anp slideshow july_2001

1

The Analytic Network Process (ANP)for Decision Making and Forecasting

with Dependence and Feedback

• With feedback the alternatives depend on the criteria as in a hierarchy but may also depend on each other.

• The criteria themselves can depend on the alternatives and on each other as well.

• Feedback improves the priorities derived from judgments and makes prediction much more accurate.

2

Linear Hierarchy

component,cluster(Level)

element

A loop indicates that eachelement depends only on itself.

Goal

Subcriteria

Criteria

Alternatives

3

Feedback Network with components having Inner and Outer Dependence among Their Elements

C4

C1

C2

C3

Feedback

Loop in a component indicates inner dependence of the elements in that componentwith respect to a common property.

Arc from componentC4 to C2 indicates theouter dependence of the elements in C2 on theelements in C4 with respectto a common property.

4

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).

The elements in a component 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.

In that case we must organize the properties or criteria and prioritize them in the framework of a control hierarchy (or a network), perform comparisons and synthesize to obtain the priorities of these properties. We then derive the influence of elements in the feedback system with respect to each of these properties. Finally, we weight the resulting influences by the importance of the properties and add to obtain the overall influence of each element.

5

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

• Composition, Additive to also handle dependence through the supermatrix

• Supermatrix: Dependence

• Neural Firing: Fredholm Kernel and Eigenfunctions

6

Inner and Outer Dependence and the Control Hierarchy cont.

Control hierarchies fall in four groups:

• Benefits, Costs, Risks, & Opportunities.

Benefits and costs measure the positive and negative contributions or importance of the alternatives if they happen, but will they happen?

Risks and opportunities measure the likelihood that the alternatives will happen and make positive and respectively negative contributions.

Each one is a hierarchy (or a network) by itself. The overall priorities of thealternatives with respect to each of these are then combined by forming the ratios:

to obtain their final overall priorities for a decision.

Benefits x Opportunities Costs x Risks

7

Weighting The Components

In the ANP one often needs to prioritize the influence of the components themselves on each other component to which the elements belong. This influence is assessed through paired comparisons with respect toa control criterion.

The priority of each component is used to weight the priorities of all the elements in that component. The reason for doing this is to enable us to perform feedback multiplication of priorities by other priorities in a cycle, an infinite number of times. The process would not converge unless the resulting matrix of priorities is column stochastic (each of its columns adds to one).

To see that one must compare clusters in real life, we note that if a person is introduced as the president it makes much difference, for example, whether he or she is the President of the United States or the president of a local labor group.

8

Functional - Structural CriteriaIndependence - Dependence

1--Criteria completely independent from alternatives - AbsoluteMeasurement, Intensities and Standards.

2--Criteria quasi dependent on alternatives - Relative Measurement: Rescale the weight of a criterion by the number of alternatives and their measurement (normalization).

3--Criteria completely dependent on alternatives - Feedback network - the Supermatrix.

9

Why ANP?• The power of the Analytic Network Process (ANP) lies in its use ofratio scales to capture all kinds of interactions and make accurate predictions, and, even further, to make better decisions. So far, it has proven itself to be a success when expert knowledge is used with it to predict sports outcomes, economic turns, business, social and political decision outcomes.

• The ANP is a mathematical theory that makes it possible for one to deal systematically with all kinds of dependence and feedback. The reason for its success is the way it elicits judgments and uses measurement to derive ratio scales. Priorities as ratio scales are a fundamental kind of number amenable to performing the basic arithmetic operations of adding within the same scale and multiplying different scales meaningfully as required by the ANP.

10

Mutual Influence Among Several Elements

Unidirectional Influence

In order to distinguish among the influence of several homogeneous elements that is exerted on a single element, the number of influencing elements cannot be more than a few. The reason is that the element that is influenced must be able to distinguish between the various influences and respond to them in relatives terms. If their number is large, the relative influence of each would be a small part of the total. On the other hand, if the number of elements is small, the relative influence of each one on any other single element would be large and distinguishable. A small change in the influence of any of these elements would not alter the receiving elements estimation of its overall influence. When the number of elements is large, they need to be put in different clusters.

A single powerful element may influence numerous other elements that do not influence it in return or influence each other. If many elements influence a single element without feedback, their number can be arbitrarily large.

11

The Questions to Answer About the Dominance of Influence

Two kinds of questions encountered in the ANP:

1. Given a criterion, which element has greater influence (is more dominant) with respect to that criterion?

Use one of the following two questions throughout an exercise.

2. Given a criterion and given an element X in any cluster, which element in the same cluster or a different cluster has greater influence on X with respect to that criterion?

2’. Given a criterion and given an element X in any cluster, which element in the same or in a different cluster is influenced more by X with respect to that criterion.

12

Example of Control Hierarchy

Optimum Function of A System

Environmental Economic Social

Influence is too general a concept and must be specified in terms of particular criteria. It is analyzed according to each criterion and then synthesized by weighting with these priorities of the “control” criteria belonging to a hierarchy or to a system.

13

The SupermatrixTake a control criterion. The priorities of the elements derived from paired comparisons with respect to that control criterion are arranged both vertically and horizontally according to components. The elements in each component are listed for that component in a matrix known as the Supermatrix. Each vector taken from a paired comparison matrix is part of the column of the supermatrix representing the impact with respect to the control criterion of the elements of that component on a single element of the same or another component listed at the top.

The Weighted SupermatrixAll the clusters are pairwise compared according to their influence on a given cluster X with respect to the control criterion. This yields a vector of priorities of the impact of all the clusters on a given criterion. Each component of a vector is used to weight all the elements in the block of column priorities of the supermatrix corresponding to the impact of the elements of that cluster on X. The process is repeated for all the clusters resulting in a weighted supermatrix.

In each block of the supermatrix, a column is either a normalized eigenvector with possibly some zero entries, or all of its elements are equal to zero. In either case it is weighted by the priority of the corresponding cluster on the left. If it is zero, that column of the supermatrix must be normalized after weighting by the cluster’s weights. This operation is equivalent to assigning a zero value to the cluster on the left when weighting a column of a block with zero entries and then re-normalizing the weights of the remaining clusters.

14

The Limiting Supermatrix

The weighted supermatrix is now column stochastic from which one then derives the limiting supermatrix. There are four major cases to consider in deriving the limiting supermatrix depending on the simplicity or multiplicity of the principle eigenvalue and on the reducibility and irreducibility of the matrix.

How to Read Off the AnswerThe desired priorities of the criteria and alternatives with respect to the corresponding control criterion can be read off the supermatrix as given or they may be structurally adjusted according to the number of elements in each cluster and appropriately re-weighted.

How to Combine Benefits, Costs, Opportunities, Risks

One must first combine the supermatrices for the benefits, then for the costs, then for the opportunities and then for the risks by using the weights of the control criteria for each. One then takes the ratio

benefits x opportunities / costs x risks for the alternatives and selects the alternative with the largest ratio.

15

Networks and the Supermatrix

c1 c2 cN

e11e12 e1n1e21e22 e2n2

eN1eN2 eNnN

W11 W12 W1N

W21 W22 W2N

WN1 WN2 WNN

W =

c1

c2

cN

e11

e12

e1n1e21

e22

e2n2eN1

eN2

eNuN

16

where

Wi1 Wi1 Wi1

Wij =

(j1) (j2) (jnj)

(j1) (j2) (jnj)Wi2 Wi2 Wi2

Wini Wini

Wini

(j1) (j2) (jnj)

17

Supermatrix of a Hierarchy

0 0 0 0 0 0

W21 0 0 0 0 0W =

Wn-1, n-2 0 00 0 0 0 Wn, n-1 I

0 W32 0 0 0 0

0 0 0

18

Wk=

Wn,n-1 Wn-1,n-2 W32 W21 Wn,n-1 Wn-1,n-2 W32

for k>n-1

Wn,n-1 Wn-1,n-2 Wn,n-1 I

00

0

00

0

00

0

00

0

00

0

… ...

19

Goal Learning Friends School life Vocational trainingCollege preparation Music classes A B CGoal 0 0 0 0 0 0 0 0 0 0

Learning 0 0 0 0 0 0 0 0 0 0Friends 0 0 0 0 0 0 0 0 0 0

School life 0 0 0 0 0 0 0 0 0 0Vocational training 0 0 0 0 0 0 0 0 0 0

College preparation 0 0 0 0 0 0 0 0 0 0Music classes 0 0 0 0 0 0 0 0 0 0Alternative A 0.3676 0.16 0.33 0.45 0.77 0.25 0.69 1 0 0Alternative B 0.3781 0.59 0.33 0.09 0.06 0.5 0.09 0 1 0Alternative C 0.2543 0.25 0.34 0.46 0.17 0.25 0.22 0 0 1

Goal Learning Friends School life Vocational trainingCollege preparation Music classes A B CGoal 0 0 0 0 0 0 0 0 0 0

Learning 0.32 0 0 0 0 0 0 0 0 0Friends 0.14 0 0 0 0 0 0 0 0 0

School life 0.03 0 0 0 0 0 0 0 0 0Vocational training 0.13 0 0 0 0 0 0 0 0 0

College preparation 0.24 0 0 0 0 0 0 0 0 0Music classes 0.14 0 0 0 0 0 0 0 0 0Alternative A 0 0.16 0.33 0.45 0.77 0.25 0.69 1 0 0Alternative B 0 0.59 0.33 0.09 0.06 0.5 0.09 0 1 0Alternative C 0 0.25 0.34 0.46 0.17 0.25 0.22 0 0 1

The School Hierarchy as Supermatrix

Limiting Supermatrix & Hierarchic Composition

20

Criteria Independent from Alternatives

When the criteria do not depend on the alternatives, the latter are kept out of the supermatrix and are evaluated in the usual hierarchic way by the distributive or ideal modes to make possible rank preservation or reversal as desired. The priorities of the criteria in terms of which the alternatives are evaluated hierarchically are taken from the limiting supermatrix. Here again benefit, cost, opportunity, and risk evaluation can be made to determine the ranks of the alternatives.

