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Decisions Involving Multiple Objectives: SMART
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Objectives and Attributes
An objective = an indication of preferred direction of movement, i.e. ‘minimize’ or ‘maximize’ An attribute is used to measure performance in relation to an objective
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An office location problem
Location of office Annual rent ($) Addison Square Bilton Village Carlisle Walk 5 000 Denver Street Elton Street Filton Village Gorton Square
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Main stages of SMART 1 Identify decision maker(s)
2 Identify alternative courses of action 3 Identify the relevant attributes 4 Assess the performance of the alternatives on each attribute 5 Determine a weight for each attribute 6 For each alternative, take a weighted average of the values assigned to that alternative 7 Make a provisional decision 8 Perform sensitivity analysis
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Value tree Benefits Costs Turnover Working conditions to customers
Rent Electricity Cleaning to customers Closeness Visibility Image parking Size Comfort Car
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Is the value tree an accurate and useful representation of the decision maker’s concerns?
Completeness Operationality 3. Decomposability 4. Absence of redundancy 5. Minimum size
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Costs associated with the seven offices
Annual Annual Office Annual cleaning electricity Total rent ($) costs ($) costs ($) costs ($) Addison Square Bilton Village Carlisle Walk Denver Street Elton Street Filton Village Gorton Square
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Direct rating for ‘Office Image’
Ranking from most preferred to least preferred. 1. Addison Square 2. Elton Street 3. Filton Village 4. Denver Street 5. Gorton Square 6. Bilton Village 7. Carlisle Walk
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Direct rating - Assigning values
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Using a value function to assign values
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Values for the office location problem
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Determining swing weights
Closeness to customers Visibility Image Size Comfort Car parking Best 100 80 Worst 70
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For example... A swing from the worst ‘image’ to the best ‘image’ is considered to be 70% as important as a swing from the worst to the best location for ‘closeness to customers’ ...so ‘image’ is assigned a weight of 70.
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Normalizing weights Normalized weights
Attribute Original weights (rounded) Closeness to customers Visibility Image Size Comfort Car-parking facilities
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Calculating aggregate benefits for each location
Addison Square Attribute Values Weight Value weight Closeness to customers Visibility Image Size Comfort Car-parking facilities 8080 so aggregate benefits = 8080/100 = 80.8
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Table 3.2 - Values and weights for the office location problem
____________________________________________________________________ Attribute Weight Office A B C D E F G _____________________________________________________________________________________ Closeness Visibility Image Size Comfort Car parking Aggregate benefits
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Trading benefits against costs
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Sensitivity analysis
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