the essentials of the analytic network process with seven examples

1. The Essentials of the Analytic Network Process with Seven Examples Decision Making with Dependence and Feedback The Super Decisions Software Thomas L. Saaty

3. A New Paradigm in Measurement We have the belief in mathematics and science that measurement demands that we always have an instrument with a scale marked on it that has a zero and an arbitrarily chosen unit to enable us to measure things one by one on that scale independently of other things. Our use of Cartesian axes makes us believe that everything in the world can be studied with functions defined in such a space with coordinates. That is not true. Our biology teaches us that we need to always compare things to decide which is bigger or better or more important more preferred or more likely to happen and so on, and that things are better understood, or in fact can only be understood relative to each other; that is they are dependent in some way of measurement on one another. To measure all things one by one and not compare them is simplistic and loses a very important property that cannot be captured with ordinary measurement. That is why the world of economics has some serious problems. I also believe that one day we will learn that our understanding of physics may lack this powerful and necessary way of looking at things. Let us look at the real world of decision making

12. Inner and Outer Dependence and the Control Hierarchy In a network, the elements in a component may be people (e.g., individuals in the White House) and those in another component may also be people (e.g., individuals in Congress), may influence other elements in the same component (inner dependence) and those in other components (outer dependence) with respect to each of several properties. We want to determine the overall influence of all the elements. ? organize the properties or criteria prioritize them in the framework of a control hierarchy perform comparisons synthesize to obtain the priorities of these properties derive the influence of elements in the feedback system weight the resulting influences obtain the overall influence of each element.

18. Main Operations of the ANP Relative measurement: Reciprocal relation Judgments: Homogeneity Hierarchy or Network: Structure of problem; the control hierarchy Priorities, Dominance and Consistency: Eigenvector Weighting the components Composition, Additive to also handle dependence through the supermatrix Supermatrix: Interdependence; raising the supermatrix to powers

26. Estimating which Food has more Protein

44. Three Supermatrices in ANP

95. Estimate American, Asian, European Car Maker�s Market Share

99. Step 1. Problem Description Describe the decision problem in detail including its objectives, criteria and subcriteria, actors and their objectives and the possible outcomes of that decision. Give details of influences that determine how that decision may come out.

100. Twelve ANP Steps Kindly follow the algorithm in the following twelve steps for successful completion of your ANP project

101. Step 2: Determine Control and SubCriteria Determine the control criteria and subcriteria in the four control hierarchies one each for the benefits, opportunities, costs and risks of that decision obtain their priorities from paired comparisons matrices. If a control criterion or subcriterion has a global priority of 3% or less, you may consider carefully eliminating it from further consideration.

102. Step 3. Determine the most general network of clusters Determine the most general network of clusters or components) and their elements that applies to all the control criteria. Number and arrange the clusters and their elements in a convenient way (perhaps in a column). Use the identical label to represent the same cluster and the same elements for all the control criteria. Determine the most general network of clusters

103. Step 4. Determine Clusters and Elements For each control criterion or subcriterion, determine the clusters of the general feedback system with their elements Connect them according to their outer and inner dependence influences. An arrow is drawn from a cluster to any cluster whose elements influence it. Describe the decision problem in detail including its objectives, criteria and subcriteria, actors and their objectives and the possible outcomes of that decision.

104. Step 5. Determine the approach Determine the approach you want to follow in the analysis of each cluster or element, influencing (the preferred approach) other clusters and elements with respect to a criterion, or being influenced by other clusters and elements. The sense (being influenced or influencing) must apply to all the criteria for the four control hierarchies for the entire decision.

105. Step 6. Supermatrix Construction For each control criterion, construct the supermatrix by laying out the clusters in the order they are numbered and all the elements in each cluster both vertically on the left and horizontally at the top. Enter in the appropriate position the priorities derived from the paired comparisons as subcolumns of the corresponding column of the supermatrix.