21

Structural AdjustAfter & Before the Final Results

After computing the limiting results, if it is desired to group together elements from two or more clusters to determine their relative influence, the priorities of each cluster may be multiplied by the relative number of elements in that cluster to the total number in the set of clusters and then the entire set is normalized.

One may think to do such structural adjustment in the weighting process of the original supermatrix. There may be occasions where that is what should be done.

22

The Management of a Water Reservoir

Here we are faced with the decision to choose one of the possibilities of maintaining the water level in a dam at: Low (L), Medium (M) or High (H) depending on the relative importance of Flood Control (F), Recreation (R) and the generation of Hydroelectric Power (E) respectively for the three levels. The first set of three matrices gives the prioritization of the alternatives with respect to the criteria and the second set, those of the criteria in terms of the alternatives.

23

A Feedback System with Two Components

Flood Recreation Hydro-Control Electric

Power

Low Intermediate HighLevel Level Level

24

1) Which level is best for flood control?

3) Which level is best for power generation?

2) Which level is best for recreation?

Flood Control

Low Med HighLowMediumHigh

Eigenvector

Consistency Ratio = .107

1 5 7 .722 1/5 1 4 .205 1/7 1/4 1 .073


Eigenvector


1 1/7 1/5 .072 7 1 3 .649 5 1/3 1 .279

Recreation


Eigenvector


1 1/5 1/9 .058 5 1 1/5 .207 9 5 1 .735

Power Generation

25

1) At Low Level, which attribute is satisfied best?

2) At Intermediate Level, which attribute is satisfied best?

3) At High Level, which attribute is satisfied best?

Low Level DamF R E Eigenvector

Flood Control 1 3 5 .637Recreation 1/3 1 3 .258Hydro-Electric 1/5 1/3 1 .105 Power


Intermediate Level DamF R E Eigenvector

Flood Control 1 1/3 1 .200Recreation 3 1 3 .600Hydro-Electric 1 1/3 1 .200 Power


High Level DamF R E Eigenvector

Flood Control 1 1/5 1/9 .060Recreation 5 1 1/4 .231Hydro-Electric 9 4 1 .709 Power


26

The six eigenvectors were then introduced as columns of the following stochastic supermatrix.

F R E L M H

0 0 0 .637 .200 .060 0 0 0 .258 .600 .231 0 0 0 .105 .200 .709.722 .072 .058 0 0 0.205 .649 .207 0 0 0.073 .279 .735 0 0 0

One must ensure that all columns sum to unity exactly.

FRELMH

27

The final priorities for both, the height of the dam and for the criteria were obtained from the limiting power of the supermatrix. The components were not weighted here because the matrix is already column stochastic and would give the same limiting result for the ratios even if multiplied by the weighting constants.

Its powers stabilize after a few iterations. We have

F R E L M H

0 0 0 .241 .241 .241 0 0 0 .374 .374 .374 0 0 0 .385 .385 .385.223 .223 .223 0 0 0.372 .372 .372 0 0 0.405 .405 .405 0 0 0

FRELMH

28

The columns of each block of this matrix are identical, so that in the top right block we can read off the overall priority of each of the three criteria from any column, and read off the overall priorities of the three alternatives from any column of the bottom left block. It is clear from this analysis that for the kind of judgments provided, there is preference for a high dam with priority .405 for hydroelectric power generation with priority .385.

29

Cost A E J Eigenvector

AEJ

11/51/3

5 1 3

31/3 1

.637

.105

.258


Repair Cost A E J Eigenvector

AEJ

11/51/2

5 1 3

21/3 1

.582

.109

.309


Durability A E J Eigenvector

AEJ

1 5 3

1/5 1 1/3

1/3 3 1

.105

.637

.258


American C R D Eigenvector

CRD

11/31/4

3 1 1

4 1 1

.634

.192

.174


European C R D Eigenvector

CRD

1 1 2

1 1 2

1/21/2 1

.250

.250

.500


Japanese C R D Eigenvector

CRD

11/2 1

2 1 2

11/2 1

.400

.200

.400


Choosing a Car: Foreign or Domestic?

30

C R D A E J 0 0 0 .634 .250 .400 0 0 0 .192 .250 .200 0 0 0 .174 .500 .400.637 .582 .105 0 0 0.105 .109 .637 0 0 0.258 .309 .258 0 0 0

CRDAEJ

C R D A E J 0 0 0 .464 .464 .464 0 0 0 .210 .210 .210 0 0 0 .326 .326 .326.452 .452 .452 0 0 0.279 .279 .279 0 0 0.269 .269 .269 0 0 0

CRDAEJ

Original Supermatrix

Limiting Supermatrix

Choose an American car. Cost is the dominant criterion.

31

Adjustment PeriodRequired forTurnaround

Primary Factors

Subfactors

Date and Strength of Recovery of U.S. Economy

The U.S. Holarchy of Factors for Forecasting Turnaround in Economic Stagnation

Conventional Economicadjustment Restructuring

Consumption (C) Financial Sector (FS)Exports (X) Defense Posture (DP)Investment (I) Global Competition (GC)Fiscal Policy (F)Monetary Policy (M)Confidence (K)

3 months 6 months 12 months 24 months

32

Consumption (C)Exports (E)Investment (I)Confidence (K)Fiscal Policy (F)Monetary Policy (M)

1 7 5 1/5 1/2 1/5 0.1181/7 1 1/5 1/5 1/5 1/7 0.0291/5 5 1 1/5 1/3 1/5 0.0585 5 5 1 5 1 0.3342 5 3 1/5 1 1/5 0.1185 7 5 1 5 1 0.343

C E I K F M WeightsVector

FS DP GC WeightsVector

Financial Sector (FS)Defense Posture (DS)Global Competition (GC)

1 3 3 0.584

1/3 1 3 0.281

1/3 1/3 1 0.135

Panel B: Which subfactor has the greater potential to influence Economic Restructuring and how strongly?

Panel A: Which subfactor has the greater potential to influence Conventional Adjustment and how strongly?

Table 1: Matrices for subfactor importance relative to primary factors influencing the Timing of Recovery

33

Table 2: Matrices for relative influence of subfactors on periods of adjustment (months) (Conventional Adjustment)

For each panel below, which time period is more likely to indicate a turnaround if the relevant factor is the sole driving force?

Panel D: Relative importance of targeted time periods for fiscal policy to drive a turnaround

Panel B: Relative importance of targeted time periods for exports to drive a turnaround

Panel C: Relative importance of targeted time periods for investment to drive a turnaround

Panel A: Relative importance of targeted time periods for consumption to drive a turnaround

Panel E: Relative importance of targeted time periods for monetary policy to drive a turnaround

Panel F: Expected time for a change of confidence indicators of consumer and investor activity to support a turnaround in the economy

3 6 12 24 Vec. Wts. 3 6 12 24 Vec. Wts.

3 6 12 24 Vec. Wts. 3 6 12 24 Vec. Wts.

3 6 12 24 Vec. Wts. 3 6 12 24 Vec. Wts.

3 months 1 1/5 1/7 1/7 .043 6 months 5 1 1/5 1/5 .11312 months 7 5 1 1/3 .31024 months 7 5 3 1 .534

3 months 1 1 1/5 1/5 .083 6 months 1 1 1/5 1/5 .08312 months 5 5 1 1 .41724 months 5 5 1 1 .417

3 months 1 1 1/5 1/5 .078 6 months 1 1 1/5 1/5 .07812 months 5 5 1 1/3 .30524 months 5 5 3 1 .538

3 months 1 1 1/3 1/5 .099 6 months 1 1 1/5 1/5 .08712 months 3 5 1 1 .38224 months 5 5 1 1 .432

3 months 1 5 7 7 .605 6 months 1/5 1 5 7 .26212 months 1/7 1/5 1 1/5 .04224 months 1/7 1/7 5 1 .091

3 months 1 3 5 5 .517 6 months 1/3 1 5 5 .30512 months 1/5 1/5 1 5 .12424 months 1/5 1/5 1/5 1 .054

34

Table 3: Matrices for relative influence of subfactors on periods of adjustment (months) (Economic Restructuring)

For each panel below, which time period is more likely to indicate a turnaround if the relevant factor is the sole driving force?

Panel B: Defense readjustment time

Panel C: Global competition adjustment time

Panel A: Financial system restructuring time3 6 12 24 Vec. Wts. 3 6 12 24 Vec. Wts.

3 6 12 24 Vec. Wts.



3 months 1 1 1/5 1/5 .078 6 months 1 1 1/5 1/5 .07812 months 5 5 1 1/3 .30524 months 5 5 3 1 .538

Table 4: Most likely factor to dominate during a specified time period

Which factor is more likely to produce a turnaround during the specified time period? Conventional Adjustment CA Restructuring R

Panel A: 3 Months Panel B: 6 Months Panel C: 1 Year Panel D: 2 Years

CA R Vec. Wts. CA R Vec. Wts. CA R Vec. Wts. CA R Vec. Wts.CA 1 5 .833 CA 1 5 .833 CA 1 1 CA 1 1/5 .167R 1/5 1 .167 R 1/5 1 .167 R 1 1 R 5 1 .833

.500

.500

35

Table 5: The Completed Supermatrix

Conven. Economic. Consum. Exports Invest. Confid. Fiscal Monet. Financ. Defense Global 3 mo. 6 mo. 1 yr. 2 years Adjust Restruc. Policy Policy Sector Posture Compet.

