Introduction. Analytical Hierarchy Process. Why AHP? 10/31/2011. The AHP is based on three principles: Decomposition of the decision problem

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1 Introduction A multi-criteria decision making process. Analytical Hierarchy Process The analytical hierarchy process (AHP) is a comprehensive, logical and structured framework. 56:134 Process Engineering Allows to improve understanding of complex decisions by decomposing the problem. Why AHP? The AHP is based on three principles: Imitates the way human think about the decision making. Simplified structure of a decision process. Both quantitative and qualitative attributes/criteria can be used. Consistency in the judgment can be checked. Simple and easy to use decision making tool. The pair-wise comparison allows the decision maker to determine the trade-offs among criteria. Decomposition of the decision problem Comparative judgment of the elements Synthesis of the priorities 1

2 Step 1 Structure the decision problem in a hierarchy Step 2 Comparison of the alternatives based on the criteria Intensity of Importance 1 Equal Importance Definition 3 Moderate Importance 5 Strong Importance 7 Very Strong Importance 9 Extreme Importance 2, 4, 6, 8 For compromises between the above Reciprocals of above In comparing elements i and j - if i is 3 compared to j - then j is 1/3 compared to i Step 3 Synthesize the comparisons to get the priorities of the alternatives with respect to each criterion and the weights of each criterion with respect to the goal Local priorities are then multiplied by the weights of the respective criterion The results are summed up to produce the overall priority of each alternative An illustrative example (from Assume that we have three projects to prioritize: Genetic markers to assist plant breeding and selection of insect-resistant varieties; Micro propagation (tissue culture) for pathogen elimination and mass propagation; Post-harvest management (low-cost storage technologies) for quality maintenance. Project selection 2

3 Criteria Hierarchical Structure Efficiency Sustainability Strategic effects (indirect research effects) Feasibility Pair wise comparison of the criteria with respect to the goal Weights of the criteria Efficiency Sustainability Strategic effects Feasibility Efficiency Sustainability Strategic effects Feasibility Sum Largest eigen value max Efficiency Sustainability Strategic effects Feasibility Weights Efficiency Sustainability Strategic effects Feasibility

4 Consistency evaluation To check for consistency in our judgment: If A B and B C A C Largest eigen value should be equal to the number of criteria (n) Pair wise comparison of projects with respect to the efficiency criterion Consistency index (CI) n RI n / n max Consistency ratio (CR): CI/RI 0.037/0.9= Since CR<10%=> judgment is consistent Local priority of efficiency w.r.t. available projects Genmarker Microprop Storage Genmarker Microprop Storage sum Pair wise comparison Additional tables for Sustainability Strategic effects, and Feasibility Genmarker Microprop Storage priority score Genmarker Microprop Storage

5 Priorities, weights, and the final ranking of the projects Final structure Sum product AHP: An Illustrative Example(1) Goal is to choose the best supplier from the available choices. Criteria: Cost Quality Delivery performance(service) Reliability Order capacity AHP: An Illustrative Example(2) Comparison of selected criteria: Cost Quality Service Reliability Capacity Cost 1 1/3 1/7 1/5 1/3 Quality 3 1 1/5 1/2 1/3 Service /7 1/5 Reliability /4 Capacity

6 AHP: An Illustrative Example(3) To determine the overall weight, each entry is divided by the sum of the column it appears in. And then each entry is expressed as a percentage of this sum Cost Quality Service Reliability Capacity Average Cost Quality Service Reliability Capacity By averaging across each row, we correct for any small inconsistencies in the decision making process. AHP: An Illustrative Example(4) Next step is to evaluate all the suppliers on cost criterion Supplier 1 Supplier2 Supplier 3 Supplier 4 Supplier 5 Supplier 1 1 1/7 1/5 1/3 1/2 Supplier /3 1/7 1/5 Supplier /3 1/3 Supplier /7 Supplier Normalizing the columns and taking average over the rows Supplier 1 Supplier2 Supplier 3 Supplier 4 Supplier 5 Average Supplier Supplier Supplier Supplier Supplier AHP Conclusion Problem extension Other criteria are evaluated in similar manner. Supplier1 = * Quality score* Service score* Reliability score* Capacity score* = x Scores for other suppliers are evaluated in similar fashion and the Supplier with highest score is chosen. In many case, we cannot rely on just one alternatives: In supplier selection problem one supplier may not meet the product demand. Results from AHP can be optimized using excel solver. Other AHP applications: Ranking Resource allocation Benchmarking (Process comparison) 6

7 AHP: Implementation steps 1. Identify goal, available alternatives. 2. Define criteria for selection 3. Structure problem into hierarchical levels 4. Make pair wise comparison between criteria 5. Check for judgment consistency 4.1. if inconsistent re-evaluate preferences 6. Estimate local priority 7. Aggregate relative weights to get global priority 8. Select the best alternative or a combination of alternatives 7