % of total utilityfor each. CRITERIONUTILITY% of max utility Salary 80 / 290 = 28% Type of work 100 / 290 = 34% Location 60 / 290 = 21% Company Size 50 / 290 = 17% Sum = 290 Sum = 100%
STEP FIVE • Determine the proportion of the weights of the attributes. • If there is only one attribute, it gets a weight of 100%. • If there are multiple attributes for a given criterion, you must proportion the weights among those attributes.
Attribute 1: Function Percent of weight: 60% Personnel 80 x .6 = 48 Retail 40 x .6 = 24 Production 75 x .6 = 45 Office 50 x .6 = 30 Info. Mgt. 10 x .6 = 6 Attribute 2: Quantitativeness Percent of weight: 40% Highly quant. 20 x .4 = 8 Somewhat quant. 50 x .4 = 20 Mixed 100 x .4 = 40 Somewhat qual. 75 x .4 = 30 Highly qual. 50 x .4 = 20 Dealing with two attributes for one criterion Criterion: Type of Work Weight: 34% For each attribute, multiply its utility value by the percentage of the weight.
STEP SIX • Apply the MAUM model and computational procedures to the feasible alternatives, and identify the one or two with the greatest overall utility.
What Our Model Says • U(job) = U(Salary) + U(Type) + U(Location) + U(Size) • We ranked each of these criterion, so they must be weighted accordingly. • U(job) = 28*U(Salary) + 34*U(Type) + 21*U(Location) + 17*U(Size)
Functional Area (34%) AREAUTILITY Personnel 80 Retail 40 Production75 Office 50 Information 100 SALARY (28%) DOLLARSUTILITY 35-40 30 41-45 50 46-5080 51-55 100 Geographic Area (21%) AREAUTILITY South Jersey 50 Central Jersey 100 North Jersey 40 Out of State 20 Number of employees (17%) PEOPLEUTILITY Less than 100 100 101-500 75 Greater than 500 50 JOB 1:Production manager with a largecompany in Newarkpaying $48,000 U(job) = 28*U(Salary) + 34*U(Area) + 21*U(Location) + 17*U(Size) U(job1) = 28*U(80) + 34*U(75) + 21*U(40) + 17*U(50)
JOB ALTERNATIVES • JOB 1: An Production Management position with a large company in Newark paying $48,000 • JOB 2: A Personnel Management job with a small bank in South Jersey paying $38,000 x x x x
COMMENTS ON MAUM • It is a SELF-EXPLICATED model. • A fancy way of saying it is “user developed.” • A Group Model can be developed for situations where more than one person’s preferences must be accounted for. • You take an average of everyone’s preferences for each criterion and attribute.
Homework Assignment • Apply MAUM to solve an actual decision situation in your life. • EG: What car to buy Where to go on spring break Which job offer to take Where to live Whom to date • Homework may be submitted anytime up until the date of the last scheduled class.
MULTI-ATTRIBUTE UTILITY MODEL Purchasing a Vehicle Dr. Lewis Hofmann Management 451 2/26/14
Introduction Multi-attribute utility models (MAUM) are mathematical tools for evaluating and comparing alternatives to assist in decision making where there are complex alternatives. They are designed to answer the question, "What's the best choice?" The models allow you to assign scores to alternative choices in a decision situation where the alternatives can be identified and analyzed. They also allow you to explore the consequences of different ways of evaluating the choices. The models are based on the assumption that the desirability of a particular alternative depends on how its attributes are viewed. For example, if you are shopping for a new car, you will prefer one over another based on what you think is important, such as price, reliability, ratings, fuel economy, and style. It is possible to make any number of changes and review the results. For example, if it appears that some attribute is too important in determining the results, the weights can be adjusted to produce different results. The Problem Situation In this paper, the multi-attribute utility model is being used to make a choice between the purchase of a Honda Odyssey mini-van, and a Toyota Sienna mini-van. Originally there were eight possible choices, but six of them were eliminated due to one or more criteria having attributes that fell outside of the acceptable range. The remaining two choices were so close in characteristics that there was not an obvious choice. Thus the MAUM model was applied.
The Criteria Seven critical criteria were identified for the decision analysis. These were price, fuel economy, road clearance, cargo space, towing capacity, drive options, and vehicle ratings. Prices were determined using the manufactures’ web site features for building your own vehicle. Similar options were selected for both vehicles. Fuel economy was a definite factor, with the better fuel economy being preferable. Ground/road clearance was an important factor for the type of terrain that would be encountered, as was type of drive option. Four-wheel drive was the most desirable, but unavailable in a minivan. All wheel drive (AHW) was the next best alternative, followed by front-wheel drive. Cargo space was important, and removable seats were a requirement. The vehicle would be used for occasional towing, so towing capacity was also critical. Professional ratings of vehicles were heavily considered, and three sources were used; Consumer Reports, Edmunds ratings, and U.S. News Automobile reports. These three ratings were averaged for each of the two vehicles.
The Data The Model The total utility (U) of each choice was measured using the following formula: U = % weight of criterion #1(utility of its attribute value) + % weight of criterion #2(utility of its attribute value) + … + % weight of criterion #7(utility of its attribute value)
The Results The Toyota Sienna has the highest utility value at 92.5, which is significantly higher than the Honda Odyssey. While many of the criteria were virtually identical, the two criteria that were deciding factors for the Toyota were the ground clearance and the AWD. The price difference between the two vehicles was negligible, but could easily become a major factor, depending on dealership price discounts and trade-in values offered.