1. Decision Technology Modeling, Software and Applications Matthew J. Liberatore Robert L. Nydick John Wiley & Sons, Inc.

2. What is the Analytic Hierarchy Process (AHP)? The AHP, developed by Tom Saaty, is a decision-making method for prioritizing alternatives when multi-criteria must be considered. An approach for structuring a problem as a hierarchy or set of integrated levels. THE AHP: OVERVIEW

3. AHP problems are structured in at least three levels: The goal, such as selecting the best car to purchase, The criteria, such as cost, safety, and appearance, The alternatives, namely the cars themselves. If additional detail is needed to describe the problem (e.g., initial purchase price, estimated yearly maintenance, and trade-in value) then subcriteria can be created. Arguably the most important part of the entire AHP process is creating the hierarchy. THE AHP: OVERVIEW

4. How does AHP really work? Simply put, the decision-maker: measures the extent to which each alternative achieves each criterion, and determines the relative importance of the criteria in meeting the goal, and synthesizes the results to determine the relative importance of the alternatives in meeting the goal. THE AHP: OVERVIEW

5. PAIRWISE COMPARISONS How does AHP capture human judgments? AHP never requires you to make an absolute judgment or assessment. You would never be asked to directly estimate the weight of a stone in kilograms. AHP does require you to make a relative assessment between two items at a time. AHP uses a ratio scale of measurement.

6. PAIRWISE COMPARISONS Suppose the weights of two stones are being assessed. AHP would ask: How much heavier (or lighter) is stone A compared to stone B? AHP might tell us that, of the total weight of stones A and B, stone A has 65% of the total weight, whereas, stone B has 35% of the total weight.

7. PAIRWISE COMPARISONS Individual AHP judgments are called pairwise comparisons. These judgments can be based on objective or subjective information. When criteria are being compared (e.g., taste and # of grams of fat if Chips Ahoy wants to evaluate a new cookie recipe), comparisons may be based on strategic issues. Alternative pairwise comparisons require data (e.g., actual # of grams of fat for each recipe).

8. WEIGHTS The AHP uses eigenvalues and eigenvectors to compute criteria, subcriteria, and alternative weights for each factor based on the pairwise comparisons. Final alternative weights are determined using a simple weighted average computation.

9. Example: FINAL CAR WEIGHTS CRITERIA WEIGHTS COST SAFETY APPEARANCE COST SAFETY APPEARANCE 0.309 0.582 0.109 0.309 0.582 0.109 CARS FINAL WEIGHTS CARS FINAL WEIGHTS Honda 0.558 0.117 0.761 0.324 Honda 0.558 0.117 0.761 0.324 Mazda 0.320 0.200 0.158 0.232 Mazda 0.320 0.200 0.158 0.232 Volvo 0.122 0.683 0.082 0.444 Volvo 0.122 0.683 0.082 0.444 Honda: (0.558)(0.309) + (0.117)(0.582) + (0.761)(0.109) = 0.324 0.173 0.068 0.083 0.173 0.068 0.083 Mazda: (0.320)(0.309) + (0.200)(0.582) + (0.158)(0.109) = 0.232 0.099 0.116 0.017 0.099 0.116 0.017 Volvo: (0.122)(0.309) + (0.683)(0.582) + (0.082)(0.109) = 0.444 0.038 0.397 0.009 0.038 0.397 0.009

10. CONSISTENCY Consistency of judgments can also be measured. Consistency is important when three or more items are being compared. Suppose we judge a basketball to be twice as large as a soccer ball and a soccer ball to be three times as large as a softball. To be perfectly consistent, a basketball must be six times as large as a softball.

11. DECISION LENS AHP does not require perfect consistency, however, it does provide a measure of consistency. Software (Decision Lens) is available to support all AHP analysis. As a decision support tool, Decision Lens helps with the creation of the hierarchy as well as conducting sensitivity analysis (measuring the impact that changes to the criteria weights have on the final alternative weights).

12. MULTI-LEVEL HIERARCHIES Tom Saaty suggests that hierarchies be limited to nine levels and nine items per level. Brainstorming can identify several dozen criteria. In this case, related items are grouped into categories, creating additional levels in the hierarchy, that is, criteria and subcriteria. This also helps to keep consistency acceptable.

13. RATINGS If many alternatives need to be evaluated, then typically a ratings approach is used. The ratings approach requires setting up a ratings scale under each criterion. Pairwise comparisons are needed to determine the relative importance of each ratings scale category (intensity). Alternatives are not pairwise compared in a rating model, rather alternatives are rated for each criterion.

14. GROUP DECISION MAKING There are many ways of applying AHP to support a group decision-making process. For example, all of the parties discuss, debate, and eventually agree on each pairwise comparison entry. Another approach is to achieve consensus mathematically. Each participant provides their own judgments for each pairwise comparison and the results must be averaged.