Conven. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ¦ 0.833 0.833 0.500 0.167 Adjust ¦Economic. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ¦ 0.167 0.167 0.500 0.833 Restru. +--------------------------

------+Consum. 0.118 ¦ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

¦Exports 0.029 ¦ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

¦Invest. 0.058 ¦0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ¦Confid. 0.334 ¦0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ¦Fiscal 0.118 ¦0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Policy ¦Monetary 0.343 ¦0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Policy ------+

+----+Financ. 0.0 ¦0.584¦ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Sector ¦ ¦

¦ ¦Defense 0.0 ¦0.281¦ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Posture ¦ ¦

¦ ¦Global 0.0 ¦0.135¦ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Compet. +----+

+------------------------------------------------------------------+3 months 0.0 0.0 ¦ 0.043 0.083 0.078 0.517 0.099 0.605 0.049 0.049 0.089 ¦ 0.0 0.0 0.0 0.0

¦ ¦6 months 0.0 0.0 ¦ 0.113 0.083 0.078 0.305 0.086 0.262 0.085 0.085 0.089 ¦ 0.0 0.0 0.0 0.0

¦ ¦1 year 0.0 0.0 ¦ 0.310 0.417 0.305 0.124 0.383 0.042 0.236 0.236 0.209 ¦ 0.0 0.0 0.0 0.0

¦ ¦ 2 years 0.0 0.0 ¦ 0.534 0.417 0.539 0.054 0.432 0.091 0.630 0.630 0.613 ¦ 0.0 0.0 0.0 0.0

36

Conven. Economic. Consum. Exports Invest. Confid. Fiscal Monet. Financ. Defense Global 3 mo. 6 mo. 1 yr. 2 years Adjust Restruc. Policy Policy Sector Posture Compet.

Conven. 0.0 0.0 0.484 0.484 0.484 0.484 0.484 0.484 0.484 0.484 0.484 0.0 0.0 0.0 0.0 Adjust Economic 0.0 0.0 0.516 0.516 0.516 0.516 0.516 0.516 0.516 0.516 0.516 0.0 0.0 0.0 0.0 Restru.

Consum. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.057 0.057 0.057 0.057 Exports 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.014 0.014 0.014 0.014 Invest. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.028 0.028 0.028 0.028 Confid. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.162 0.162 0.162 0.162 Fiscal 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.057 0.057 0.057 0.057 Policy Monetary 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.166 0.166 0.166 0.166 Policy Financ. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.301 0.301 0.301 0.301 Sector Defense 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.145 0.145 0.145 0.145 Posture Global 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.070 0.070 0.070 0.070 Compet. 3 months 0.224 0.224 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6 months 0.151 0.151 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1 year 0.201 0.201 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2 years 0.424 0.424 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Table 6: The Limiting Supermatrix

37

Synthesis/ResultsWhen the judgments were made, the AHP framework was used to perform a synthesis which produced the following results. First a meaningful turnaround in the economy would likely require an additional ten to eleven months, occurring during the fourth quarter of 1992. This forecast is derived from weights generated in the first column of the limiting matrix in Table 6, coupled with the mid-points of the alternate time periods (so as to provide unbiased estimates:

.224 x 1.5 + .151 x 4.5 + .201 x 9 + .424 x 18 =10.45 months from late December 1991/early January 1992

38

The Strength of Recovery

Primary Factors Conventional EconomicAdjustment Restructuring

Subfactors Consumption (C) Financial Sector (FS)Exports (X) Defense Posture (DP)Investment (I) Global Competition (GC)Fiscal Policy (F)Monetary Policy (M)Confidence (K)

Very Strong Strong Moderate Weak(5.5-6.5% GNP) (4.5-5.5% GNP) (3-4.5% GNP) (2-3% GNP)

39

Table 7: Matrices for Primary and Subfactors for Strength of Recovery

Panel A: Which primary factor will be more influential in determining the Strength of Recovery?

Panel B: Which subfactor is more important in influencing Conventional Adjustment?

Panel C: Which subfactor is more important in influencing Economic Restructuring?

Vector CA R Weights

Conventional Adjustment (CA) 1 1/5 .167Restructuring (R) 5 1 .833

Consumption (C)Exports (E)Investment (I)Confidence (K)Fiscal Policy (F)Monetary Policy (M)

1 7 3 1 7 3 0.3171/7 1 1/5 1/5 1 1/5 0.0371/3 5 1 1/3 1/3 1/5 0.0991 5 3 1 7 3 0.3051/7 1 3 1/7 1 1/7 0.0351/3 7 5 1/3 7 1 0.207

C E I K F M WeightsVector

FS DP GC WeightsVector

Financial Sector (FS)Defense Posture (DS)Global Competition (GC)

1 1/5 1/3 0.105

5 1 3 0.637

3 1/3 1 0.258

CI = 0.037

40

Table 8: Matrices for relative influence of subfactors on Strength of Recovery (Conventional Adjustment)

For each panel below, which intensity is more likely to obtain if the designated factor drives the recovery?

Panel D: Relative likelihood of the strength of recovery if confidence drives the expansion

Panel B: Relative likelihood of the strength of recovery if exports drives the expansion

Panel C: Relative likelihood of the strength of recovery if investment drives the expansion

Panel A: Relative likelihood of the strength of recovery if consumption drives the expansion

Panel E: Relative likelihood of the strength of recovery if fiscal policy drive the expansion

Panel F: Relative likelihood of the strength of recovery if monetary policy drives the expansion

V S M W Vec. Wts. V S M W Vec. Wts.

Very Strong (V) Strong (S) Moderate (M) Weak (W)



111/51/7

111/51/7

5511/3

7731

.423

.423

.104

.051


1135

1135

1/31/313

1/51/51/31

.095

.095

.249

.560


1131/2

1131/2

1/31/311/6

2261

.182

.182

.545

.091


111/31/5

111/31/5

331/31/7

5571

.376

.376

.193

.054


1151

1151

1/51/511/5

1151

.125

.125

.625

.125


1153

1153

1/51/511/7

1/31/371

.084

.084

.649

.183

CI = 0.028CI = 0.016

CI = 0.0 CI = 0.101

CI = 0.0 CI = 0.101

41

Table 9: Matrices for relative influence of subfactors on Strength of Recovery (Restructuring)

For each panel below, which intensity is more likely to obtain if the designated factor drives the recovery?

Panel B: Relative likelihood of the strength of recovery if defense posture drives the expansion

Panel C: Relative likelihood of the strength of recovery if global competition drives the expansion

Panel A: Relative likelihood of the strength of recovery if financial sector drives the expansion



V S M W Vec. Wts.

1135

1135

1/31/311/3

1/51/51/31

.095

.095

.249

.560


1357

1/3135

1/51/313

1/71/51/31

.055

.118

.262

.565


1135

1135

1/31/311

1/51/511

.101

.101

.348

.449

CI = 0.016

CI = 0.012

CI = 0.044

Table 10: Overall Results for Strength of Recovery% GNP Growth

Very Strong (5.5-6.5) Strong (4.5-.5) Moderate

(3-4.5)Weak (2-3)

0.1080.1410.2900.461

% GNP Recovery Rate* 3.6

*% GNP Recovery rate calculated using the relative strength of conventional adjustment and restructuring in Table 5 Panel A each used to multiply midpoints of % GNP Growth and then summed.

42

Hamburger ModelEstimating Market Share of Wendy’s, Burger King and McDonald’s

with respect to the single economic control criterion

43

How to Pose the Question toMake Paired Comparisons

• One must answer questions of the following kind: givenMcDonald’s (in the Alternatives cluster) is its economicstrength derived more from Creativity or from Frequency(both in the Advertising cluster)? Conversely, givenCreativity in the Advertising cluster who is moredominant, McDonald’s or Burger King?

• Then, again, by comparing the dominance impact of theclusters of Advertising and Quality of Food on theeconomic success of McDonald by weighting andnormalizing we can relate the relative effect of elements inthese different clusters.

44

Local: Menu Cleanliness

Speed Service Location Price Reputation

TakeOut

Portion Taste Nutrition

Frequency

Promotion

Creativity

Wendy’s BurgerKing

McDon-ald’s

Menu Item 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1930 0.0000 0.0000 0.0000 0.0000 0.3110 0.1670 0.1350 0.1570 0.0510 0.1590Cleanliness 0.6370 0.0000 0.0000 0.5190 0.0000 0.0000 0.2390 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2760 0.1100 0.3330Speed 0.1940 0.7500 0.0000 0.2850 0.0000 0.0000 0.0830 0.2900 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0640 0.1400 0.0480Service 0.0000 0.0780 0.1880 0.0000 0.0000 0.0000 0.0450 0.0550 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0650 0.1430 0.0240Location 0.0530 0.1710 0.0000 0.0980 0.0000 0.5000 0.2640 0.6550 0.0000 0.0000 0.0000 0.1960 0.0000 0.7100 0.1420 0.2240 0.1070Price 0.1170 0.0000 0.0000 0.0000 0.0000 0.0000 0.0620 0.0000 0.8570 0.0000 0.0000 0.0000 0.8330 0.0000 0.0300 0.2390 0.0330Reputation 0.0000 0.0000 0.0810 0.0980 0.0000 0.0000 0.0570 0.0000 0.0000 0.0000 0.0000 0.4930 0.0000 0.1550 0.2070 0.0420 0.2230Take-Out 0.0000 0.0000 0.7310 0.0000 0.0000 0.5000 0.0570 0.0000 0.1430 0.0000 0.0000 0.0000 0.0000 0.0000 0.0590 0.0510 0.0740Portion 0.2290 0.0000 0.0000 0.0000 0.0000 0.8330 0.2800 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0940 0.6490 0.5280Taste 0.6960 0.0000 0.0000 0.0000 0.0000 0.0000 0.6270 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2800 0.0720 0.1400Nutrition 0.0750 0.0000 0.0000 0.0000 0.0000 0.1670 0.0940 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.6270 0.2790 0.3320Frequency 0.7500 0.0000 0.0000 0.0000 0.0000 0.1670 0.5500 0.0000 0.0000 0.0000 0.0000 0.0000 0.6670 0.8750 0.6490 0.7090 0.6610Promotion 0.1710 0.0000 0.0000 0.0000 0.0000 0.8330 0.3680 0.0000 0.0000 0.0000 0.0000 0.5000 0.0000 0.1250 0.0720 0.1130 0.1310Creativity 0.0780 0.0000 0.0000 0.0000 0.0000 0.0000 0.0820 0.0000 0.0000 0.0000 0.0000 0.5000 0.3330 0.0000 0.2790 0.1790 0.2080Wendy's 0.3110 0.5000 0.0990 0.5280 0.0950 0.0950 0.1010 0.1960 0.2760 0.6050 0.5940 0.0880 0.0880 0.1170 0.0000 0.1670 0.2000Burger King 0.1960 0.2500 0.3640 0.1400 0.2500 0.2500 0.2260 0.3110 0.1280 0.1050 0.1570 0.1950 0.1950 0.2680 0.2500 0.0000 0.8000McDonald’s 0.4930 0.2500 0.5370 0.3330 0.6550 0.6550 0.6740 0.4940 0.5950 0.2910 0.2490 0.7170 0.7170 0.6140 0.7500 0.8330 0.0000

