Transcript Analytic Network Process (ANP) slides

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.
1
Linear Hierarchy
Goal
Criteria
component,
cluster
(Level)
Subcriteria
element
Alternatives
A loop indicates that each
element depends only on itself.
2
Feedback Network with components having
Inner and Outer Dependence among Their Elements
C4
C1
Feedback
Arc from component
C4 to C2 indicates the
outer dependence of the
elements in C2 on the
elements in C4 with respect
to a common property.
C2
C3
Loop in a component indicates inner dependence of the elements in that component
with respect to a common property.
3
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.
4
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
5
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 the
alternatives with respect to each of these are then combined by forming the ratios:
Benefits x Opportunities
Costs x Risks
to obtain their final overall priorities for a decision.
6
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 to
a 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.
7
Functional - Structural Criteria
Independence - Dependence
1--Criteria completely independent from alternatives - Absolute
Measurement, 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.
8
Why ANP?
• The power of the Analytic Network Process (ANP) lies in its use of
ratio 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.
9
Mutual Influence Among Several Elements
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.
Unidirectional Influence
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.
10
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.
11
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.
12
The Supermatrix
Take 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 Supermatrix
All 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.
13
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 Answer
The 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.
14
Networks and the Supermatrix
c1
e11e12
c1
e11
e12
c2
e1n1
e21e22
cN
e2n2
eN1eN2
eNnN
W11
W12
W1N
W21
W22
W2N
WN1
WN2
WNN
e1n1
W=
c2
e21
e22
e2n2
cN
eN1
eN2
eNuN
15
where
(j1)
Wi1
Wij =
(j1)
Wi2
(j1)
Wini
(j2)
Wi1
(j2)
Wi2
(j2)
Wini
(jnj)
Wi1
(jnj)
Wi2
(jnj)
Wini
16
Supermatrix of a Hierarchy
0
W=
0
0
0
0
0
W21 0
0
0
0
0
0 W32 0
0
0
0
0
0
0
0
0
0
Wn-1, n-2 0
0
0 Wn, n-1 I
17
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Wk=
Wn,n-1 Wn-1,n-2 … W32 W21
Wn,n-1 Wn-1,n-2 ... W32
Wn,n-1 Wn-1,n-2 Wn,n-1 I
for k>n-1
18
The School Hierarchy as Supermatrix
Goal
Learning
Friends
School life
Vocational training
College preparation
Music classes
Alternative A
Alternative B
Alternative C
Goal
0
0.32
0.14
0.03
0.13
0.24
0.14
0
0
0
Learning
0
0
0
0
0
0
0
0.16
0.59
0.25
Friends
0
0
0
0
0
0
0
0.33
0.33
0.34
School life Vocational trainingCollege preparation Music classes
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
0.45
0.77
0.25
0.69
0.09
0.06
0.5
0.09
0.46
0.17
0.25
0.22
A
0
0
0
0
0
0
0
1
0
0
B
0
0
0
0
0
0
0
0
1
0
C
0
0
0
0
0
0
0
0
0
1
Limiting Supermatrix & Hierarchic Composition
Goal
Learning
Friends
School life
Vocational training
College preparation
Music classes
Alternative A
Alternative B
Alternative C
Goal
0
0
0
0
0
0
0
0.3676
0.3781
0.2543
Learning
0
0
0
0
0
0
0
0.16
0.59
0.25
Friends
0
0
0
0
0
0
0
0.33
0.33
0.34
School life Vocational trainingCollege preparation Music classes
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
0.45
0.77
0.25
0.69
0.09
0.06
0.5
0.09
0.46
0.17
0.25
0.22
A
0
0
0
0
0
0
0
1
0
0
B
0
0
0
0
0
0
0
0
1
0
C
0
0
0
0
0
0
0
0
0
1
19
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.
20
Structural Adjust
After & 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.
21
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.
22
A Feedback System with Two Components
Flood
Control
Low
Level
Recreation
Intermediate
Level
HydroElectric
Power
High
Level
23
1) Which level is best for flood control?
Flood Control
Low
Low
1
Medium 1/5
High
1/7
Med
5
1
1/4
High Eigenvector
7
.722
4
.205
1
.073
Consistency Ratio = .107
3) Which level is best for power generation?
Power Generation
Low
Low
1
Medium 5
High
9
Med
1/5
1
5
High Eigenvector
1/9
.058
1/5
.207
1
.735
2) Which level is best for recreation?
Recreation
Low
Low
1
Medium 7
High
5
Med
1/7
1
1/3
High Eigenvector
1/5
.072
3
.649
1
.279
Consistency Ratio = .056
Consistency Ratio = .101
24
Flood Control
Recreation
Hydro-Electric
Power
2) At
Intermediate
Level, which
attribute is
satisfied best?
Flood Control
Recreation
Hydro-Electric
Power
Low Level Dam
F
R
E
1
3
5
1/3
1
3
1/5
1/3
1
Eigenvector
.637
.258
.105
1) At Low
Level, which
attribute is
satisfied best?
Consistency Ratio = .033
Flood Control
Recreation
Hydro-Electric
Power
F
1
5
9
Intermediate Level Dam
F
R
E
1
1/3
1
3
1
3
1
1/3
1
Eigenvector
.200
.600
.200
Consistency Ratio = .000
High Level Dam
R
E
1/5
1/9
1
1/4
4
1
Eigenvector
.060
.231
.709
3) At High
Level, which
attribute is
satisfied best?
Consistency Ratio = .061
25
The six eigenvectors were then introduced as
columns of the following stochastic supermatrix.
F
F
R
E
L
M
H
0
0
0
.722
.205
.073
R
E
L
M
H
0
0
0
.072
.649
.279
0
0
0
.058
.207
.735
.637
.258
.105
0
0
0
.200
.600
.200
0
0
0
.060
.231
.709
0
0
0
One must ensure that all columns sum to unity exactly.
26
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
F
R
E
L
M
H
0
0
0
.223
.372
.405
0
0
0
.223
.372
.405
0
0
0
.223
.372
.405
.241
.374
.385
0
0
0
.241
.374
.385
0
0
0
