MCDM Process Powerpoint

Multi-Criteria Decision Making
September 10, 2019
1
Decision-Making
• With you neighbors, come up with a few examples of

decisions you make that involves some analysis
– What kind of car should I buy?
– Which fraternity/sorority should I join?
– Which smart phone should I buy?
– Which type of dog should I get?
– Where should I go out to dinner?
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Decision-Making
• What if several factors are interrelated or even

contradictory? How do you take them all into
consideration simultaneously?
– Example: Going out to dinner
• Factor 1: Cost
• Factor 2: Quality
• How do we reconcile wanting both a high quality meal
with not wanting to spend much money?
3
Decision-Making
• We all balance pros and cons for a given situation, even

if we aren’t necessarily aware of the process
• MCDM gives us an opportunity to analyze their own
decision-making process in a way that acknowledges
their personal preferences
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1.2 Enrique Ramirez Chooses a College
Enrique Ramirez has been accepted at four colleges:

Canisius (cuh-NEE-shuss) College in Buffalo, NY; Clark
University in Worcester, MA; Drexel University in
Philadelphia, PA; and Suffolk University in Boston, MA.
Now he must decide which one to attend.
Enrique asks his friend Anna for help. Enrique and Anna
realize that there are many different issues to consider
when making this decision. They also realize that the
issues of interest to Enrique and their relative importance
are not the same as those for Anna.
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Using the MCDM Process
(Multi- Criteria Decision Making)
• Step 1: Identify Criteria & Measures
• Step 2: Collect Data
• Step 3: Find the Range of Each Measure
• Step 4: Rescale Each Measure to a Common Unit
• Step 5: Calculate Weights
• Step 6: Calculate Total Scores
• Step 7: Analyze Results, Make a Decision
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– Criteria – Factors that influence your decision making
process (these are BIG ideas, not specifics!)
• Example: Cost
– Measures – Specific ways you can measure each of
your criteria
• Examples: Tuition, Room & Board
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– With your neighbor, come up with two criteria
(remember these are BIG ideas!) for choosing a
college
– Once you have your criteria, outline three different
ways you could measure each criterion
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– Types of Measures:
• Continuous – Measures that can take on any numerical value in a
given range
• Categorical – Measures that can be grouped into a finite number of
categories
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– Step 1: Identify Criteria & Measures

• Here are Enrique’s criteria and measures:
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– Now we must go out and research each of the
measures we outlined and collect our data
– Today we will simply show you the data presented in
the textbook
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– Step 2: Collect Data
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• Need to determine logical ranges for each measure,
there are different procedures for continuous and
categorical
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• Range for Categorical Measures
– Outline all the possible categories for each
categorical measure (there should not be ANY other
choices)
• Measure:
– Academic culture
• Categories:
– Seriously academic (Middle choice, 2)
– Balanced (Most preferable, 1)
– Party school (Least preferable, 3)
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• Range for Continuous Measures
– Give a plausible range for each continuous measure
that includes all data points
• Measure:
– SAT score
• Range: 1400 – 1800
– Doesn’t have to have your actual data’s minimum and maximum as the lower and
upper limits
– Make sure all data fall within your range
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• We now have a table of data, but each measure has its
own unit, we can’t compare them
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– Step 4: Rescale Each Measure to a Common Unit
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• In order to compare one measure to another, we must
rescale all our data to a common unit
• Common unit ranges from 0-1 with 0 being least
preferable and 1 being most preferable
– Categorical Measures
• Most preferable choice  1
• Least preferable choice  0
• Break down other choices sensibly
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• Example: Categorical Measure
– Measure:
• Academic culture
– Categories:
• Seriously academic (Most preferable, 1)
• Balanced (Middle choice, 0.5)
• Party school (Least preferable, 0)
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• Common unit ranges from 0-1 with 0 being least
preferable and 1 being most preferable
– Continuous Measures
• Use proportional scale to convert continuous data to common units
• Most preferable (max or min)  1
• Least preferable (min or max)  0
• Set up a ratio to compute middle choices
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• Example: Continuous Measure
– Measure:
• SAT score
– Range
• Minimum (Least preferable, 0): 1400
• Maximum (Most preferable, 1): 1800
• Use these values to rescale the actual data
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– Example: Continuous Measure
1400 1590 1800
0 x 1
part
whole
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– You Try!
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– You Try!
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• Notice: There are no data points that match the minimum
or maximum values for SAT score, so we won’t have a
common unit score of 0 or 1 for that measure
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Canisius Clark Drexel Suffolk