Hamburger Model Supermatrix

Cluster: Other Quality Advertising CompetitionOther 0.198 0.500 0.131 0.187Quality 0.066 0.000 0.000 0.066Advertising 0.607 0.000 0.622 0.533Competition 0.129 0.500 0.247 0.215

Cluster Priorities Matrix

Other

Q

AdComp

Other Quality CompetitionAdvertising

45

Weighted SupermatrixWeighted: Menu Cleanli

nessSpeed Service Location Price Reputa

tionTakeOut


Frequency

Promotion

Creativity


McDon-ald’s

Menu Item 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0382 0.0000 0.0000 0.0000 0.0000 0.0407 0.0219 0.0177 0.0293 0.0095 0.0297Cleanliness 0.1262 0.0000 0.0000 0.3141 0.0000 0.0000 0.0473 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0516 0.0205 0.0622Speed 0.0384 0.4544 0.0000 0.1725 0.0000 0.0000 0.0164 0.1755 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0120 0.0261 0.0090Service 0.0000 0.0473 0.1138 0.0000 0.0000 0.0000 0.0089 0.0333 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0121 0.0267 0.0045Location 0.0105 0.1036 0.0000 0.0593 0.0000 0.0990 0.0523 0.3964 0.0000 0.0000 0.0000 0.0257 0.0000 0.0930 0.0265 0.0418 0.0200Price 0.0232 0.0000 0.0000 0.0000 0.0000 0.0000 0.0123 0.0000 0.4287 0.0000 0.0000 0.0000 0.1091 0.0000 0.0056 0.0446 0.0062Reputation 0.0000 0.0000 0.0490 0.0593 0.0000 0.0000 0.0113 0.0000 0.0000 0.0000 0.0000 0.0646 0.0000 0.0203 0.0387 0.0078 0.0417Take-Out 0.0000 0.0000 0.4426 0.0000 0.0000 0.0990 0.0113 0.0000 0.0715 0.0000 0.0000 0.0000 0.0000 0.0000 0.0110 0.0095 0.0138Portion 0.0151 0.0000 0.0000 0.0000 0.0000 0.0550 0.0185 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0062 0.0428 0.0348Taste 0.0460 0.0000 0.0000 0.0000 0.0000 0.0000 0.0414 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0185 0.0047 0.0092Nutrition 0.0050 0.0000 0.0000 0.0000 0.0000 0.0110 0.0062 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0413 0.0184 0.0219Frequency 0.4554 0.0000 0.0000 0.0000 0.0000 0.1014 0.3338 0.0000 0.0000 0.0000 0.0000 0.0000 0.4149 0.5444 0.3455 0.3773 0.3519Promotion 0.1038 0.0000 0.0000 0.0000 0.0000 0.5056 0.2233 0.0000 0.0000 0.0000 0.0000 0.3110 0.0000 0.0778 0.0383 0.0601 0.0697Creativity 0.0474 0.0000 0.0000 0.0000 0.0000 0.0000 0.0498 0.0000 0.0000 0.0000 0.0000 0.3110 0.2071 0.0000 0.1485 0.0953 0.1107Wendy's 0.0401 0.1974 0.0391 0.2082 0.0950 0.0123 0.0130 0.0773 0.1381 0.6044 0.5940 0.0217 0.0217 0.0289 0.0000 0.0359 0.0429Burger King 0.0253 0.0987 0.1436 0.0552 0.2500 0.0323 0.0291 0.1226 0.0640 0.1049 0.1570 0.0482 0.0482 0.0662 0.0537 0.0000 0.1718McDonald ‘s 0.0636 0.0987 0.2118 0.1313 0.6550 0.0845 0.0869 0.1948 0.2976 0.2907 0.2490 0.1771 0.1771 0.1517 0.1611 0.1788 0.0000

Synthesized:Global

Menu Cleanliness

Speed Service Location Price Reputation

TakeOut


Frequency

Promotion

Creativity


McDon-ald’s

Menu Item 0.0234 0.0234 0.0234 0.0234 0.0234 0.0234 0.0234 0.0234 0.0234 0.0234 0.0234 0.0234 0.0234 0.0234 0.0234 0.0234 0.0234Cleanliness 0.0203 0.0203 0.0203 0.0203 0.0203 0.0203 0.0203 0.0203 0.0203 0.0203 0.0203 0.0203 0.0203 0.0203 0.0203 0.0203 0.0203Speed 0.0185 0.0185 0.0185 0.0185 0.0185 0.0185 0.0185 0.0185 0.0185 0.0185 0.0185 0.0185 0.0185 0.0185 0.0185 0.0185 0.0185Service 0.0072 0.0072 0.0072 0.0072 0.0072 0.0072 0.0072 0.0072 0.0072 0.0072 0.0072 0.0072 0.0072 0.0072 0.0072 0.0072 0.0072Location 0.0397 0.0397 0.0397 0.0397 0.0397 0.0397 0.0397 0.0397 0.0397 0.0397 0.0397 0.0397 0.0397 0.0397 0.0397 0.0397 0.0397Price 0.0244 0.0244 0.0244 0.0244 0.0244 0.0244 0.0244 0.0244 0.0244 0.0244 0.0244 0.0244 0.0244 0.0244 0.0244 0.0244 0.0244Reputation 0.0296 0.0296 0.0296 0.0296 0.0296 0.0296 0.0296 0.0296 0.0296 0.0296 0.0296 0.0296 0.0296 0.0296 0.0296 0.0296 0.0296Take-Out 0.0152 0.0152 0.0152 0.0152 0.0152 0.0152 0.0152 0.0152 0.0152 0.0152 0.0152 0.0152 0.0152 0.0152 0.0152 0.0152 0.0152Portion 0.0114 0.0114 0.0114 0.0114 0.0114 0.0114 0.0114 0.0114 0.0114 0.0114 0.0114 0.0114 0.0114 0.0114 0.0114 0.0114 0.0114Taste 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049Nutrition 0.0073 0.0073 0.0073 0.0073 0.0073 0.0073 0.0073 0.0073 0.0073 0.0073 0.0073 0.0073 0.0073 0.0073 0.0073 0.0073 0.0073Frequency 0.2518 0.2518 0.2518 0.2518 0.2518 0.2518 0.2518 0.2518 0.2518 0.2518 0.2518 0.2518 0.2518 0.2518 0.2518 0.2518 0.2518Promotion 0.1279 0.1279 0.1279 0.1279 0.1279 0.1279 0.1279 0.1279 0.1279 0.1279 0.1279 0.1279 0.1279 0.1279 0.1279 0.1279 0.1279Creativity 0.1388 0.1388 0.1388 0.1388 0.1388 0.1388 0.1388 0.1388 0.1388 0.1388 0.1388 0.1388 0.1388 0.1388 0.1388 0.1388 0.1388Wendy's 0.0435 0.0435 0.0435 0.0435 0.0435 0.0435 0.0435 0.0435 0.0435 0.0435 0.0435 0.0435 0.0435 0.0435 0.0435 0.0435 0.0435Burger King 0.0784 0.0784 0.0784 0.0784 0.0784 0.0784 0.0784 0.0784 0.0784 0.0784 0.0784 0.0784 0.0784 0.0784 0.0784 0.0784 0.0784McDonald’s 0.1579 0.1579 0.1579 0.1579 0.1579 0.1579 0.1579 0.1579 0.1579 0.1579 0.1579 0.1579 0.1579 0.1579 0.1579 0.1579 0.1579

{

Limiting Supermatrix

Relative local weights: Wendy’s= 0.156, Burger King =0.281, and McDonald’s=0.566

46

Validation

The same problem worked as a simple anda complex hierarchy and as a feedback network.

47

Hamburger ModelSynthesized Local:

Other Menu Item 0.132Cleanliness 0.115Speed 0.104Service 0.040Location 0.224Price 0.138Reputation 0.167Take-Out 0.086

Quality Portion 0.494Taste 0.214Nutrition 0.316

Advertising Frequency 0.485Promotion 0.246Creativity 0.267

Competition Wendy’s 0.156Burger King 0.281McDonald’s 0.566

Synthesized Local Cont’d:

Simple Hierarchy Complex Hierarchy Feedback Actual(Three Level) (Several Levels) Network Market

ShareWendy’s 0.3055 0.1884 0.156 0.1320

Burger King 0.2305 0.2689 0.281 0.2857

McDonald’s 0.4640 0.5427 0.566 0.5823

49

Strategic Planning

for the Future of the

University of Pittsburgh Medical Center

Using the Analytic Network Process(ANP)

50

S oc ia l E conom ic P o litica l

B ene fits


C os ts


R isk s

Social Benefits Network Submodel

Economic Benefits Network Submodel

Political Benefits Network Submodel

Social Costs Network Submodel

Economic CostsNetwork Submodel

Political Costs Network Submodel

Social Risks Network Submodel

Economic Risks Network Submodel

Political Risks Network Submodel

Benefits Control Model Costs Control Model Risks Control Model

Evaluate Strategies for the University Health Network to Compete in a Managed Care Environment

51

List of Clusters and Elements (Not all the Clusters appear in all 9 of the sub-models.)