.241
.374
.385
0
0
0
27
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.
28
Choosing a Car: Foreign or Domestic?
Cost
A
E
J
A
E
J
1
1/5
1/3
5
1
3
3
1/3
1
Eigenvector
.637
.105
.258
American
C
R
D
C
1
1/3
1/4
R
D
3
1
1
4
1
1
Consistency Ratio = .033
Repair Cost
A
E
J
A
E
1
1/5
1/2
J
5
1
3
2
1/3
1
A
E
J
A
E
J
Eigenvector
European
C
R
D
.582
.109
.309
C
R
D
1
1
2
1
1
2
1/2
1/2
1
1
5
3
1/5
1
1/3
1/3
3
1
Eigenvector
.105
.637
.258
Consistency Ratio = .033
.634
.192
.174
Consistency Ratio = .008
Consistency Ratio = .003
Durability
Eigenvector
Eigenvector
.250
.250
.500
Consistency Ratio = .008
Japanese
C
R
D
C
R
D
1
1/2
1
2
1
2
1
1/2
1
Eigenvector
.400
.200
.400
Consistency Ratio = .000
29
Original Supermatrix
C
R
D
A
E
J
C
0
0
0
.637
.105
.258
R
0
0
0
.582
.109
.309
D
0
0
0
.105
.637
.258
A
.634
.192
.174
0
0
0
E
.250
.250
.500
0
0
0
J
.400
.200
.400
0
0
0
Limiting Supermatrix
C
R
D
A
E
J
C
0
0
0
.452
.279
.269
R
0
0
0
.452
.279
.269
D
0
0
0
.452
.279
.269
A
.464
.210
.326
0
0
0
E
.464
.210
.326
0
0
0
J
.464
.210
.326
0
0
0
Choose an American car. Cost is the dominant criterion.
30
Date and Strength of Recovery of U.S. Economy
Primary Factors
Subfactors
Adjustment Period
Required for
Turnaround
Conventional
adjustment
Economic
Restructuring
Consumption (C)
Exports (X)
Investment (I)
Fiscal Policy (F)
Monetary Policy (M)
Confidence (K)
Financial Sector (FS)
Defense Posture (DP)
Global Competition (GC)
3 months
6 months
12 months
24 months
The U.S. Holarchy of Factors for Forecasting Turnaround in Economic Stagnation
31
Table 1: Matrices for subfactor importance relative to primary factors influencing the Timing of Recovery
Panel A: Which subfactor has the greater potential to influence Conventional Adjustment and how strongly?
Consumption
(C)
Exports
(E)
Investment
(I)
Confidence
(K)
Fiscal Policy
(F)
Monetary Policy (M)
C
E
I
K
F
M
Vector
Weights
1
1/7
1/5
5
2
5
7
1
5
5
5
7
5
1/5
1
5
3
5
1/5
1/5
1/5
1
1/5
1
1/2
1/5
1/3
5
1
5
1/5
1/7
1/5
1
1/5
1
0.118
0.029
0.058
0.334
0.118
0.343
Panel B: Which subfactor has the greater potential to influence Economic Restructuring and how strongly?
Financial
Sector
(FS)
Defense
Posture
(DS)
Global
Competition (GC)
FS
DP
GC
Vector
Weights
1
3
3
0.584
1/3
1
3
0.281
1/3
1/3
1
0.135
32
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 A: Relative importance of targeted time periods for
consumption to drive a turnaround
3
6
12
24
Vec. Wts.
3 months
6 months
12 months
24 months
1
5
7
7
1/5
1
5
5
1/7
1/5
1
3
1/7
1/5
1/3
1
.043
.113
.310
.534
Panel C: Relative importance of targeted time periods for
investment to drive a turnaround
3
6
12
24
Vec. Wts.
3 months
6 months
12 months
24 months
1
1
5
5
1
1
5
5
1/5
1/5
1
3
1/5
1/5
1/3
1
.078
.078
.305
.538
Panel E: Relative importance of targeted time periods for
monetary policy to drive a turnaround
3 months
6 months
12 months
24 months
3
6
12
24
1
1/5
1/7
1/7
5
1
1/5
1/7
7
5
1
5
7
7
1/5
1
Vec. Wts.
.605
.262
.042
.091
Panel B: Relative importance of targeted time periods for
exports to drive a turnaround
3
3 months
6 months
12 months
24 months
1
1
5
5
6
1
1
5
5
12
1/5
1/5
1
1
24
1/5
1/5
1
1
Vec. Wts.
.083
.083
.417
.417
Panel D: Relative importance of targeted time periods for
fiscal policy to drive a turnaround
3
6
12
24
Vec. Wts.
3 months
6 months
12 months
24 months
1
1
3
5
1
1
5
5
1/3
1/5
1
1
1/5
1/5
1
1
.099
.087
.382
.432
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 months
6 months
12 months
24 months
1
1/3
1/5
1/5
3
1
1/5
1/5
5
5
1
1/5
5
5
5
1
.517
.305
.124
.054
33
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 A: Financial system restructuring time
3
6
12
24
Vec. Wts.
3 months
6 months
12 months
24 months
1
3
5
7
1/3
1
5
7
1/5
1/5
1
5
1/7
1/7
1/5
1
Panel B: Defense readjustment time
3
6
12
24
.049
.085
.236
.630
3 months
6 months
12 months
24 months
1
3
5
7
1/3
1
5
7
1/5
1/5
1
5
1/7
1/7
1/5
1
Vec. Wts.
.049
.085
.236
.630
Panel C: Global competition adjustment time
3
6
12
24
Vec. Wts.
3 months
6 months
12 months
24 months
1
1
5
5
1
1
5
5
1/5
1/5
1
3
1/5
1/5
1/3
1
.078
.078
.305
.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?
Panel A: 3 Months
CA
R
CA
1
1/5
R
5
1
Vec. Wts.
.833
.167
Panel B: 6 Months
CA
CA 1
R 1/5
R
5
1
Vec. Wts.
.833
.167
Conventional Adjustment
Restructuring
Panel C: 1 Year
CA
CA 1
R
1
R
1
1
Vec. Wts.
.500
.500
CA
R
Panel D: 2 Years
CA
CA 1
R
5
R Vec. Wts.
1/5
.167
1
.833
34
Table 5: The Completed Supermatrix
Conven.
Adjust
Economic.
Restru.
Conven. Economic. Consum.
Adjust Restruc.
Exports
Invest.
Confid.
Fiscal
Policy
Monet.
Policy
Financ.
Sector
Defense
Posture
Global
Compet.
3 mo.
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
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
¦ 0.833 0.833
0.500
0.167
¦
¦ 0.167 0.167
0.500
0.833
+--------------------------
------+
0.118 ¦ 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
¦
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
¦
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
¦
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
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
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
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
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
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
¦
¦
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
¦
¦
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
¦
¦
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

