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Week 11

“Decision Making

Methods 3”

Dr Ramesh Vahidi [email protected]

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Southampton Business School

12th May 22

Aims of week 11: Let’s Decide or Find Resolutions

• Introducing the most used Multiple Criteria

Decision Making Method, its applications,

process, potential advantages and disadvantages.

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PART 1

Background to the AHP

method

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Southampton Business School

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“Problem Formulation,

Decision Making/Analysis

Method based on:

The Analytic Hierarchy Process (AHP)

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Southampton Business School

What is AHP?

✓ An MCDM developed in 1970s by Prof Thomas Saaty.

✓ Based on mathematics and psychology of DM.

✓ Most used DM method with unlimited applications.

✓ Facilitates problem structuring (modelling) and making

complex decisions.

✓ Based on pairwise comparisons.

✓ NASA, HP, IBM, KPMG, Ford, Shell, governments, …

✓ Well supported by software.

✓ Widely studied, developed … still room in PM.

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http://www.youtube.com/watch?v=vC9Aeu06wjA

PART 2

Problem structuring and

AHP Process

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Southampton Business School

Overview of AHP: Problem Formulation

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AHP: Problem/Decision Formulation (Structure)

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Goal / Objective

Criterion 1 Criterion 2 Criterion 3 Criterion N

Alternative 1 Alternative 2 … Alternative N

Both terms ‘Criteria’ or ‘Attribute’ might be used in AHP. Both terms ‘Alternative’ or ‘Option’ might be used in AHP.

Extension of the Hierarchy

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You Might also have different sub-Objectives or sub-Goals before the

criteria layer

Example – Hierarchy for Decision on Buying a Car

MANG6312©RameshVahidi2022 AHP

Buying a Car

Style Reliability Fuel Consumption

Civic Saturn Escort

AHP Steps (Stages)

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Step 1: Set up the decision Hierarchy.

Step 2: Make pairwise comparisons of criteria (attributes) and alternatives.

Step 3: Transform the comparisons into weights.

Step 4: Use the weights to obtain scores for the different options and make a decision.

Step 5: Perform sensitivity analysis. (Goodwin and Wright, 2014, pp.76-80)

PART 3-1

An example of DM with

AHP

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Southampton Business School

AHP Example

Buying a Car

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Step 1 – Build the Hierarchy

MANG6312©RameshVahidi2022 AHP

Buying a Car

Style Reliability Fuel Consumption

Civic Saturn Escort

Step 1 – Build the Hierarchy

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Buying a Car

For the next lecture, let’s decide about the car (or something else) you would like

to buy after your first few handsome monthly salaries!

Let’s Model your decision:

1) What is your goal? (be as specific as you could) → Add this to the model!

2) List your criteria for this purchase. Select the 3 main criteria (for the purposes of this exercise)? → Add these to the model.

3) List your options. Select the 3 most desired/possible options (for the purposes of this exercise)? → Add these to the model!

Try modelling a decision yourself!

Step 2 – Pairwise Comparison

Make tables like these for your decision and bring to the next lecture

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Step 2 – Pairwise Comparisons

We need to know/ask for the

priorities through comparing them

in pairs, i.e. finding out:

• The relative importance of the

criteria for achieving the goal;

• The relative importance/merit

of the alternatives (options) in

terms of or in relation to each

criteria. MANG6312©RameshVahidi2022 19

Step 2 – Pairwise Comparison

Compare the importance of the criteria against each other

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AHP Part 1

https://www.youtube.com/watch?v=ht0Wm3 3xEno

WATCH this video and see how far you could go with completing the scoring tables!

Example of AHP Steps

https://www.youtube.com/watch?v=ht0Wm33xEno

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Can You Compare ‘Apples’ and ‘Oranges’?

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Intensity of

Importance Definition Explanation

1 Equal Importance Two activities contribute equally to the

objectives

3 Moderate Importance Experience and judgement slightly favour one

activity over another

5 Strong Importance Experience and judgement strongly favour one

activity over another

Very strong Importance An activity is favoured very strongly over

another; its dominance demonstrated in

practice

Extreme Importance The evidence favouring one activity over

another is of the highest possible order of

affirmation

2, 4, 6, 8 Intermediate values

Step 2 – Basis for Pairwise Comparisons

Step 2 – Pairwise Comparison - Criteria

Compare the importance of the criteria against each other

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Implementation Method: asking relevant decision

makers about their preferences.

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Step 2 – Pairwise Comparison - Alternatives

Comparing Alternatives against each Criteria

Implementation Method: asking relevant decision

makers about their preferences.