Cluster Names Cluster ElementsClients Businesses- businesses that offer employees health care plans

Consumers- individuals who purchase their own health coverage

Insurers- companies who sell health insurance

Competition Competitors- other hospitals in Pittsburgh that compete w/ UPMC

Convenience Time- expended by customer scheduling, traveling, and actual waiting room

Safety- safety of location

Internal Stakeholders Physicians- working for UPMC

Administrators- planners, managers, decision makers of UPMC

Alliances- outside organizations, involved: isurers, hospitals, physician networks

Staff- non-physician, non-administrative personel

Public Relations Public Relations- UPMC’s public image: TV, Newspaper, Radio

Quality Specialty quality non-general health services,

Diversity- range of health services offered by UPMC

Care- quality of general health services

Research- quality of research at UPMC

*Strategies Improve and Measure Outcomes- measure effectiveness to improve service

Capitalization- negotiated insurance contracts with fixed payments

Develop a Primary Network- increase number of primary care physicians

Internal Cost Reduction- cut facilities, employees, and high cost procedures

Teach Primary Care- shift focus from curative care to preventive care

Variety of Services Internal Medicine and Surgery- Curative specialty services and hospitalization

Cancer Treatment- cancer treatment cure

Outpatient Care- preventive care and short term medical treatments

*Strategies apperar in every sub-moadel as alternatives of choice

52

Clusters and Elements in the Economic Benefits Sub-model

53

Benefits & Costs

Predicting the Superbowl Winner ‘96 & ‘97

54

Team Benefits Costs B/C

Miami vs. 0.701 0.612 1.145Buffalo 0.745 0.590 1.263

Indianapolis vs. 0.687 0.622 1.105San Diego 0.660 0.650 1.015

Detroit vs. 0.625 0.636 0.983Philadelphia 0.695 0.580 1.198

Atlanta vs. 0.590 0.612 0.964Green Bay 0.785 0.515 1.524

Second Round

Pittsburgh vs. 0.740 0.581 1.274Buffalo 0.704 0.605 1.164

Indianapolis vs. 0.695 0.590 1.178Kansas City 0.750 0.575 1.304

Green Bay vs. 0.755 0.590 1.280San Francisco 0.751 0.585 1.284

Philadelphia vs. 0.732 0.641 1.142Dallas 0.759 0.576 1.318

Divisional Playoffs

Dallas vs. 0.742 0.540 1.370Green Bay 0.756 0.561 1.350

Pittsburgh vs. 0.699 0.555 1.260Indianapolis 0.741 0.598 1.240

The Super Bowl

Dallas vs. 0.761 0.728 1.045Pittsburgh 0.748 0.735 1.018

Kansas kicker missed 3 field goals & ruined them. No way to know his ailments that day.

Was too close to determine the winner.Green Bay won.

All predictions correct except for two games below.Wild Card Games

1996

Pla

yoff

s

Pre-start (early December 1995)

55

1997

Pla

yoff

sWrong prediction.

Wrong prediction.

Wrong prediction.

The first predictions were wrongon three games which thenrequired revision.

Pre-start (early December 1996)

Playoff Predictions

Pre-Start

Predicted Outcomes

AFC

Team Benefits Costs B/C Winner Las Vegas

Wild Cards

Indianapolis 0.588 0.489 1.2 PittsburghPittsburgh 0.592 0.477 1.24

Jacksonville 0.601 0.501 1.2 BuffaloBuffalo 0.594 0.487 1.22

Conference Finals

Pittsburgh 0.609 0.479 1.27 PittsburghNew England 0.516 0.419 1.23

Buffalo 0.551 0.488 1.13 DenverDenver 0.62 0.447 1.39

Pittsburgh 0.633 0.523 1.21 DenverDenver 0.686 0.5318 1.29

NFC

Wild Cards

Philadelphia 0.557 0.467 1.19 San FranciscoSan Francisco 0.621 0.444 1.4

Minnesota 0.545 0.488 1.12 DallasDallas 0.571 0.476 1.2

Conference Finals

San Francisco 0.585 0.5 1.17 Green BayGreen Bay 0.685 0.46 1.49

Dallas 0.522 0.494 1.06 CarolinaCarolina 0.51 0.448 1.14

Carolina 0.511 0.498 1.03 Green BayGreen Bay 0.643 0.521 1.23 Super Bowl

Green Bay 0.618 0.457 1.35 Green BayDenver 0.556 0.476 1.17

56

Post-start (before Conference Finals)

Playoff Predictions

Predicted Outcomes

AFCTeam Benefits Costs B/C Winner Actual

Conference Finals

Jacksonville 0.545 0.488 1.12 DenverDenver 0.612 0.447 1.37 Jax

Jacksonville 0.576 0.515 1.12 New EngNew England 0.645 0.519 1.24 NE

Super Bowl

New England 0.627 0.554 1.13Green Bay 0.653 0.506 1.29 Green Bay

A gains error in one game.

57

The Benefits

The Costs

58

Benefits Supermatrix

Offense Emotions Outside Teams0.0000 0.2449 0.6442 0.71720.2176 0.0000 0.0852 0.19470.0914 0.0902 0.0000 0.08810.6910 0.6648 0.2706 0.0000

OffenseEmotionsOutsideTeam

CLUSTER WEIGHTS

Local Weights Offensive Emotions Outside Teams

Offense

Emotions

Outside

Teams

Global Local QB Ability Running Play Above Coaching Emotions Home Field Road Ahead Dallas Green BayQB AbilityRunningPlay AboveAbilityCoachingEmotional StateHome FieldRoad AheadDallasGreen Bay

0.02970.3140

0.00370.02350.09230.04330.36700.12270.0039

0.08640.9136

0.03090.19620.77240.10550.89450.96930.0308

1.0000 1.0000

1.0000

1.0000

0.80000.2000

1.00000.75000.2500

1.0000.8000.2000

1.0000

1.0000

1.0000

0.75000.2500

1.0000

1.00001.0000

0.80000.2000

0.20000.8000

59

Weighted SupermatrixCluster Weights Offensive Emotions Outside Teams

Offense

Emotions

Outside

Teams

Global Local QB Ability Running Play Above Coaching Emotions Home Field Road Ahead Dallas Green BayQB AbilityRunningPlay AboveAbilityCoachingEmotional StateHome FieldRoad AheadDallasGreen Bay

0.02970.3140

0.00370.02350.09230.04330.36700.12270.0039

0.08640.9136

0.03090.19620.77240.10550.89450.96930.0308

1.0000 1.0000

0.7308

0.2692

0.19590.0490

0.09020.49860.1662

0.7308

0.05380.2153

0.51540.1288

0.0852

0.2706

0.6442

0.06390.0213

0.2706

0.68850.3115

0.71250.1781

0.02190.0875

Offensive Emotions Outside Teams Global Local QB Ability Running Play Above Coaching Emotions Home Field Road Ahead Dallas Green Bay

QB AbilityRunningPlay AboveAbilityCoachingEmotional StateHome FieldRoad AheadDallasGreen Bay

0.02970.3140

0.00370.02350.09230.04330.36700.12270.0039

Offense

Emotions

Outside

Teams

0.02970.3140

0.00370.02350.09230.04330.36700.12270.0039

0.02970.3140

0.00370.02350.09230.04330.36700.12270.0039

0.02970.3140

0.00370.02350.09230.04330.36700.12270.0039

0.02970.3140

0.00370.02350.09230.04330.36700.12270.0039

0.02970.3140

0.00370.02350.09230.04330.36700.12270.0039

0.02970.3140

0.00370.02350.09230.04330.36700.12270.0039

0.02970.3140

0.00370.02350.09230.04330.36700.12270.0039

0.02970.3140

0.00370.02350.09230.04330.36700.12270.0039

0.02970.3140

0.00370.02350.09230.04330.36700.12270.0039

0.02970.3140

0.00370.02350.09230.04330.36700.12270.0039

Limiting Benefits Supermatrix

60

Offense Emotions Outside Teams0.0000 0.3614 0.6267 0.71720.0877 0.0000 0.0936 0.19470.1392 0.0650 0.0000 0.08810.7731 0.5736 0.2797 0.0000

OffenseEmotionsOutsideTeam

CLUSTER WEIGHTS

Local Weights Offensive Emotions Outside Teams

Offense

History

Outside

Teams

Global Local Road Ahead Players Strength Cinderella Ability Failures State Weather Dallas Green BayRoad AheadImmature PlayersNot Full StrengthCinderellaPlay Bey AbilityPast FailuresMental StateWeatherDallasGreen Bay

0.15290.00000.22610.00110.20020.07380.01210.16830.16530.0000

0.40340.00000.59660.00410.72780.26830.06730.93321.00020.0000

1.00000.85710.1429

0.83330.1667

1.0000

0.8000

0.2000

1.00001.0000

1.0000 1.0000

0.75000.2500

1.0000

0.7500

0.2500

1.00000.83330.1667

0.20000.80000.75000.2500

1.000

Immature Not FullPlay

beyond Past Mental

0.8000

0.20001.0000

1.0000

Costs Supermatrix

61

Cluster Weighted Offensive Emotions Outside Teams

Offense

History

Outside

Teams


0.15290.00000.22610.00110.20020.07380.01210.16830.16530.0000

0.40340.00000.59660.00410.72780.26830.06730.93321.00020.0000

1.00000.85710.1429

0.83330.1667

1.0000

0.2891

0.0723 1.0000 0.6267

0.07020.0234

0.2797

0.5379

0.1793

0.19470.07340.0147

0.14340.5738

0.14600.04870.0881


beyond Past Mental

0.5014

0.12530.0936

0.2797

Offensive Emotions Outside Teams

Offense

History

Outside

Teams


0.1529

0.00000.22610.00110.20020.07380.02120.16830.16530.0000


beyond Past Mental

0.1529

0.00000.22610.00110.20020.07380.02120.16830.16530.0000

0.1529

0.00000.22610.00110.20020.07380.02120.16830.16530.0000

0.1529

0.00000.22610.00110.20020.07380.02120.16830.16530.0000

0.1529

0.00000.22610.00110.20020.07380.02120.16830.16530.0000

0.1529

0.00000.22610.00110.20020.07380.02120.16830.16530.0000

0.1529

0.00000.22610.00110.20020.07380.02120.16830.16530.0000

0.1529

0.00000.22610.00110.20020.07380.02120.16830.16530.0000

0.1529

0.00000.22610.00110.20020.07380.02120.16830.16530.0000

0.1529

0.00000.22610.00110.20020.07380.02120.16830.16530.0000

0.1529

0.00000.22610.00110.20020.07380.02120.16830.16530.0000

0.1529

0.00000.22610.00110.20020.07380.02120.16830.16530.0000

Weighted Supermatrix

Limiting Costs Supermatrix

62

Benefits Intensity Priorities

Quarterback (0.030):Average (0.091) Good (0.281) High Ability (0.691)GB,D

Running Game (0.314):Average (0.084) Good (0.211)GB High Ability (0.705)D

Play Above Potential (0.004):Average (0.075) Good (0.229)D High Play Level (0.696)GB

