Using Measurement and the Saaty Method to Choose the Best Decision Alternative

1. Using Measurement and the Saaty Method to Choose the Best Decision Alternative Peter Baxter, DISTRIBUTIVE MANAGEMENT Hampton Roads INCOSE Decision Analysis Conference - Nov 2009

2. Objectives Learn: • How to construct and weight evaluation criteria. • How to make pair-wise comparisons of alternatives. • How to expand the example for more complex, nested types of criteria. • How a measurement process can support the Saaty method. distributive management

3. What is the AHP/Saaty Method?

4. Simple Definition The Analytic Hierarchy Process (AHP) Compute the matrix values for a and … voila! distributive management

5. Compare the Sizes of these Circles A B C D E distributive management

6. Scale of Comparison Don’t need an absolute scale (if you already know the size of all but one) Relative scale approximates difference distributive management

7. Simple Experiment One test is worth 1000 expert opinions distributive management

8. Weber’s Experiment In 1846 Weber found, for example, that people while holding in their hand different weights, could distinguish between a weight of 20 g and a weight of 21 g, but could not if the second weight is only 20.5 g. On the other hand, while they could not distinguish between 40 g and 41 g, they could between 40 g and 42 g, and so on at higher levels. We need to increase a stimulus s by a minimum amount Δs to reach a point where our senses can first discriminate between s and s+Δs. Δs is called the just noticeable difference (jnd). The ratio r = Δs/s does not depend on s. Weber’s law states that change in sensation is noticed when the stimulus is increased by a constant percentage of the stimulus itself. This law holds in ranges where Δs is small when compared with s, and hence in practice it fails to hold when s is either too small or too large. distributive management

9. Why It Works • People are inconsistent at providing an absolute scale to evaluate objects. How much does Rock A weigh? How much does Rock B weigh? • There are better at comparing pairs of objects. Does Rock A weigh more than Rock B? distributive management

10. Applying The Technique Select criteria(s) to evaluate Define comparison scale Perform pair-wise comparison Check consistency Calculate values distributive management

11. Applying the method

12. Example #1Software Estimation • A controlled test where existing software sizes are known. • Ask 30 grad students to estimate the SLOC of common data structures like stack, queue, list. • Estimate SLOC three ways: • Guess a number. • Compare to one reference structure using numeric scale. • Compare to one reference structure using relative scale. • Plot results From “Establishing Software Size Using Pair-wise Comparison Method” by Eduardo Miranda distributive management

13. Example #1 Software Estimation distributive management

14. Example #1 Observations Miranda’s Observations The high variability of the “finger in the wind approach”, which is almost two to three times bigger than the corresponding paired comparisons method. The high correlation, r = .979, existing between the relative sizes of modules independent of the estimation method employed. This seems to corroborate the premise that the human mind is better at establishing differences than at guessing absolute values. distributive management

15. Example #2 System Requirements From an SEI study “Requirements Prioritization Case Study Using AHP” by Nancy Mead. Given nine security requirements, decide which one(s) have greatest cost-benefit. Benefits “By using AHP, the requirements engineer can also confirm the consistency of the result. AHP can prevent subjective judgment errors and increase the likelihood that the results are reliable.” distributive management

16. Example #2 Approach Approach Review requirements for completeness. Apply pair-wise comparison for value. Apply pair-wise comparison for implementation cost. Calculate AHP matrix and diagram for value & cost. Use resulting diagram for analyzing requirements. distributive management

17. Example #2 Comparison Scale distributive management

18. Example #2 Comparison #1 is same as #1 #1 is greater than #2 #2 is much less than #8 Compare one attribute of each requirement to another requirement using a relative scale. distributive management

19. About Consistency If: A > B > C Then: C > A is wrong AHP contains a technique to calculate the extent of pair-wise consistency, which can then be compared to a consistency tolerance. AHP can also indicate which pair-wise comparison (like the one above) is inconsistent. distributive management

20. Example #2 Comparison Summary distributive management

21. Example #2 Findings Client feedback It may be beneficial to see the consistency matrix. Understand weight of cost and value. Difficult to understand the motivation of each reviewer. distributive management

22. Other Examples From Saaty: • Evaluate the best city in China for Disney to build a new theme park. • Determine optimum foreign relations policy for dealing with Iran. • Estimate market share of “super” retail stores. • Selecting a school. distributive management

23. Measurement and AHP

24. Measurement and AHP Use AHP Measurement Process Goal is for Measurement to support AHP estimation distributive management

25. Typical Measurement Process USER FEEDBACK Technical and Management Processes ANALYSIS RESULTS INFORMATION NEEDS Core Measurement Process Establish Capability Plan Perform MEAS- UREMENT PLAN Experience Base ANALYSIS RESULTS AND PERFORMANCE MEASURES IMPROVEMENT ACTIONS Evaluate Measurement Process

26. What To Measure? Measurement “Requirements” = information needs • Based on your business needs.(not a pre-defined list) • Information needs are: • “Input” to the measurement process. • Provided by the management and technical process that need information to perform their jobs. • Become the requirements for measurement process. • Refined into measures and then resulting information products are provided to the “users”. distributive management

27. Common Project Measures Factors estimated using AHP Usually there is opportunity for measurement to support AHP since there is overlap between what is estimated and what is measured Cost Staffing , Staff Hours Functional / Requirements Size SLOC Defects distributive management

28. Measurement Guide AHP • Measurement contains project attributes: • Lifecycle model • Principle architecture • Application domain • AHP estimation of projects with similar attributes. • Reference sizes should not differ by more than an order of magnitude. distributive management

29. AHP in use Estimate total staff hours in person years using data from five completed projects sharing similar attributes. distributive management

30. Resources “Requirements Prioritization Case Study Using AHP” by Nancy Mead Software Engineering Institute “Establishing Software Size Using the Paired Comparisons Method” by Eduardo Miranda “Relative Measurement and Its Generalization in Decision Making Why Pairwise Comparisons are Central in Mathematics for the Measurement of Intangible Factors The Analytic Hierarchy/Network Process” by Thomas Saaty distributive management

31. Questions distributive management

32. Peter Baxter Distributive Management www.distributive.com pbaxter@distributive.com distributive management