106. Step 7. Perform Paired Comparisons Perform paired comparisons on the elements within the clusters themselves according to their influence on each element in another cluster they are connected to (outer dependence) or on elements in their own cluster (inner dependence). Comparisons of elements according to which element influences a given element more and how strongly more than another element it is compared with are made with a control criterion or subcriterion of the control hierarchy in mind.

107. Step 8. Paired Comparisons on the Clusters Perform paired comparisons on the clusters as they influence each cluster to which they are connected with respect to the given control criterion. The derived weights are used to weight the elements of the corresponding column blocks of the supermatrix. Assign a zero when there is no influence. Thus obtain the weighted column stochastic supermatrix.

108. Step 9. Compute Limit Priorities of the Stochastic Supermatrix Compute the limit priorities of the stochastic supermatrix according to whether it is irreducible (primitive or imprimitive [cyclic]) or reducible with one being a simple or a multiple root and whether the system is cyclic or not. Two kinds of outcomes are possible. In the first all the columns of the matrix are identical and each gives the relative priorities of the elements from which the priorities of the elements in each cluster are normalized to one. In the second the limit cycles in blocks and the different limits are summed and averaged and again normalized to one for each cluster.

109. Step 10. Synthesize the Limiting Priorities 10. Synthesize the limiting priorities by weighting each idealized limit vector by the weight of its control criterion and adding the resulting vectors for each of the four merits: Benefits (B), Opportunities (O), Costs (C) and Risks (R). There are now four vectors, one for each of the four merits. An answer involving marginal values of the merits is obtained by forming the ratio BO/CR for each alternative from the four vectors. The alternative with the largest ratio is chosen for some decisions. Companies and individuals with limited resources often prefer this type of synthesis.

110. Step 11. Determine the strategic criteria and their priorities Determine strategic criteria and their priorities to rate the four merits one at a time. Normalize the four ratings thus obtained. For each alternative, subtract the costs and risks from the sum of the benefits and opportunities. At other times one may add the weighted reciprocals of the costs and risks. Still at other times one may subtract the costs from one and risks from one and then weight and add them to the weighted benefits and opportunities. In all, we have four different formulas for synthesis.

111. Step 12. Sensitivity Analysis Perform sensitivity analysis on the final outcome and interpret the results of sensitivity observing how large or small these ratios are. Can another outcome that is close also serve as a best outcome? Why? By noting how stable this outcome is. Compare it with the other outcomes by taking ratios. Can another outcome that is close also serve as a best outcome? Why?