Coaching Ability to Inspire (0.023):Not A lot (0.078) Somewhat (0.205)D Heroic (0.717)GB

Emotional State (0.092):Apathy (0.082) Mediocre (0.236) Excitement (0.682)GB,D

Home Field Advantage (0.043): SignificantNeutral (0.105) Some Effect (0.258)GB Effect (0.637)D

VeryThe Road Ahead (0.367): Some Effect (0.236)D Confident (0.682)GB

No Effect (0.082)

Dallas’ Effect on the Ultimate Greatly Outcome (0.123): Medium (0.280) Influenced (0.627)GB,D

Low Effect (0.094)

Green Bay’s Effect on the Ultimate Greatly Outcome (0.004): Medium (0.258) Influenced (0.637)GB,D

Not Much (0.105)

The Road Ahead (0.153):Low Effect (0.085) Somewhat (0.271)GB,D High Effect (0.644)

Not at Full Strength (0.226): Some Big InjuryFew Injuries (0.091) Injuries (0.218) Problems (0.644) GB,D

Playing Beyond Ability (0.200):Not a factor (0.094) GB,D May Falter (0.288) Venerable (0.627)

Past Failures (0.074): Can’t getGood History (0.082) GB Mixed Past (0.236)D it Gone (0.682)

Mental State of Preparedness (0.012): May beReady (0.122)GB Hurt (0.230)D Unready (0.648)

Cinderalla Team (0.001): Good TeamNot Cinderalla (0.082) GB,D Lucky (0.236) It’s Midnight (0.682)

Weather Sensitivity (0.168): Small HighAnything Goes (0.095)D Sensitivity (0.250)GB Sensitivity (0.655)

Dallas’ Effect (0.165):Small (0.163) Medium (0.297) High (0.540)GB,D

Green Bay’s Effect (0.000)Small (0.105)D Medium (0.258) Big Effect (0.637)GB

Immature Players (0.000) Some YoungVeterans (0.082)D Experience (0.236)GB Players (0.682)

Costs Intensity Priorities

Each of the two teams obtained a total score from the intensities.

63

Illustrative Considerations in the Evaluationof 1996 Dallas - Green Bay Game

For the Benefits Model:

- With respect to Green Bay, Quarterback is equally to moderately more important than Dallas. Here we are comparing an aspect of the Green Bay team to their opponent, Dallas effectively, we are asking ourselves, which is more important to Green Bay’s success, the fact that they have Brett Favre, or the fact that they are playing Dallas. The judgment was made that while Favre is an outstanding quarterback, the fact that he is facing Dallas may be enough to counteract his abilities.

- With respect to Dallas, the Road Ahead is strongly more important than Home Field Advantage. The Road Ahead refers to future games that the team may have to play if the team continues on. Here, the relative ease of the road ahead for Dallas, based on the record of the AFC in the Super Bowl, causes it to be less important than the fact that Dallas is playing Green Bay, possibly its biggest obstacle to winning the Super Bowl, on its home turf.

- With respect to Dallas, Running Game is equally to moderately stronger than Quarterback. This judgment is based on the fact that while Dallas’ quarterback is excellent the team’s Running Game is quite often the league’s best.

- With respect to Dallas, Quarterback is strongly to very strongly more important than Coaching Inspiration. The basis for this is the fact that Barry Switzer has exhibited no great gift for inspiration, the team simply is full of talent, especially in the quarterback position.

64

For the Costs Model:

Conclusion

- With respect to Green Bay, Mental State is strongly more important than Weather Sensitivity, simply because Green Bay’s Mental State could be more easily called into question (may not be tough enough) than their Weather Sensitivity (they are very insensitive to poor weather conditions.

- With respect to Dallas, Mental State is moderately more important than Weather Sensitivity. While the team is not highly Weather Sensitive, their arrogant attitudes causes us a bit of concern that it may be their undoing.

- With respect to Green Bay, Not at Full Strength is moderately more important than The Road Ahead. The basis for this being that Reggie White, a very important player on the team, is not 100%, and this is likely to have a larger impact than any AFC team that Green Bay might meet in the Super Bowl because, as we stated before, AFC teams do not traditionally pose a threat. Conversely, if we looked at an AFC matchup, the Road Ahead would in most cases have a large impact due to the fact that the AFC teams are usually unsuccessful against the NFC teams in the Super Bowl.

- With respect o Green Bay, Dallas is strongly more important than Cinderella. This translates to mean that any Cinderella story that Green Bay may be enjoying is likely to be overshadowed by the fact that they are playing Dallas. While Green Bay is not widely considered to be a Cinderella, the label would have a larger effect on a team like the Indianapolis Colts when they played Kansas City.

- With respect to Dallas, Not at Full Strength is strongly more important than Immature Players. While Dallas has many veterans, its biggest problem in this comparison could be injuries to key players such as Charles Haley.

- With respect to Dallas, Past Failures are equally important as Play Beyond Ability. Not only is Dallas playing up to its potential, it has a few grave failures of the past to look back on.

- Now that we have looked at several examples of judgments, we can move on to the results of the model. The elements in the model are given weights based on our judgment. We can rate the teams using information that we have collected. For instance, if Green Bay’s passing statistics are traditionally low against Dallas, Green Bay’s likelihood of success against Dallas is comprised by the fact that the team relies heavily on that kind of play. We determined that passing is important to Green Bay in our judgments, and find that their passing suffers against Dallas in the statistical data that we collected.

It is our hope to use this model to forecast future Super Bowl competitions. Undoubtedly, there will be additional modifications. This basic ideas learned here can be used to forecast the outcome of other competitive games. It appears that the use of intangibles is significantly more important in the forecast than the strict accuracy of the statistics, although one cannot do without the statistics which tell more about performance than about attitude and environment.

65

Two models were used to predict the matches for the top 16 ranked players in the tournament. In the firstmodel, a feedback network modeled past performance. Here, we examined performances of players inprevious tournaments. The factors and weights were then included in the second model.

In the second model, a hierarchy was developed to model the intensities that will be used in the ratingsmodule to rate the players. Past Performance from the network model in the first stage was the firstcriterion added. Another two criteria: Technique and Conditioning were also included.

Prediction:

7 of the top 8 players were correctly predicted to meet in the final rounds of the tournament with the finalbetween Sampras and Chang. In reality, the final was a match between Moya and Sampras, with the topseed winning the outcome. As Moya was ranked 58th in the world prior to the start of the tournament, hewas not even included in the model.

Prediction of the 1997 Australian Tennis Open

66

Sampras 0.658Chang 0.638Becker 0.516Agassi 0.512Ivanisevic 0.483Krajicek 0.460Muster 0.468Courier 0.462Kafelnikov 0.438Martin 0.422Washington 0.421Enqvist 0.398Ferreira 0.374Rios 0.366Costa 0.334mantilla 0.329

67

Hong Kong Competes with Singapore and somewhat less with Tokyo

as Financial Center in Asia in the 21st Century

Gang Hu (Tianjin), Chia-Shuan Huang (Taiwan), Hong Li (Beijing), Thomas Saaty (Pittsburgh), Torsten Schmidt (Germany), and Yu-Chan Wang (Taiwan).

68

The PurposeThe purpose of this project is to study the potential impact imposed through the takeover of Hong Kong by China in 1997. The analysis focuses on the following questions:

• What set of criteria does an Asian location have to meet in order to be a Financial Center?

• Which city is the best candidate for the Financial Center in the Asia-Pacific region in 1996?

• What is the most likely policy of the Chinese government towards Hong Kong after 1997?

• What impact does the Chinese policy have towards Hong Kong as a Financial Center?

• Which city is the most likely candidate to be the Financial Center is the Asia-Pacific region in the year 2000?

69

The ApproachThese five questions are studied with the methodology and technique provided by a combination of the AHP and ANP. A dual-model approach was developed. The first model, the “Financial Center model” which is an ANP model, was used to examine the first two of the above questions. The second model, the “Mainland China Policy model” is an AHP model, used to focus on the third question above to generate a policy package most likely to be adopted by the Chinese government. Based on changed in the political, economic, and social environments incurred by the estimated policy package, the “Financial Center model” was re-evaluated. The fourth and fifth questions above are thus answered.

The two models complement one another because:

1. The Financial Center model provides the relevant factors for a focused examination under the China model in order to find the relevant factors which may be changed by the Chinese government, and

2. The China model provides a package of feasible (for mainland China) and likely policies to be adopted by the Chinese government after 1997. Based on the package of policies, a second evaluation of the Financial Center model was made in order to estimate the future status of Hong Kong as a Financial Center.

70

Influencing Factors

A).Economic-Benefits:1. Geographic advantage.2. Free flow of information.3. Free flow of people.4. Free flow of capital.5. Internationalization.6. Investment.7. Educated workforce.8. Convertible currencies.9. Assistance from government.11. Modern infrastructure.12. Deregulated market.

B).Political-Benefits:1. Efficient government.2. Independent legal system.3. Assistance from government.4. Free flow of people.5. Free flow of information.

C).Social-Benefits:1. Free flow of people.2. Free flow of information.3. Educated workforce.4. Open culture.5. Internationalized language.6. Availability of businessprofessionals.

D).Economic-Costs:1. Labor cost.2. Corruption.3. Protection from government.4. Operating cost.5. Tax.

E).Political-Costs:

1. Tax.2. Corruption.3. Protection from government.

F).Social-Costs:1. Environment.2. Corruption.3. Protection from government.

G).Economic-Opportunities:1. Investment.2. Access to potential market.3. Regional economic growth,membership of internationalorganizations (GATT.WTO).

H).Political- Opportunities:1. Political credit.2. Investment.3. Membership of internationalorganization (GATT,WTO).

I).Social-Opportunities:1. Social wealth.2. Access to potential market.

J).Political-Risks:1. Political instability.2. Instability of local government.3. Political restriction.

K).Economic-Risks:1. Instability of local financial market.2. Inflation.3. Competition from local business.

L).Social-Risks:1. Industry resistance.2. Public industry.3. Instability of local society.

71

*

*

Benefits Control Model Opportunities Control Model

Costs Control Model Risks Control Model

The Set of Four Control Hierarchies

72

Cos

tsB

enef

its

73

Opp

ortu

nitie

sR

isks

74

Economic Benefits Sub-Model

75

There are twelve supermatrices associated with the complete model. With each of these supermatrices is associated a cluster priority matrix, a weighted supermatrix, and a limiting supermatrix from which the priorities of the three contending centers are derived. These twelve sets of priorities are weighted by the priorities of the corresponding control criteria and summed to obtain the final ranking.

Results

76

The output from the first Financial Center model

We assume that all the situation will remain the same after 1997. In other words, themain land China government will adopt a set of feasible policies toward Hong Kong. Based onthis assumption, we made the judgments. After synthesis, we got the results below:

Benefits

Economic Political Social

Hong Kong 0.4131 0.5034 0.4416

Singapore 0.2836 0.1503 0.2164

Tokyo 0.3033 0.3465 0.342

CostsEconomic Political Social

Hong Kong 0.2393 0.1922 0.2519Singapore 0.2804 0.3625 0.1803Tokyo 0.4803 0.4453 0.5678

OpportunitiesEconomic Political Social


RisksEconomic Political Social


Alternatives Rank (B*O)/(C*R)Hong Kong 1 1.6498Singapore 2 0.906Tokyo 3 0.5338

The overall result is listed below:

It is clear that Hong Kong has the highest priority, which means if mainland Chinagovernment adopt all the policies described above toward Hong Kong, it will remain to be thefinancial center in the Asia-Pacific region.

77

Likely Policies Followed by ChinaAffecting the Future of Hong Kong

About 50 potential Chinese policies were identified and ranked in a hierarchy. The most likely policies were identified and the network sub-models were re-assessed given this information. The hierarchy and the policies are shown next.

78

Sample Hierarchy for Assessing Benefit Intensities

79

Policy Rating

80

Optimal and most likely policies1 free flow of information 02 free flow of people 03 educated workforce +4 convertible currency +5 deregulated market 06 assistance from government +7 inflation +8 independent legal system 09 political restrcitions 0

10 instability of local society +11 availability of business professionals +12 public insecurity +13 corruption +14 tax +15 protectionist barrier 016 investment +17 political credit +18 access to potential market +

The output from the Chinese policies model

We picked 18 different factors (in the Financial Center model) which are highlydependent on the policies of the mainland China government. For each of the factors, we dividedit into three situations(positive +, mutual 0, negative -), which denote the different Chinesepolicies toward it. And then, we put them into the China government model(absolute hierarchymodel, including four sub-model: benefits, costs, opportunities and risks). After synthesis, wegot the overall score for each policy. Based on the scores, we draw the optimal and most likelypolicies package(it is shown below).

81

The output from the second Financial Center model

Based on the optimal and most likely policies package we got, we made another set ofjudgments for the Financial Center model. This is, with the assumptions we have made, anestimation of the location of the financial center in the Asian-Pacific region. The results arelisted below:

BenefitsEconomic Political Social


CostsEconomic Political Social


OpportunitiesEconomic Political Social


RisksEconomic Political Social


Alternatives Rank (B*O)/(C*R)Hong Kong 1 1.1822Singapore 2 1.1093Tokyo 3 0.5949

The overall result is as below

We can see that Hong Kong can still maintain the financial center status after 1997, butthe gap between Hong Kong and other cities is much smaller. Especially, Singapore becomesvery competitive.

82

Economic Benefits

Local: Sing Toky Hong assi free conv mode good dere

Singapore 0 0 0 0.3196 0.1692 0.1396 0.1692 0.3333 0.2081

Tokyo 0 0 0 0.122 0.4434 0.5278 0.4434 0.3333 0.1311

Hong Kong 0 0 0 0.5584 0.3874 0.3325 0.3874 0.3333 0.6608

assistance from government 0.0538 0.0459 0.0501 0 0 0 0 0

free flow of people 0.044 0.0526 0.0369 0 0 0 0 0

convertible currency 0.0379 0.0796 0.0625 0 0 0 0 0

modern infrastructure 0.0843 0.189 0.0925 0 0 0 0 0

good auditing systems 0.105 0.0801 0.0619 0 0 0 0 0

deregulated market 0.0367 0.0296 0.1166 0 0 0 0 0

geographic advantages 0.1713 0.1599 0.1593 0 0 0 0 0

free flow of information 0.0168 0.0837 0.0594 0 0 0 0 0

free flow of capital 0.1389 0.0917 0.0928 0 0 0 0 0

educated workforce 0.0602 0.0996 0.0537 0 0 0 0 0

internationalized language 0.0961 0.0283 0.0555 0 0 0 0 0

investment from outside 0.1551 0.06 0.1588 0 0 0 0 0

Original Economic Benefits Sub-Model Supermatrix(Truncated to save space)

83

Economic Benefits

Weighted: Sing Toky Hong assi free conv mode good dere

Singapore 0 0 0 0.3196 0.1692 0.1396 0.1692 0.3333 0.2081

Tokyo 0 0 0 0.122 0.4434 0.5279 0.4434 0.3333 0.1311

Hong Kong 0 0 0 0.5584 0.3874 0.3325 0.3874 0.3333 0.6608

assistance from government 0.0538 0.0459 0.0501 0 0 0 0 0

free flow of people 0.044 0.0526 0.0369 0 0 0 0 0

convertible currency 0.0379 0.0796 0.0625 0 0 0 0 0

modern infrastructure 0.0843 0.189 0.0925 0 0 0 0 0

good auditing systems 0.105 0.0801 0.0619 0 0 0 0 0

deregulated market 0.0367 0.0296 0.1166 0 0 0 0 0

geographic advantages 0.1713 0.1599 0.1593 0 0 0 0 0

free flow of information 0.0168 0.0837 0.0594 0 0 0 0 0

free flow of capital 0.1389 0.0917 0.0928 0 0 0 0 0

educated workforce 0.0602 0.0996 0.0537 0 0 0 0 0

internationalized language 0.0961 0.0283 0.0555 0 0 0 0 0

investment from outside 0.1551 0.06 0.1588 0 0 0 0 0

Weighted Economic Benefits Sub-Model Supermatrix(Truncated to save space)

84

Economic Benefits

Synthesized: Global Sing Toky Hong assi free conv mode good dere

Singapore 0.2836 0.2836 0.2836 0.2836 0.2836 0.2836 0.2836 0.2836 0.2836

Tokyo 0.3033 0.3033 0.3033 0.3033 0.3033 0.3033 0.3033 0.3033 0.3033

Hong Kong 0.4131 0.4131 0.4131 0.4131 0.4131 0.4131 0.4131 0.4131 0.4131

assistance from government 0.0499 0.0499 0.0499 0.0499 0.0499 0.0499 0.0499 0.0499 0.0499

free flow of people 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437

convertible currency 0.0607 0.0607 0.0607 0.0607 0.0607 0.0607 0.0607 0.0607 0.0607

modern infrastructure 0.1194 0.1194 0.1194 0.1194 0.1194 0.1194 0.1194 0.1194 0.1194

good auditing systems 0.0796 0.0796 0.0796 0.0796 0.0796 0.0796 0.0796 0.0796 0.0796

deregulated market 0.0676 0.0676 0.0676 0.0676 0.0676 0.0676 0.0676 0.0676 0.0676

geographic advantages 0.1629 0.1629 0.1629 0.1629 0.1629 0.1629 0.1629 0.1629 0.1629

free flow of information 0.0547 0.0547 0.0547 0.0547 0.0547 0.0547 0.0547 0.0547 0.0547

free flow of capital 0.1055 0.1055 0.1055 0.1055 0.1055 0.1055 0.1055 0.1055 0.1055

educated workforce 0.0695 0.0695 0.0695 0.0695 0.0695 0.0695 0.0695 0.0695 0.0695

internationalized language 0.0588 0.0588 0.0588 0.0588 0.0588 0.0588 0.0588 0.0588 0.0588

investment from outside 0.1278 0.1278 0.1278 0.1278 0.1278 0.1278 0.1278 0.1278 0.1278

Limiting Economic Benefits Sub-Model Supermatrix(Truncated to save space)

85

Economic Benefits

Synthesized Local:

Singapore 0.2836

Tokyo 0.3033

Hong Kong 0.4131

assistance from government 0.0499

free flow of people 0.0437

convertible currency 0.0607

modern infrastructure 0.1194

good auditing systems 0.0796

deregulated market 0.0675

geographic advantages 0.1629

free flow of information 0.0547

free flow of capital 0.1055

educated workforce 0.0695

internationalized language 0.0588

investment from outside 0.1278

Normalized by Cluster - Results from Limiting Economic Benefits Sub-Model Supermatrix

86

The Result• The first result from the Financial Center model:

•If the Chinese government is able to maintain the current status of Hong Kong, Hong Kong would still be the Financial Center is the Asia-Pacific region in 2000.

• The first result from the Mainland China Policy model:

•For interests of the mainland Chinese government, no negative policy should be adopted towards Hong Kong after 1997. A careful and sensitive approach towards the future Hong Kong policy is suggested by this result, which is also reinforced by the next result.

• The second result from the Financial Center model:

•Although Hong Kong may still be the best choice for a Financial Center, Singapore will become a strong competitor for the Center in 2000.

