Peter Baxter, DISTRIBUTIVE MANAGEMENT Hampton Roads INCOSE Decision Analysis Conference - Nov 2009 U SING M EASUREMENT AND THE S AATY M ETHOD TO C HOOSE THE B EST D ECISION A LTERNATIVE

O BJECTIVES 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 2

W HAT IS THE AHP/S AATY M ETHOD ?

S IMPLE D EFINITION Compute the matrix values for a and … voila! The Analytic Hierarchy Process (AHP) DISTRIBUTIVE MANAGEMENT 4

C OMPARE THE S IZES OF THESE C IRCLES ABCDE ABCDE A17953 B1/7131/51/7 C1/91/311/71/9 D1/55711/3 E 7931 DISTRIBUTIVE MANAGEMENT 5

S CALE OF C OMPARISON  Don’t need an absolute scale (if you already know the size of all but one)  Relative scale approximates difference DISTRIBUTIVE MANAGEMENT 6

S IMPLE E XPERIMENT One test is worth 1000 expert opinions DISTRIBUTIVE MANAGEMENT 7

W EBER ’ S E XPERIMENT 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 8

W HY I T W ORKS  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 9

A PPLYING T HE T ECHNIQUE 1. Select criteria(s) to evaluate 2. Define comparison scale 3. Perform pair-wise comparison 4. Check consistency 5. Calculate values DISTRIBUTIVE MANAGEMENT 10

A PPLYING THE METHOD

E XAMPLE #1 S OFTWARE E STIMATION  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: 1. Guess a number. 2. Compare to one reference structure using numeric scale. 3. Compare to one reference structure using relative scale.  Plot results From “Establishing Software Size Using Pair-wise Comparison Method” by Eduardo Miranda DISTRIBUTIVE MANAGEMENT 12

E XAMPLE #1 S OFTWARE E STIMATION DISTRIBUTIVE MANAGEMENT 13

E XAMPLE #1 O BSERVATIONS 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 14

E XAMPLE #2 S YSTEM R EQUIREMENTS  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 15

E XAMPLE #2 A PPROACH Approach 1. Review requirements for completeness. 2. Apply pair-wise comparison for value. 3. Apply pair-wise comparison for implementation cost. 4. Calculate AHP matrix and diagram for value & cost. 5. Use resulting diagram for analyzing requirements. DISTRIBUTIVE MANAGEMENT 16

E XAMPLE #2 C OMPARISON S CALE DISTRIBUTIVE MANAGEMENT 17

E XAMPLE #2 C OMPARISON Compare one attribute of each requirement to another requirement using a relative scale. #1 is same as #1 #1 is greater than #2 #2 is much less than #8 DISTRIBUTIVE MANAGEMENT 18

A BOUT C ONSISTENCY  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 19

E XAMPLE #2 C OMPARISON S UMMARY DISTRIBUTIVE MANAGEMENT 20

E XAMPLE #2 F INDINGS 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 21

O THER E XAMPLES 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 22

M EASUREMENT AND AHP

Goal is for Measurement to support AHP estimation EstimatePlan Monitor & Control Capitalize Measurement Process Use AHP DISTRIBUTIVE MANAGEMENT 24

T YPICAL M EASUREMENT P ROCESS Evaluate Establish Capability Technical and Management Processes INFORMATION NEEDS ANALYSIS RESULTS ANALYSIS RESULTS AND PERFORMANCE MEASURES IMPROVEMENT ACTIONS Measurement Process USER FEEDBACK PlanPerform Core Measurement Process Experience Base MEAS- UREMENT PLAN 25

W HAT T O M EASURE ? 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 26

C OMMON P ROJECT M EASURES  Cost  Staffing, Staff Hours  Functional / Requirements Size  SLOC  Defects EstimationProject/ProgramStore Factors estimated using AHP DISTRIBUTIVE MANAGEMENT 27 Usually there is opportunity for measurement to support AHP since there is overlap between what is estimated and what is measured

M EASUREMENT G UIDE 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 28

AHP IN USE Estimate total staff hours in person years using data from five completed projects sharing similar attributes. DISTRIBUTIVE MANAGEMENT 29

R ESOURCES “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 30

Q UESTIONS DISTRIBUTIVE MANAGEMENT 31

Peter Baxter Distributive Management m DISTRIBUTIVE MANAGEMENT 32