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Analytical hierarchy process
- 1. © 2014 IHS Information| Analytics | Expertise ANALYTICAL HIERARCHY PROCESS (AHP) JULY 2014 MN Wasif Defence Reference Researcher C4ISR & Mission Systems
- 2. © 2014 IHS AHPprinciples WHAT IS AHP ? IT IS A TECHNIQUE USED FOR MCDM TO ARRIVE AT THE BEST POSSIBLE DECISION WHAT IS MCDM ? MCDM STANDS FOR MULTI-CRITERIA DECISION MAKING WHERE IS IT USED? USED WHERE COMPLEX DECISION MAKING FOR WHICH SIMPLE FACTORS (SUCH AS COST) ARE TO BE SET ASIDE UNTIL THE BENEFIT OF THE ALTERNATIVES ARE EVALUATED
- 3. © 2014 IHS3 BRIEF HISTORY • DEVELOPED BY THOMAS L SAATY IN THE EARLY 1970’S • HAS BEEN USED TO ASSIST GOVERNMENT AND CORPORATE DECISION MAKING BODIES E.G., • Deciding how best to reduce the impact of global climate change (Fondazione Eni Enrico Mattei) • Quantifying the overall quality of software systems (Microsoft Corporation) • Selecting university faculty (Bloomsburg University of Pennsylvania) • Deciding where to locate offshore manufacturing plants (University of Cambridge) • Assessing risk in operating cross-country petroleum pipelines (American Society of Civil Engineers) • Deciding how best to manage U.S. watersheds (U.S. Department of Agriculture)
- 4. © 2014 IHS4 PROCESS • INFORMATION IS DECOMPOSED INTO A HIERARCHY OF CRITERIA AND ALTERNATIVES • THE INFORMATION IS THEN SYNTHESISED TO DETERMINE THE RELATIVE RANKING OF ALTERNATIVES • QUALITATIVE AND QUANTITATIVE CRITERIA CAN BE COMPARED USING INFORMED JUDGEMENT TO DERIVE WEIGHTAGE AND PRIORITIES TO THE ALTERNATIVES
- 5. © 2014 IHS5 EXAMPLE – SELECTING A FIGHTER AIRCRAFT • STATE THE OBJECTIVE - SELECT A FIGHTER AIRCRAFT • DEFINE THE CRITERIA - TECHNICAL SPECIFICATIONS OF EACH FIGHTER - SPEED RANGE AND THRUST • PICK THE ALTERNATIVES - Rafale Typhoon JAS-39 Gripen MiG-35
- 6. © 2014 IHS ARRANGINGTHE INFORMATION IN A HIERARCHICAL TREE SELECT A FIGHTER AIRCRAFT SPEED Rafale Typhoon JAS-39 Gripen MiG-35 RANGE Rafale Typhoon JAS-39 Gripen MiG-35 THRUST Rafale Typhoon JAS-39 Gripen MiG-35
- 7. © 2014 IHS USINGPAIRWISE COMPARISIONS THE RELATIVE IMPORTANCE OF ONE CRITERION VIS-À-VIS ANOTHER CAN BE EXPRESSED SPEED RANGE THRUST SPEED 1/1 1/2 3/1 RANGE 2/1 1/1 4/1 THRUST 1/3 1/4 1/1 1- EQUAL 3-MODERATE 5-STRONG 7-VERY STRONG 9-EXTREME
- 8. © 2014 IHS EIGENVECTORSOLUTION • MATHEMATICALLY AS DEMONSTRATED BY DR THOMAS L SAATY THE EIGENVECTOR SOLUTION IS THE BEST APPROACH • SQUARE THE PAIRWISE MATRIX SUCCESIVELY • CALCULATE AND NORMALISE THE ROW SUMS • STOP WHEN THE DIFFERENCE BETWEEN SUMS IN TWO SUCCESIVE CALCULATIONS GOES BELOW A THRESHOLD LEVEL (SAY 0.01)
- 9. © 2014 IHS STEP1. SQUARING THE MATRIX WE OBTAINED FOR OUR EXAMPLE WE GET :-
- 10. © 2014 IHS STEP2. COMPUTING OUR FIRST EIGENVECTOR
- 11. © 2014 IHS EIGENVECTORITERATION NO.2:
- 12. © 2014 IHS COMPUTINGTHE 2ND EIGENVECTOR AND MINUSING FROM THE 1ST :
- 13. © 2014 IHS OBTAININGNORMALIZED VALUE FOR EACH CRITERIA, LETS SAY THRUST: THRUST NORMALISED THRUST RAFALE 34 34/113 = 0.3010 TYPHOON 27 27/113 = 0.2390 JAS-39 GRIPEN 24 24/113 = 0.2120 MIG-35 28 28/113 = 0.2480 TOTAL 113 1.0000 NORMALIZING THE THRUST ALLOWS US TO USE IT WITH OTHER RANKINGS
- 14. © 2014 IHS FINDINGTHE SOLUTION USING MATRIX ALGEBRA SPEED RANGE THRUST CRITERIA RANKING RAFALE 0.1160 0.3790 0.3010 0.3196 SPEED TYPHOON 0.2470 0.2900 0.2390 X 0.5584 RANGE JAS-39 GRIPEN 0.0600 0.0740 0.2120 0.1220 THRUST MIG-35 0.5770 0.2570 0.2480 II.E. FOR THE RAFALE (.1160X.3196)+(.379X.5584)+(.3010X.1220) = 0.3060 RAFALE 0.3060 TYPHOON 0.2720 JAS-39 GRIPEN 0.0940 MIG-35 0.3280 AND THE WINNER IS….. MIG-35 IS THE HIGHEST RANKED FIGHTER
- 15. © 2014 IHS FACTORINGIN THE COST……. • IN COMPLEX DECISIONS COSTS SHOULD BE SET ASIDE UNTIL TECHNICAL BENEFITS OF EACH ALTERNATIVE IS EVALUATED • DISCUSSING COSTS WITH BENEFITS/PERFORMANCE CAN BRING FORTH MANY POLITICAL/EMOTIONAL RESPONSES
- 16. © 2014 IHS HOWTO BALANCE BENEFITS VS COST 1. GRAPHICALLY PLOTTING THE BENEFITS VS COST OF EACH ALTERNATIVE 2. CALCULATING BENEFITS VS COST RATIO (AFTER NORMALISING COST) 3. LINEAR PROGRAMMING 4. SEPARATE COST AND BENEFIT HIERARCHICAL TREES AND THEN COMBINE THE RESULTS
- 17. © 2014 IHS EXAMPLE:USING BENEFIT TO COST RATIOS COST ($ MILLIONS) NORMALIZED COST BENEFIT-COST RATIO MIG-35 18 0.3333 0.3280/0.3333 = 0.9840 RAFALE 12 0.2222 0.3060/0/2222 = 1.3771 TYPHOON 15 0.2778 0.2720/0.2778 = 0.9791 JAS-39 GRIPEN 9 0.1667 0.940/0.1667 = 0.5639 54 AND…… THE RAFALE IS THE WINNER WITH THE HIGHEST BENEFIT TO COST RATIO!
- 18. © 2014 IHS SOMEAPPLICATIONS OF AHP • STRATEGIC PLANNING • RESOURCE ALLOCATION • SOURCE SELECTION • BUSINESS/GOVERNMENT POLICY • PROGRAM SELECTION • TECHNICAL BIDS EVALUATION • BENCHMARKING • QUALITY MANAGEMENT • CONFLICT RESOLUTION
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