1. 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 ( M athematics IN struction using D ecision S cience and E ngineering T ools ) CHAPTER 1 Making Hard Decisions— Multi-Criteria Decision Making 1

2. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET 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

3. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET 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

4. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET 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

5. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET 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

6. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET 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

7. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET Step 1: Identify Criteria and Measures To measure these criteria, Isabelle uses the following: How would you measure your criteria? 7 CriteriaMeasures Cost Monthly Service Charge Contract Features Number of Minutes per Month Minimum Contract Length Free Unlimited Texting Included Data Plan Phone Features Quality of Service

8. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET Step 1: Identify Criteria and Measures Isabelle needs to label the measures as either categorical or continuous: Which of the measures are continuous? Which are categorical? 8 CriteriaMeasuresType of Measure Cost Monthly Service Charge Contract Features Number of Minutes per Month Minimum Contract Length Free Unlimited Texting Included Data Plan Phone Features Quality of Service

9. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET Step 2: Collect Data Isabelle collects data for three cell phone plans 9 Plan Monthly Charge Minutes per Month Minimum Contract Length Free Unlimited Texting Included Data Plan Quality of Service Trot $604006 monthsnoyesGood UST&T $755002 yearsyesnoExcellent Horizon $856001 yearyesno Very Good

10. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET Step 3: Find the Range of Each Measure Next she needs the scale ranges for each measure How can we compare this raw data? 10 MeasureScale range Monthly Charge Minutes per Month Minimum Contract Length Free Unlimited Texting Included Data Plan Quality of Service

11. 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 ( M athematics IN struction using D ecision S cience and E ngineering T ools ) 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

12. 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 ( M athematics IN struction using D ecision S cience and E ngineering T ools ) ASSIGN COMMON UNITS FOR EACH: PLANMonthly Charge ($) Minutes per Month Min. Contract Length Free Unlimited Texting Included Data Plan Quality of Service Trot UST&T Horizon 12 Is there an issue with any of the categories?

13. 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 ( M athematics IN struction using D ecision S cience and E ngineering T ools ) 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

14. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET 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

15. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET Step 4: Rescale Each Measure to a Common Unit Isabelle converts the continuous measures using a proportional scale ▪Consider the monthly service charge 15

16. 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 ( M athematics IN struction using D ecision S cience and E ngineering T ools ) ASSIGN COMMON UNITS FOR EACH: PLANMonthly Charge ($) Minutes per Month Min. Contract Length Free Unlimited Texting Included Data Plan Quality of Service Trot101010 UST&T0.40.50101 Horizon010.510 16 Based on this could you decide which cell phone plan is best?

17. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET 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

18. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET 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 18 Measure Monthly Charge ($) Minutes per Month Minimum Contract Length Free Unlimited Texting Included Data Plan Quality of Service Rank146253

19. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET Step 5: Conduct an Interview to Calculate Weights 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 19 Measure Monthly Charge ($) Minutes per Month Minimum Contract Length Free Unlimited Texting Included Data Plan Quality of Service Rank146253 Points1007550906080

20. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET Step 5: Conduct an Interview to Calculate Weights 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 20 Measure Monthly Charge ($) Minutes per Month Minimum Contract Length Free Unlimited Texting Included Data Plan Quality of Service Total Rank146253--- Points1007550906080455 Weight 100/455 = 0.22

21. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET 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 Plan Monthly Charge ($) Minutes per Month Minimum Contract Length Free Unlimited Texting Included Data Plan Quality of Service Total 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

22. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET 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 Plan Monthly Charge ($) Minutes per Month Minimum Contract Length Free Unlimited Texting Included Data Plan Quality of Service Total Trot0.2200.1100.1300.46 UST&T0.0880.0800.2000.180.548 Horizon00.160.0550.2000.090.505

23. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET 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

24. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET 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 24

25. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET 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 25

26. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET Step 6: Calculate Total Scores MeasureRankPointsWeight 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)

27. www.MINDSETproject.org © 2011 North Carolina State University: MINDSET 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