www.mindsetproject.org © 2011 north carolina state university: mindset sponsored by the national...

www.MINDSETproject.org

© 2011 North Carolina State University: MINDSET

Sponsored by the National Science Foundation, Directorate for Education and Human Resources, project DRL-0733137

MINDSET (Mathematics INstruction using Decision Science and Engineering Tools)

CHAPTER 1

Making Hard Decisions—

Multi-Criteria Decision Making

1



Multi-Criteria Decision Making (MCDM)

• A structured method for mathematizing the decision-making process

▪ Used when one needs to make a hard decision with many criteria

• The method presented in this chapter is one form of MCDM

2



Opening Activity: Choosing a New Cell Phone Plan

• Make a list of possible cell phone plans that you would consider using

• What factors or criteria would you consider if you were choosing a cell phone plan?

• Explain why you might choose one plan over another.

3



Opening Activity: Choosing a New Cell Phone Plan

• What possible issues do you foresee with using these steps to choose a cell phone plan?

4



Choosing a New Cell Phone Plan

• We are going to use a more formal method for making large decisions such as choosing a new cell phone plan

• Problem Context:▪ Isabelle Nueva needs to help her mother and

father decide on the best cell phone plan for her family

▪ She and her friend, Angelo Franco, will use the MCDM process to help her parents make this decision

5



Step 1: Identify Criteria and Measures

• The criteria important to Isabelle’s parents are:▪ Cost▪ Contract features▪ Phone features

• What criteria would be important to you?

6




• To measure these criteria, Isabelle uses the following:

• How would you measure your criteria?

7

Criteria MeasuresCost Monthly Service Charge

Contract Features

Number of Minutes per MonthMinimum Contract LengthFree Unlimited TextingIncluded Data Plan

Phone Features Quality of Service




• Isabelle needs to label the measures as either categorical or continuous:

• Which of the measures are continuous? Which are categorical?

8

Criteria Measures Type of MeasureCost Monthly Service Charge

Contract Features

Number of Minutes per MonthMinimum Contract LengthFree Unlimited TextingIncluded Data Plan

Phone Features Quality of Service



Step 2: Collect Data

• Isabelle collects data for three cell phone plans

9

PlanMonthly Charge

Minutes per

Month

Minimum Contract Length

Free Unlimited Texting

Included Data Plan

Quality of Service

Trot $60 400 6 months no yes Good

UST&T $75 500 2 years yes no Excellent

Horizon $85 600 1 year yes noVery Good



Step 3: Find the Range of Each Measure

• Next she needs the scale ranges for each measure

• How can we compare this raw data?

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Measure Scale range Monthly ChargeMinutes per Month


Free Unlimited TextingIncluded Data Plan

Quality of Service




MINDSET (Mathematics INstruction using Decision Science and Engineering Tools)STEP 4: RESCALE EACH MEASURE

TO A COMMON UNIT

- Isabelle needs to convert the range of each measure to a Common Unit.

- A Value between 0 – 1

Worst value?

Best value?

How should these values be assigned to the data?

11





ASSIGN COMMON UNITS FOR EACH:

PLAN Monthly Charge ($)

Minutes per Month

Min. Contract Length


Included Data Plan

Quality of Service

Trot

UST&T

Horizon

12

Is there an issue with any of the categories?





What about the $75?-Is $75 closer to the worst or the best option?- How far is $75 to the worst option? To the best option?- What do you think the $75 could be converted to?

13

Monthly Charge ($)

60

75

85



Step 4: Rescale Each Measure to a Common Unit• Isabelle converts continuous measures using a

proportional scale▪ Consider the monthly service charge

14

1

$85

0

$60$75

x



Step 4: Rescale Each Measure to a Common Unit

• Isabelle converts the continuous measures using a proportional scale

▪ Consider the monthly service charge

15

75 85 0

60 85 1 0

10

25 1

0.4

x

x

x





ASSIGN COMMON UNITS FOR EACH:

PLAN Monthly Charge ($)

Minutes per Month

Min. Contract Length


Included Data Plan

Quality of Service

Trot 1 0 1 0 1 0

UST&T 0.4 0.5 0 1 0 1

Horizon 0 1 0.5 1 0 0.5

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Based on this could you decide which cell phone plan is best?



Step 4: Rescale Each Measure to a Common Unit

▪ How did you make this decision?

• Which plan do you think Isabelle should recommend to her parents? Why?

▪ What are some reasons why you wouldn’t want to make a decision based on the common unit values alone?

17



Step 5: Conduct an Interview to Calculate Weights

• Isabelle and Angelo interview Isabelle’s parents to determine their preferences

• They begin by rank-ordering the measures, where 1 is most important

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MeasureMonthly Charge

($)

Minutes per

Month



Included Data Plan

Quality of

Service

Rank 1 4 6 2 5 3




• Isabelle and Angelo ask Mr. and Mrs. Nueva to assign 100 points to the measure they ranked #1

• Then, they ask them to assign a number of points less than 100 to the measure they ranked #2

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($)

Minutes per

Month



Included Data Plan

Quality of

Service

Rank 1 4 6 2 5 3

Points 100 75 50 90 60 80




• Next, Isabelle and Angelo total all of the assigned points and obtain 455.

• Then, they divide the point assignment for each measure by that total; this number is the weight of that measure

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($)

Minutes per

Month



Included Data Plan

Quality of

ServiceTotal

Rank 1 4 6 2 5 3 ---

Points 100 75 50 90 60 80 455

Weight100/455 = 0.22



Step 6: Calculate Total Scores

• The total score is an example of a weighted average

• They multiply each common unit value by the corresponding weight. Then for each plan, they add those six products together to get the total score

21

PlanMonthly Charge

($)

Minutes per

Month



Included Data Plan

Quality of

ServiceTotal

Trot(0.22)(1)= 0.22

(0.16)(0) = 0

(0.11)(1)= 0.11

(0.20)(0) = 0

(0.13)(1)= 0.13

(0.18)(0) = 0

UST&T

Horizon



Step 7: Interpret Results

• Why may UST&T not be the obvious choice?• For which measures does UST&T have a higher

weighted score than Horizon? For which does Horizon outscore UST&T?

• What are the ranks of the measures where UST&T scored higher than Horizon? What are the ranks for the measures where Horizon was higher?

22

PlanMonthly Charge

($)

Minutes per

Month



Included Data Plan

Quality of

ServiceTotal

Trot 0.22 0 0.11 0 0.13 0 0.46

UST&T 0.088 0.08 0 0.20 0 0.18 0.548

Horizon 0 0.16 0.055 0.20 0 0.09 0.505



Summary of MCDM Steps

1) Identify Criteria and Measures

2) Collect Data

3) Find the Range of Each Measure

4) Rescale Each Measure to a Common Unit

23



Summary of MCDM Steps

5) Conduct an Interview to Calculate Weights

a) Rank-order the measures

b) Assign points from 0 to 100 to each measure

c) Calculate a proportional weight between 0 and 1 for each measure

6) Calculate a Total Score for Each Alternative

a) Multiply each common unit value by the corresponding weight

b) For each plan, add those products together to get the total score

7) Interpret Results

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On Your own Try:

▪ Rank-order the measures, where 1 is most important to YOU

▪ Assign 100 points to the measure ranked #1, a number less than 100 to the measure ranked #2, etc.

▪ Total all of the assigned points ▪ Find the weight of each measure▪ Compute the total score for your plan

Weight x Common Unit then Total

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Step 6: Calculate Total Scores

Measure Rank Points Weight TROT UST&T HORIZON

Monthly Charge

Minutes/ Month

Min. Contract length

Free texting

Free Data

Service Quality

TOTAL:

26

You will need the CU’s (Step 4 from Handout)



Chapter 1 Objectives

• Identify and interpret the steps required to employ Multi-Criteria Decision Making

• Use MCDM to make a decision• Analyze and interpret results

27

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