112. Outline of the Steps of the ANP Describe the decision problem in detail including its objectives, criteria and subcriteria, actors and their objectives and the possible outcomes of that decision. Give details of influences that determine how that decision may come out. comparisons are made simply in terms of benefits, opportunities, costs, and risks in the aggregate without using control criteria and subcriteria. 3. Determine the most general network of clusters (or components) and their elements that applies to all the control criteria. To better organize the development of the model as well as you can, number and arrange the clusters and their elements in a convenient way (perhaps in a column). Use the identical label to represent the same cluster and the same elements for all the control criteria. 4. For each control criterion or subcriterion, determine the clusters of the general feedback system with their elements and connect them according to their outer and inner dependence influences. An arrow is drawn from a cluster to any cluster whose elements influence it. 5. Determine the approach you want to follow in the analysis of each cluster or element, influencing (the preferred approach) other clusters and elements with respect to a criterion, or being influenced by other clusters and elements. The sense (being influenced or influencing) must apply to all the criteria for the four control hierarchies for the entire decision. 6. For each control criterion, construct the supermatrix by laying out the clusters in the order they are numbered and all the elements in each cluster both vertically on the left and horizontally at the top. Enter in the appropriate position the priorities derived from the paired comparisons as subcolumns of the corresponding column of the supermatrix. 7. Perform paired comparisons on the elements within the clusters themselves according to their influence on each element in another cluster they are connected to (outer dependence) or on elements in their own cluster (inner dependence). In making comparisons, you must always have a criterion in mind. Comparisons of elements according to which element influences a given element more and how strongly more than another element it is compared with are made with a control criterion or subcriterion of the control hierarchy in mind. 8. Perform paired comparisons on the clusters as they influence each cluster to which they are connected with respect to the given control criterion. The derived weights are used to weight the elements of the corresponding column blocks of the supermatrix. Assign a zero when there is no influence. Thus obtain the weighted column stochastic supermatrix. 9. Compute the limit priorities of the stochastic supermatrix according to whether it is irreducible (primitive or imprimitive [cyclic]) or it is reducible with one being a simple or a multiple root and whether the system is cyclic or not. Two kinds of outcomes are possible. In the first all the columns of the matrix are identical and each gives the relative priorities of the elements from which the priorities of the elements in each cluster are normalized to one. In the second the limit cycles in blocks and the different limits are summed and averaged and again normalized to one for each cluster. Although the priority vectors are entered in the supermatrix in normalized form, the limit priorities are put in idealized form because the control criteria do not depend on the alternatives. 10. Synthesize the limiting priorities by weighting each idealized limit vector by the weight of its control criterion and adding the resulting vectors for each of the four merits: Benefits (B), Opportunities (O), Costs (C) and Risks (R). There are now four vectors, one for each of the four merits. An answer involving marginal values of the merits is obtained by forming the ratio BO/CR for each alternative from the four vectors. The alternative with the largest ratio is chosen for some decisions. Companies and individuals with limited resources often prefer this type of synthesis. 11. Governments prefer this type of outcome. Determine strategic criteria and their priorities to rate the four merits one at a time. Normalize the four ratings thus obtained and use them to calculate the overall synthesis of the four vectors. For each alternative, subtract the costs and risks from the sum of the benefits and opportunities. At other times one may add the weighted reciprocals of the costs and risks. Still at other times one may subtract the costs from one and risks from one and then weight and add them to the weighted benefits and opportunities. In all, we have four different formulas for synthesis. 12. Perform sensitivity analysis on the final outcome and interpret the results of sensitivity observing how large or small these ratios are. Can another outcome that is close also serve as a best outcome? Why? By noting how stable this outcome is. Compare it with the other outcomes by taking ratios. Can another outcome that is close also serve as a best outcome? Why?

134. SHORTCUTS WHEN IMPLEMENTING THE ANP PROCESS

144. Three Auto Industry Models

145. Ford Explorer/Firestone Tire

146. Top Level View of Model : Benefits, Costs and Risks

147. Macro View of the Decision Network under Benefits, Economic

153. Should Porsche enter the SUV Market?

154. Top Level View of Model : the Benefits, Costs and Risks

159. ANP Applications (cont.) Forecasting the Date of a Turnaround in the U.S. Economy Estimating the Market Shares of Fast Food Restaurants (McDonalds, Wendy`s, Burger King) Decision by the U.S. Congress on China`s Trade Status Where to Dispose of Nuclear Waste Whether or not to Commit U.S. to the Deployment of a Nationale Missile Defense System

160. The Most Hopeful Outcome in the Middle East Conflict Good afternoon, I am in operations research and have spent my life in problem solving and work on really complex problems and as a person from Turkey a friend of both sides, I would like to show a proposed solution of the middle east conflict that seems to have long term stability potential on which people from both sides have worked. � Good afternoon, I am in operations research and have spent my life in problem solving and work on really complex problems and as a person from Turkey a friend of both sides, I would like to show a proposed solution of the middle east conflict that seems to have long term stability potential on which people from both sides have worked. �

161. I would like to talk about Analytic Network Process just to give some basic idea before we go over our analysis, because we used ANP. For solving problems we evaluate the benefits, opportunities, costs and risks. For instance we will decide which policy is the best to solve this problem. We have to consider the benefits, opportunities, costs and risks of each policy. But on the other hand, these merits may have different importances. We may have such a problem that risk may be much more important than the other merits. So in order to differentiate these we use some criteria decided by us. For this problem we use Middle East Peace, International Politics and Human Well-beingI would like to talk about Analytic Network Process just to give some basic idea before we go over our analysis, because we used ANP. For solving problems we evaluate the benefits, opportunities, costs and risks. For instance we will decide which policy is the best to solve this problem. We have to consider the benefits, opportunities, costs and risks of each policy. But on the other hand, these merits may have different importances. We may have such a problem that risk may be much more important than the other merits. So in order to differentiate these we use some criteria decided by us. For this problem we use Middle East Peace, International Politics and Human Well-being