Step 3 - Synthesis : Prioritizing Criteria & Alts

The process of calculating the priority of each criterion in terms of

its contribution to the overall goal:

1) Sum values in each column of pairwise comparison matrix

2) Divide each element by its column total (gives normalized

pairwise comparison matrix)

3) Compute average of elements in each row (gives estimate of

relative priorities of elements being compared)

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Step 3 – Prioritize Criteria

1) Sum values in each column

2) Divide each element

by its column total

(gives normalized

pairwise comparison

matrix)

Priorities of criteria

Step 3 – Prioritize Alts in terms of Style

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Alternatives Civic Saturn Escort

Civic 1 4 1/3

Saturn ¼ 1 1/7

Escort 3 7 1

SUM 4.25 12 1.47

STYLE

Step 3 – Prioritize Alts in terms of Reliability

Reliability

Alt.s Civic Saturn Escort

Civic 1 1/6 1

Saturn 6 1 6

Escort 1 1/6 1

SUM 8 8/6 8

Alt.s Civic Saturn Escort Avg.

Civic .125 .125 .125 .125

Saturn .75 .75 .75 .75

Escort .125 .125 .125 .125

Reliability

Step 3 - Prioritize Alts in terms of Fuel Cons.

Alt.s Civic Saturn Escort Avg.

Civic .755 .790 .667 .737

Saturn .151 .158 .25 .186

Escort .094 .053 .083 .077

Fuel Consumption

Criteria Style

.701

Reliability

.100

Fuel Cons.

.197 Final Priority

Civic .266 .125 .737 0.344

Saturn .080 .75 .186 0.168

Escort .654 .125 .077 0.486

Example:

Civic: .701 x .266 + .100 x .125 + .197 x .737 = .0344

Step 4 - Prioritize Alts based on their Total Scores

AHP Part 1

https://www.youtube.com/watch?v=ht0Wm3 3xEno

WATCH now if you had not done it already! Example of AHP Steps

https://www.youtube.com/watch?v=ht0Wm33xEno

PART 4

Concluding remarks

Southampton Business School

Review of the AHP Approach to DM

“When we think, we identify objects or ideas and

also relations among them. When we identify

anything, we decompose the complexity which

we encounter. When we discover the relations,

we synthesize. This is the fundamental process

underlying perception: decomposition and

synthesis.”

(Saaty, 1988, p.3)

Further Remarks …

• Consistency →

- A is 2 times preferred to B, B is 3 times preferred to C ➔ A should be 6 times preferred to C

- Higher than a percentage not accepted (→ perhaps random comparisons)

• Sensitivity analysis →

- How the final results will change with the change of comparisons

- Aided with software

• AHP in group DM →

- Comparisons discussed (our previous discussions re group DM applies)

- Average of comparisons (matter of extensive research)

AHP Advantages

• Structured approach: Clarity in problem formulation,

analysis process, documentation, tracing back and tracking

the DM Process;

• Multiple objectives: Possibility of considering and dealing

with conflicting objectives;

• Facilitates group DM: Different decision makers can

share their ideas and easily get involved in the procedure;

AHP Advantages

• No limitation for Criteria: Both tangible and

intangible criteria;

• No limitation for Measures: Both qualitative and

quantitative measures;

• Ease of application: No need for DM to know the

complex math (just sum and average of course!) use

Readings

Saaty, T. (2008) ‘Decision making with the analytic hierarchy process’. Int. J. Services Sciences, 1(1). pp. 83-98. (http://www.rafikulislam.com/uploads/resourses/197245512559a37aadea6d.pdf)

Vaidya, O.S. & Kumar, S. (2006) ‘Analytic Hierarchy Process: An overview of applications’, European Journal of Operational Research, 169, pp.1-29.

von Solms, SH (2011) ‘Validity of the AHP/ANP: Comparing Apples and Oranges’. International Journal of the Analytic Hierarchy Process, 3(1), pp. 2-27.

W. Saaty, R. (2007) ‘Validating the Analytic Hierarchy/Network Processes’. ISAHP- International Symposium on the Analytic hierarchy process. Viña del Mar, Chile, August 3-8, pp.1-27.

Zahedi, F. (1986) ‘The Analytic Hierarchy Process - A Survey of the Method and its Applications’. Interfaces, 16 (4), pp. 96-108.

http://www.rafikulislam.com/uploads/resourses/197245512559a37aadea6d.pdf

Readings Al-Harbi , K.M.A. (2001) ‘Application of the AHP in project management’, International Journal of Project Management, 19 (2001), pp.19-27.

Goodwin, P. & Wright, G. (2014) Decision analysis for management judgement. 5th edn. West Essex: John Wiley & Sons. (for AHP and other models)

Ho, W. (2008) ‘Integrated analytic hierarchy process and its applications - A literature review’, European Journal of Operational Research,186, pp.211–228.

Ishizaka, A. & Labib, A. (2009) ‘Analytic Hierarchy Process and Expert Choice - Benefits and Limitations’, OR Insight, 22(4), pp. 201–220.