Total
6.351 5.143 4.714 4.405
Score
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• Teacher Notes:
– Students struggle with rescaling a continuous
measure when the most preferable option is the
minimum value
– Need to really stress the importance of continuous
reflection here, students should be constantly
evaluating their model
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• We need a way to incorporate how one measure might
be more important than another into our model, we do
this using weights
– Rank the measures, with 1 representing the most
important
– Assign 100 points to the top measure
– Assign points to each measure representing your
preferences and each measure’s relative importance
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– Step 5: Calculate Weights
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• Now we need to use our scores to create weights
– Sum your assigned points to get a total score
– Divide each measure’s score by the total score to get
the weight for each measure
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• Now we need to apply the weights to our common unit
scores
– Multiply each common unit score within a measure by
the weight for that measure
– Add up the scores for each choice (this is now a
weighted score)
Measure Weight Canisius Clark Drexel Suffolk
(0.145)(0.475) = (0.145)( 0.875) = (0.145)(0.750) = (0.145)(0.200) =

Average SAT Score 0.145
0.069 0.127 0.109 0.029
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– Step 6: Calculate Total Scores
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Canisius Clark Drexel Suffolk

Total
6.351 5.143 4.714 4.405
Score
Weighted
0.69 0.641 0.501 0.512
Score
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• Now that we have our final scores, we need to analyze
our model and its results in order to make a decision
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• Discussion Questions:
– Why might Enrique not choose Canisius, even though
it was ranked first?
– On many of the measures, Clark received better
scores than Canisius. Why did Canisius end up
having the higher total score?
– Suppose Enrique was offered a scholarship at Clark
for $5,000. How do you think this would affect
Enrique’s decision?
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Multi-Criteria Decision Making

September 10, 2019

• With you neighbors, come up with a few examples of

• What if several factors are interrelated or even

• We all balance pros and cons for a given situation, even

Enrique Ramirez has been accepted at four colleges:

• Step 1: Identify Criteria & Measures

• Step 1: Identify Criteria & Measures

• Step 1: Identify Criteria & Measures

– Step 1: Identify Criteria & Measures

• Step 1: Identify Criteria & Measures

• Step 2: Collect Data

– Step 2: Collect Data

• Step 1: Identify Criteria & Measures

• Step 3: Find the Range of Each Measure

• Step 3: Find the Range of Each Measure

• Step 3: Find the Range of Each Measure

• Step 1: Identify Criteria & Measures

• Step 4: Rescale Each Measure to a Common Unit

– Step 4: Rescale Each Measure to a Common Unit

• Step 4: Rescale Each Measure to a Common Unit

• Step 4: Rescale Each Measure to a Common Unit

• Step 4: Rescale Each Measure to a Common Unit

• Step 4: Rescale Each Measure to a Common Unit

1400 1590 1800

– Step 4: Rescale Each Measure to a Common Unit

– Step 4: Rescale Each Measure to a Common Unit

• Step 4: Rescale Each Measure to a Common Unit

• Step 4: Rescale Each Measure to a Common Unit

Canisius Clark Drexel Suffolk

• Step 4: Rescale Each Measure to a Common Unit

• Step 1: Identify Criteria & Measures

• Step 5: Calculate Weights

– Step 5: Calculate Weights

• Step 5: Calculate Weights

– Step 5: Calculate Weights

– Step 5: Calculate Weights

• Step 1: Identify Criteria & Measures

• Step 6: Calculate Total Scores

(0.145)(0.475) = (0.145)( 0.875) = (0.145)(0.750) = (0.145)(0.200) =

– Step 6: Calculate Total Scores

Canisius Clark Drexel Suffolk

• Step 1: Identify Criteria & Measures

• Step 7: Analyze Results, Make a Decision

• Step 7: Analyze Results, Make a Decision

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