166. Strategic criteia yi nasil anlatabilirim, burada ANP den once bir tanimlayalim Ask TomStrategic criteia yi nasil anlatabilirim, burada ANP den once bir tanimlayalim Ask Tom

170. Nasil yapildi anlat Among the three strategic criteria to evaluate the BOCR merits, Middle East Peace has the highest priority, 0.569 as opposed to International Politics of 0.129 and Human Well-Being of 0.301. Nasil yapildi anlat Among the three strategic criteria to evaluate the BOCR merits, Middle East Peace has the highest priority, 0.569 as opposed to International Politics of 0.129 and Human Well-Being of 0.301.

172. Ask Tom, what does it mean, both friendly and hostile, does it mean some arab countries are friend with Palestinians but some are hostile ? If this is true ask who are hostile, who are friendly ?Ask Tom, what does it mean, both friendly and hostile, does it mean some arab countries are friend with Palestinians but some are hostile ? If this is true ask who are hostile, who are friendly ?

183. All subnets under each of the four BOCR merits are composed of three benefits criteria: economic, political, and social.All subnets under each of the four BOCR merits are composed of three benefits criteria: economic, political, and social.

191. This study infers that the policy of the economic assistance to the Palestinians is the most beneficial to all actors. In order to make sure how stable the outcome of the analysis, sensitivity analysis is conducted. This study infers that the policy of the economic assistance to the Palestinians is the most beneficial to all actors. In order to make sure how stable the outcome of the analysis, sensitivity analysis is conducted.

192. Similarly, if opportunities increase from its original priority 0.169 to 0.5, the economic assistance policy is preserved as the best policy as well. Similarly, if opportunities increase from its original priority 0.169 to 0.5, the economic assistance policy is preserved as the best policy as well.

194. Additionally, if costs priority increases from its original priority 0.328 to 0.5, the economic assistance policy still turns out to be the best policy to deal with. It is found that the overall rank of the five alternatives is preserved although the magnitudes of the priorities slightly change. Similarly, as the priority of risks increases from its original priority 0.226 to 0.5, the economic assistance policy is still preserved as the best policy although its superiority decreases gradually. However, we find that the overall rank of the five alternatives never change although the magnitudes of the priorities change to some extent. � Additionally, if costs priority increases from its original priority 0.328 to 0.5, the economic assistance policy still turns out to be the best policy to deal with. It is found that the overall rank of the five alternatives is preserved although the magnitudes of the priorities slightly change. Similarly, as the priority of risks increases from its original priority 0.226 to 0.5, the economic assistance policy is still preserved as the best policy although its superiority decreases gradually. However, we find that the overall rank of the five alternatives never change although the magnitudes of the priorities change to some extent. �

195. Similarly, if opportunities increase from its original priority 0.169 to 0.5, the economic assistance policy is preserved as the best policy as well. Similarly, if opportunities increase from its original priority 0.169 to 0.5, the economic assistance policy is preserved as the best policy as well.

197. ANP and Bayes Theory The counterpart of an ANP model in statistical decision analysis is the influence diagram. Bayes theorem is the computational basis of influence diagrams. Influence diagrams are directed acyclic graphs (no feedback allowed). There are situations in which influence diagrams do not capture all the Interactions among the elements (e.g., medical diagnosis where symptoms are not independent). ANP allows feedback and under very specific assumptions (e.G., No feedback as in a hierarchy) yields results obtained using influence diagrams. Chapter 6 of the ANP book shows the relationship and extensions of ANP and Bayes theory in a medical diagnosis setting.