15. GROUP DECISION MAKING For example, suppose two individuals compared cost to safety and provide judgments of 9 and 1/9. The arithmetic mean is 4.56 ((9+(1/9))/2). Do you think this is the best estimate? Probably not! Since both judgments are at opposite ends of scale, we would expect the combined judgment to be 1.00. The geometric mean produces this result. In general, if there are n individuals that provide judgments, the geometric mean is defined as the nth root of the product of the n judgments.

16. GROUP DECISION MAKING As another example, in comparing cost to safety suppose the judgments of three individuals are 2, 4, and 8. The geometric mean is the cube root of their product (64) which is 4. Decision Lens manages the entire group decision making process and achieves consensus mathematically by computing the geometric mean.

17. AHP APPLICATIONS AHP has been successfully applied to a variety of problems. 1.R&D projects and research papers; 2.vendors, transport carriers, and site locations; 3.employee appraisal and salary increases; 4.product formulation and pharmaceutical licensing; 5.capital budgeting and strategic planning; 6.surgical residents, medical treatment, and diagnostic testing.

18. AHP APPLICATIONS The product and service evaluations prepared by consumer testing services is another potential application. Products and services, such as self propelled lawn mowers are evaluated. Factors include: bagging, mulching, discharging, handling, and ease of use. An overall score for each mower is determined.

19. AHP APPLICATIONS Would you make your purchasing decision based solely on this score? Probably not! Some of the information will be helpful. Some additional questions are: How important is each criterion? Would you weigh the criteria the same way? Are all of the criteria considered important to you? Are there other criteria that are important to you? Have you ever thought about these issues?

20. There was a need to perform a health technology assessment for the selection of expensive neonatal ventilators for a new women’s health addition at a hospital. The small size of premature babies (as little as 1 pound) presents many electromechanical requirements. Neonatal ventilators must be able to accurately deliver rapid, tiny puffs of precisely blended air and oxygen. If not, damage could be done to the babies lungs. Health Technology Assessment

21. Neonatal ventilators range in price from around $18,000 to nearly $40,000 and features vary widely. They also have a significant life-cycle cost of ownership due to supplies and maintenance, which can be much larger than the original purchase price. This hospital was looking to purchase 24 or more units, thus making this a million-dollar commitment. Two senior department directors (Respiratory Therapy (RT) and Clinical Engineering (CE)) worked on this project. Health Technology Assessment

22. The RT provides the routine clinical staffing to support the patients and the CE evaluates, installs, inspects, repairs, and maintains the devices. Before meeting with the directors, we produced a simplistic hierarchy (ventilator1.ahp). This is important since neither director had any AHP experience. Each director then focused on the parts of the hierarchy that most impacted their work, changing, adding, or deleting criteria and subcriteria. Health Technology Assessment

23. These brainstorming sessions are critical to success in that ideas need time to “ferment.” There were five iterations and the final hierarchy is provided in ventilator6.ahp. Focus next shifted to the alternatives. Since there were 46 bottom level subcriteria and possibly a dozen ventilators, the ratings approach was used. The directors created and defined the ratings scale intensities. This allowed easy ventilator evaluation as it was understood what performance was required to achieve each rating. Health Technology Assessment

24. Several of the ratings terms, descriptions, and final weights are shown below. Hospital staff can easily grasp the meaning of this information and can also interpret the weights.

25. Subcriteria and criteria pairwise comparison were next performed. Again, each director took the lead for their part of the hierarchy. This did not work for the criteria comparisons. In this case, both directors worked together to reach a consensus for these pairwise comparisons. Criteria and subcriteria were ranked before conducting pairwise comparisons. This way the directors did not have to worry about the direction of preference. It also helped with consistency. They also chose the graphical comparison mode. Health Technology Assessment

26. Each director was shown the pairwise comparison screen after the weights were computed. The weights are visually depicted as shaded bars where each criterion name appears. Each director had an opportunity to make “minor” changes to the weights if desired. The bars can be moved and Expert Choice will determine the pairwise comparisons that produced these revised weights.

27. The final weights for each ventilator appear in ventilator7.ahp. The directors felt comfortable with these results. They believed that AHP allowed them to easily identify what criteria were important to them and then to capture their judgments that reflected the importance of each factor. The AHP results will be used to help them make a final ventilator decision. Health Technology Assessment

28. COPYRIGHT Copyright  Matthew J. Liberatore and Robert L. Nydick. All rights reserved. Reproduction or translation of this work beyond that named in Section 117 of the United States Copyright Act without the express written consent of the copyright owners is unlawful. Requests for further information should be addressed to Matthew J. Liberatore and Robert L. Nydick. Adopters of the textbook are granted permission to make back-up copies for their own use only, to make copies for distribution to students of the course the textbook is used in, and to modify this material to best suit their instructional needs. Under no circumstances can copies be made for resale. Matthew J. Liberatore and Robert L. Nydick assume no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein.