Decisions Involving

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• Decisions Involving
• Multiple Objectives
• SMART
• (Simple Multi-attribute Rating Technique)

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Objectives and Attributes

• An objective an indication of preferred
  direction of movement, i.e. minimize or
  maximize
• Example minimize cost or maximize market share.

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Objective and attributes..cont

• An attribute is used to measure performance in
  relation to an objective
• Example if the objective is to maximize
  exposure of a TV advertisement we may use the
  number of people surveyed who recall seeing it to
  measure the degree to which the objective was
  achieved.
• Proxy attributes using attribute not directly
  related to the objective (e.g. employee turnover
  and job satisfaction)

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An office Location Problem
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An office location problem

• Location of office Annual rent ()
• Addison Square 30 000
• Bilton Village 15 000
• Carlisle Walk  5 000
• Denver Street 12 000
• Elton Street 30 000
• Filton Village 15 000
• Gorton Square 10 000

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An office Location..Continued

• The owner would like to keep the costs as low as
  possible, while considering other factors such as
  closeness to customers and location visibility
  and comfort. The owner is unsure how to set about
  making his choice, given the number of choices
  involved?

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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
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Is the value tree an accurate and useful
representation of the decision makers concerns?

• Completeness all the attributes of concern has
  been included
• Operationality all attributes are specific
  enough to evaluate
• 3. Decomposability each attribute is
  independent from other attributes
• 4. Absence of redundancy no duplicate of
  attributes
• 5. Minimum size attributes should not be
  decomposed beyond the level where they can be
  evaluated

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• Costs associated with the seven offices
• Annual Annual Office Annual cleaning el
  ectricity Total
• rent () costs () costs ()
  costs ()
• Addison Square 30 000 3000 2000 35 000
• Bilton Village 15 000 2000 800 17 800
• Carlisle Walk 5 000 1000 700 6 700
• Denver Street 12 000 1000 1100 14 100
• Elton Street 30 000 2500 2300 34 800
• Filton Village 15 000 1000 2600 18 600
• Gorton Square 10 000 1100 900 12 000

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Direct rating for Office Image

• The owner is asked to Rank attributes from most
  preferred to least preferred regarding image.
• 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 (image)

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Size for each office location
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Using a value function to assign values (size)
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Values for the office location problem
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Determining swing weights
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Swing weights

• They are assigned by decision maker for the
  attributes available.
• 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 100 32
• Visibility 80 26
• Image 70 23
• Size 30 10
• Comfort 20 6
• Car-parking facilities 10
  3
• 310 100

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Calculating aggregate benefits for each location

• Addison Square
• Attribute Values Weight Value ? weight
• Closeness to customers 100 32 3200
• Visibility 60 26 1560
• Image 100 23 2300
• Size 75 10 750
• Comfort 0 6 0
• Car-parking facilities 90 3 270
• 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 32
100 20 80 70 40 0 60 Visibility
26 60 80 70 50 60 0
100 Image 23 100 10
0 30 90 70 20 Size 10 75 30
0 55 100 0 50 Comfort
6 0 100 10 30
60 80 50 Car parking 3 90
30 100 90 70 0 80 Aggregate benefits 80.8 39.
4 47.4 52.3 64.8 20.9 60.2 ________________
__________________________________________________
___________________
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Trading benefits against costs
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Problem (2)

• Buying new Machine
• You need a new corrugation machine to support
  your manufacturing operations at a cars factory.
  Employer does not pay attention to the cost of
  the machine, but he pays most attention to speed,
  strength, life span, and ease of use, ease of
  maintenance. Employer assigns 70, 100, 90, 40,
  and 30 swing weights for each attribute
  respectively. A supplier has provided relevant
  information for seven different options. The
  life span in years for each option are as
  follows A 10, B 15, C12, D13, E9, F7, G14.

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Problem(2)

• Using the information provided in the table
  below, use the direct rating method to decide
  about the best option to buy from?
• Note use graphical methods to decide about any
  ratings required, using the midpoint in
  attributes as a 50 weight.

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Table of ratings for Problem (2)
Speed Strength Life Span Ease of Use Ease of maintenance
A 100 10 -- 35 50
B 20 80 -- 70 70
C 90 50 -- 20 0
D 85 30 -- 40 90
E 0 100 -- 100 40
F 40 70 -- 0 100
G 30 0 -- 55 20