201. Background of the Problem What has brought us to this question? - For 10 years, Iraq has been under UN sanctions for refusal to comply with UN resolutions mandating WMD inspections - The Bush Administration�s rhetoric has emphasized the idea of U.S. hegemony, providing a foundation for unilateral, pre-emptive action - Citing a sincere concern for Iraq�s possession/use of WMD, the U.S., backed by its �War on Terrorism�, intends to pursue an agenda of aggression against Iraq

202. The Four Alternatives (1) The U.S. should make a unilateral, pre-emptive attack against Iraq (2) The U.S. should attack Iraq only with Allied support and/or help (3) The U.S. should exhaust diplomatic options by working with UN weapons inspectors to ensure inspections (4) Sanctions against Iraq should be removed

203. Possible Outcomes Option 1 : Pre-emptive, Unilateral Action Pro: A unilateral, pre-emptive attack may do the most to �disarm� Iraq of potential WMD, by seeking and destroying any weapons-making programs or facilities by air or ground force. Additionally, it would serve well the U.S. goal of regime change. Con: A unilateral, pre-emptive attack might alienate the United States from her allies (and future allied support), might threaten the legitimacy and/or future viability of the U.N., may provoke Iraq into using any current WMD as retaliation and, further, might cause a potential increase both in terrorism and/or negative Arab sentiment towards the United States. Additionally, a unilateral strike would place all cost concerns and future Iraqi nation-building upon the U.S.

204. Possible Outcomes Option 2 : Attacking only with Allied Support Pro: : Attacking only with Allied help and/or support would be a slightly more cautious approach that would still target potential Iraqi WMD threats without alienating American allies or threatening the viability of International Governmental Organizations (IGOs, such as the U.N.) Moreover, it would share the burdens of monetary cost and future peacekeeping/nation-building. Con: Attacking Iraq, even with allied help, would still result in Iraqi retaliation that might result in use of biological or chemical WMD. Additionally, this action might serve to further polarize the Arab and Western worlds.

205. Possible Outcomes Option 3:Working with the U.N. to exhaust Diplomatic Options Pro: : Exhausting diplomatic options by working with U.N. weapons inspectors would not only uphold the future viability of the UN (and respect for the UN Security Council), but might also serve the intended purpose of determining if/where Iraq has WMD or means to proliferate WMD. This option serves to respect sovereignty, limit cost, and champion diplomacy. Con: Having a decade-long history of non-cooperation with U.N. weapons inspectors, allowing Iraq to continue to draw out the situation may simply give them more time to create WMD, while also mocking the usefulness and viability of the United Nations.

206. Possible Outcomes Option 4: Remove Sanctions Pro: Removing sanctions might result in an improved quality of life for the Iraqi people, since many believe that the U.N. sanctions have little to no effect on Saddam Hussein and, instead, merely serve to hurt the Iraqi people and give credence to Hussein�s villianization of the United States. Con: Removing sanctions might serve to remove a great deal of credibility from the U.N. as an organization, to threaten future sanction enforcement attempts, and to reduce the viability of future UN operations. Further, removing sanctions might relinquish any leverage that the UN has on Hussein�s power and capacity to proliferate and use WMD, giving him a dictatorial carte blanche.

207. Consideration of Strategic Criteria Economic : 1. Monetary Cost of War 2. Change in Oil Prices 3. Focus Shift Away from U.S.Economy Social : 1. Public Opinion 2. Iraqi Civilian Life Political : 1. Regime Change 2. Allies Reaction 3. Arab World Reaction Military : 1. WMD 2. U.S. Military Casualties 3. Removal of Dictator

208. Benefits, Opportunities, Costs & Risks: The BOCR model In the BOCR model, the Benefits model indicates which alternative would be most beneficial while the Opportunities model shows which alternative would provide the greatest opportunities. Similarly, the Risk model designates which alternative has the highest associated risk, and the Costs model shows which alternative would be most costly. It is important to recognize, however, that the model is being created & evaluated in regards to a U.S. policy option. Therefore, Benefits does not necessarily indicate which Alternative would be most beneficial to other countries, including Iraq.

209. BOCR Ratings

210. Benefits Subnet

211. Opportunities Subnet

212. Costs Subnet

213. Risks Subnet

214. Synthesized Results

215. Comments or Questions??