1. This Briefing is: UNCLASSIFIED Aha! Analytics 2278 Baldwin Drive Phone: (937) 477-2983, FAX: (866) 450-3812 1 An Overview of the Analytic Hierarchy Process (AHP) April 2011 Dave Lush, SME Aha! Analytics

2. UNCLASSIFIED 2 Topics  Background  Objectives  Proposed Approach: Analytic Hierarchy Process (AHP)  Overview of the AHP Method  Key Concepts  The Steps in the Process  Example Application of AHP  Conclusions

3. UNCLASSIFIED 3 Background  Prioritization Problems Abound!  No Common, Standard, Repeatable Approach  Standard Repeatable Approaches Exist and Are Widely Used in Real World  One of the Most Prevalent Methods Is the Analytic Hierarch Process (AHP)

4. UNCLASSIFIED 4 The Core Objectives  Acquire, Deploy a Framework and Methodology for the Weighting or “Valuation” of a Set of Alternatives in the Context of Multiple Criteria  Acquire an Understanding of AHP and Make a Decision As to Whether or Not to Deploy

5. UNCLASSIFIED 5 Proposed Approach: Analytic Hierarchy Process (AHP)  The Most Prevalent Multi-criteria Decision Technique in Real World  Developed by Dr. Thomas Saaty (Currently a Faculty Member at Carnegie Melon University CMU)  AHP Is Automated by Readily Available and Affordable COTS e.g. Expert Choice

6. UNCLASSIFIED 6 Overview of AHP Key Concepts/Process  Decision Problem Is Modeled in Context of a Hierarchy of Goal Criteria, and Alternatives/Actions  The Ultimate Outcome Is the Valuation or Weighting of the Alternatives/Actions in Context of the Goal and Criteria Above  Criteria and Alternatives Can Have Sub Levels So As to Manage Situations Which Have Many Criteria and Many Alternatives  The Valuation or Weighting Is Based on Capturing Quantified Pair-wise Preferences Between Elements at One Level of the Hierarchy in Context of the Parent Elements in the Level Above  The Items at Any Given Level Are Grouped According to Commonality of Parent Element in the Hierarchy  i.e. Elements Are in the Same Group If They have the Same Parent Element

7. UNCLASSIFIED 7 Overview of AHP Key Concepts/Process  The Items in Each Group Are Weighted or Valuated Via a Process Based on Quantifying Pair-wise Preferences of the Elements in the Group  Pair-wise Preference Values a ij Are Captured in a Matrix and Assigned As Follows:  If ith element is extremely preferable to the jth, then a ij =9  If ith element is strongly preferable to the jth, then a ij =7  If ith element is preferable to the jth, then a ij =5  If ith element is slightly preferable to the jth, then a ij =3  If ith element is equally preferable to the jth, then a ij =1  The Preference Matrix Is Constrained to Be “Reciprocal”  i.e. if the i-j th element is a ij then the j-i th element is 1/a ij

8. UNCLASSIFIED 8 Overview of AHP Key Concepts/Process  The Preference Matrices Are Viewed As Estimates of a So Called Value Ratio Matrix Which Is Composed of the Pair-wise Ratios of the Actual But Unknown Weights or Values Associated with Each Element in the Group Being Valuated.  The Normalized Principle Eigenvector of the Reciprocal Matrix Is An Estimate of the Vector of Weights or Valuations for the Elements in the Group Being Weighted or Valuated  The Eigenvector Components (the element weights) Can Be Estimated by Summing the Rows of the Preference Matrices and Normalizing  The Weights So Determined Are “Local” Weights in Context of the Superior Parent Element Which Has Already Been Given a Weight Via This Overall Process

9. UNCLASSIFIED 9 Overview of AHP Key Concepts/Process  The Weights Determined for Each Group in a Given Row Are Then “Globalized” by Multiplying by the Weight of Its Parent Element Which Has Been Previously Determined  So, Conducting This Process in a Top Down Fashion Results in a Set of Weights for the Alternatives Which Have Been Determined in the Context of the Weights Previously Given to Criteria That Set the Context for the Alternatives

10. UNCLASSIFIED 10 The Hierarchy Goal G Criteria C 1 C 2 … C M-1 C M Alternatives A 1 A 2 A K-1 A K

11. UNCLASSIFIED 11 Example Preference Matrix The parent element C3 has already been assigned weight =.6 The i th row contains the preference of the i th element over the other elements. An estimate of the local element weights is obtained by summing up the rows and normalizing. The global weights are given by multiply local weights by weight of parent element C3

12. UNCLASSIFIED 12 A Notional Example Givens  We Have a Goal: To Arrive at a “Valuation” or “Weighting” of the Analysis/Production Portfolio  Let’s Say We Have the Following Criteria:  C 1 : Impact on National Security  C 2 : National Level Sponsorship/Guidance  C 3 : Customer Importance  Let’s Say We Have 4 Top Level Alternatives:  A 1 : Data Processing, Exploitation, Dissemination  A 2 : Aero Related System Analysis/Production  A 3 : Space/Missile Related System Analysis/Production  A 4 : Force Capabilities Related Analysis/Production

13. UNCLASSIFIED 13 Weighting the Criteria

14. UNCLASSIFIED 14 Valuating the Items (in context of C1)

15. UNCLASSIFIED 15 Weighting the Items (in context of C2)

16. UNCLASSIFIED 16 Valuating the Items (in context of C3)

17. UNCLASSIFIED 17 The Final Valuation Calculate Final Valuations As Average of Element Values Across All Valuators

18. UNCLASSIFIED 18 Questions? ???

19. UNCLASSIFIED 19