87

Conclusions1) Based on the first output of our Financial Center model, we can see that if all conditions remain the same, in other words, if China adopts all the positive policies toward Hong Kong, in other words if the Chinese government is able to maintain or even improve the current status of Hong Kong, it is quite sure that Hong Kong will remain one of the important financial centers in the Asia-Pacific region.

2) Among the influencing factors of the financial center status, many of them are dependent directly on the government’s policies. Therefore, Hong Kong’s future as a financial center is highly dependent on the political attitude of the Chinese government.

3) Based on the result of our mainland China policy model, we found, among the 18 factors, the Chinese government should adopt positive policies on 12 of them, and mixed policies on 6 of them. In other words, for the interests of China itself (not Hong Kong), China should avoid implementing negative policies, as defined in this study towards Hong Kong as a financial center.

4) Based on the second output of the Financial Center model, Hong Kong will maintain its financial status after 1997. But at the same time, Singapore will become very competitive. Therefore, our conclusion is that if Chinese government adopts rational policies toward Hong Kong as estimated in this study, Hong Kong will remain the number one financial center of the Asian-Pacific region. But at the same time, the position of Hong Kong as a financial center will be weakened. If any negative policies are implemented, Singapore will become the number one financial center of this Asia-Pacific region followed by Hong Kong.

88

The eigenvectors of the paired comparison matrices are each part of a column of the supermatrix. The supermatrix may not be column stochastic. Its column blocks would be weighted by the priorities of the clusters to render the matrix stochastic. The supermatrix must now be raised to powers to capture all the interactions and feedback among its elements. What is desired is its limiting power

limW k

k

The power of a matrix is function of that matrix. Entire functions (series expansion converges for all values) of a matrix can be represented by the formula:

Wk = n

i=1 k

i

II(jI-W)jiII(j-i)ji

if the eigenvalues are distinct, or if they are not then by:

Wk = m

i=1

1 d mi-1

(mi-1)! d mi-1k

i (I-W)-1

nII (- i)i=1nII (- i)i=mi+1

= i

One is the largest eigenvalue of a stochastic matrix. This follows from

max max i

n

j=1

aij

and the sum on the right is equal to the one for a column stochastic matrix. It is obvious that the moduli of the remaining eigenvalues of a stochastic matrix are less than or equal to one.

One is a simple eigenvalue if the matrix is positive. It can be a multiple eigenvalue or there may be other eigenvalues whose moduli are equal to one if there is a sufficient number of zeros in the matrix so that it is reducible. When the supermatrix has some zero entries, it may be that some power of it is positive and hence the matrix remains positive for still larger powers and is called primitive.

One is a simple eigenvalue of a primitive matrix. One may be a simple eigenvalue whether the matrix is primitive or not or a multiple eigenvalue yet there may not be other eigenvalues whose moduli is equal to one. The powers take on a certain form in the limit for each of these three cases. On the other hand if there are other such roots whose module is one, the powers of the supermatrix would cycle with a period of cyclicity and the limit is given by the same expression in all three cases namely when the supermatrix is imprimitive or when one is a simple or a multiple eigenvalue.

Feedback Measurement as the Limiting Power of the Supermatrix

89

Irreducible Stochastic ( = 1 is a simple root)

W =

No other roots with modulus equal to one(primitive)

Other roots with modulus equal to one(imprimitive with cyclicity c).

Case APrimitive if trace is positive.Raise W to powers.All columns the same and any column can also beobtained as the solution of the eigenvalueproblem Ww = w.

Case A

)())((1 1 cc WWIWIc 2c

90

Reducible Stochastic

W =

No other roots with modulus equal to one Other roots with modulus equal to one (cyclicwith cyclicity c).

= 1Simple

Case B

normalizedWIAdjoWI)1(

)int()1(

)1(1)(

Case B


= 1multiple

Case C

11

)(

)(

1

1

01 |)(

)(

)(

)(

!)1(

1

11

k

n

knn

k

k WIkn

nn

Case C


The desired outcome for Case C can often be obtained by introducing loops at all sinks and raising thematrix to limiting powers.

91

C o m p u t a t i o n a l l y , t h e f o r e g o i n g c l a s s i f i c a t i o n m a y b e s i m p l i f i e d a l o n g t h e f o l l o w i n g l i n e s . D e f i n e m a x =

1 . W e h a v e :

P r o p e r

| i | < 1 i > 1A p r i m i t i v e s t o c h a s t i c m a t r i x i s p r o p e r

I m p r o p e r

| i | 1 ( f o r s e v e r a l i )R o o t s o f u n i t y o f c y c l i c i t y c .

1 = 1 s i m p l e r o o t

1 = 1 m u l t i p l e r o o t

o f m u l t i p l i c i t y n 1

( 1 )F u l l y R e g u l a r

T h e i n d e x k = 1 i n t h e d i a g o n a l p r i m i t i v e b l o c km a t r i c e s o f t h e n o r m a l f o r m

)1(

)int(

)1(

)1()( 1

WIAdjoWI

N o r m a l i z e t h e c o l u m n s o f t h e a d j o i n t t o g e t W

.W h e n W i s p r i m i t i v e o n e c a n s i m p l y r a i s e W t ov e r y l a r g e p o w e r s o n a p e r s o n a l c o m p u t e r .

( 3 )

I f a n d o n l y i f m a t r i c e s A 1 , … , A k i n u p p e r p a r t o fd i a g o n a l o f n o r m a l f o r m a r e p r i m i t i v e

11

)(

)(

0 1

11 |)(

)(

)(

)!(

!)1(

1

11

kn

knn

k

k WIkn

nn

( 2 )

)())((1 1 cc WWIWIc

( 4 )

)())((1 1 cc WWIWIc

A s i m p l e p r a c t i c a l r u l e f o r o b t a i n i n g a l i m i t i n g m a t r i x f o r a g i v e n n b y n n o n n e g a t i v e a n d s t o c h a s t i cs u p e r m a t r i x W i s f i r s t t o t e s t i t f o r i r r e d u c i b i l i t y w i t h t h e c o n d i t i o n ( I + W ) n - 1 > 0 . I f i t i s i r r e d u c i b l e , t h e n m a x = 1 i s s i m p l e a n d o n e o f t h e t w o f o r m u l a s a p p l i e s . I t i s t h e n t e s t e d f o r c y c l i c i t y a n d t h e a n s w e r i so b t a i n e d u s i n g t h e a b o v e .

W h e n a l t e r n a t i v e s d o n o t f e e d b a c k i n t o t h e c r i t e r i a , i t i s b e s t n o t t o i n c l u d e t h e m i n t h e s u p e r m a t r i x . T h er e a s o n i s t h a t i f t h e s u p e r m a t r i x c y c l e s , t h e n t h e a v e r a g e v a l u e w o u l d f i r s t h a v e t o b e c a l c u l a t e d . T h ea v e r a g e w e i g h t s o f t h e c r i t e r i a a r e t h e n u s e d t o w e i g h t t h e a l t e r n a t i v e s i n a s e p a r a t e h i e r a r c h y .

92

ANP PROJECTS1996 United States Presidential ElectionA Day at the Races: Predicting a Harness Race at the Meadows: An Application of the ANPA Prediction of Opportunities for Job Growth by U.S. RegionAlternative Fuels for AutomobilesAn ANP Approach for Commodity Markets Demand/Supply Ratio ModelAnalysis of the Market for 32-Bit Operating SystemsBridge Management DecisionChoosing the Best Location for Permanent Storage of High-Level Nuclear WasteCommodity MarketsConvocation CenterCorporate Market Value in the Computer IndustryCorporate Restructuring at ChryslerCorporate Strategies for CompetitorsCrime and PunishmentDisney America: Should Disney Build a Theme Park?Given $10 Million, What Would be the Best Allocation to Each of the Proposed Programs thatContribute to Decreasing Gang Activity?Health Insurance SystemsHow to Implement Flex TimeJustify the Existence of the Economic Black MarketLake Levels and Flow ReleasesManagement Consulting ModelMarket Share Predictions for Aqueous Intra-Nasal SteroidsMedical Center: Strategic Planning with the ANPMergers and AcquisitionsMode of Transportation to SchoolModeling a Reservoir Operations for Managing of Ecological InterestsMulti-Objective Decision Making Analysis with Engineering and Business Applications

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ANP REFERENCES cont’dNBA Playoffs for 1991Net Dollar Value for IBM, Apple, Intel and MicrosoftNetwork Analysis of Illegal Drug Marketing in the United StatesPlanning Strategies for Incubator Space using the ANPPredicting the Outcome of Legislative Debate over Superfund ReauthorizationPredicting the Winner of the 1995-1996 NHL Stanley CupPredicting the Winner of the 1996 Chase Championship with the ANPPrediction of 1997 Australian Tennis OpenPrediction of the 1997 Wimbledon Tennis ChampionshipsPrediction of the CPU MarketPrioritizing Flow Alternatives for Social ObjectivesRanking Countries in Telecommunications as a Subset of Locating a Business ProblemStadium Placement and Optimal FundingStrategic Staffing – Extra Care ProvidersStrategies for Improvement at the Joseph M. Katz Graduate School of BusinessTeenage PregnancyTelecommunications Network Design and PerformanceThe Decision to Market Nimbex (new drug) vs. Continuing to Market Tracruim (old drug)The Emerging Information Technologies of the Future: The “Prize” of Firms and IndustriesThe Future of East Central EuropeThe Future of Major League Baseball in Pittsburgh: Strategic Planning with the ANPThe Future of the University of Pittsburgh’s Medical CenterThe Middle EastThe Optimal MBA Program StructureThe Teenage Smoking ProblemTransportation to WorkUnderstanding the Tiananmen Massacre in ChinaWhat will be the worth? (Predicting Average Starting Salaries for MBA Graduates)Where to Invest in Capital Markets

anp slideshow july_2001

Technology

influence of elements

component inner dependence

control hierarchy priorities

kinds of dependence

components outer dependence

number of alternatives

component c4

overall influence