Consum.
6 mo.
1 yr.
 2 years
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
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
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
35
Table 6: The Limiting Supermatrix
Conven. Economic. Consum.
Adjust Restruc.
Conven.
Adjust
Economic
Restru.
Consum.
Exports
Invest.
Confid.
Fiscal
Policy
Monetary
Policy
Financ.
Sector
Defense
Posture
Global
Compet.
3 months
6 months
1 year
 2 years
Exports
Invest.
Confid.
Fiscal
Policy
Monet.
Policy
Financ.
Sector
Defense
Posture
Global
Compet.
3 mo.
6 mo.
1 yr.
 2 years
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


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


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

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

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

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

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

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

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

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

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


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

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

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

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
36
Synthesis/Results
When 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
37
The Strength of Recovery
Primary Factors
Conventional
Adjustment
Subfactors
Consumption (C)
Exports (X)
Investment (I)
Fiscal Policy (F)
Monetary Policy (M)
Confidence (K)
Very Strong
(5.5-6.5% GNP)
Strong
(4.5-5.5% GNP)
Economic
Restructuring
Financial Sector (FS)
Defense Posture (DP)
Global Competition (GC)
Moderate
(3-4.5% GNP)
Weak
(2-3% GNP)
38
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?
Vector
CA
R
Weights
Conventional
Adjustment (CA)
Restructuring (R)
1
5
1/5
1
.167
.833
Panel B: Which subfactor is more important in influencing Conventional Adjustment?
Consumption
(C)
Exports
(E)
Investment
(I)
Confidence
(K)
Fiscal Policy
(F)
Monetary Policy (M)
C
E
I
K
F
M
Vector
Weights
1
1/7
1/3
1
1/7
1/3
7
1
5
5
1
7
3
1/5
1
3
3
5
1
1/5
1/3
1
1/7
1/3
7
1
1/3
7
1
7
3
1/5
1/5
3
1/7
1
0.317
0.037
0.099
0.305
0.035
0.207
Panel C: Which subfactor is more important in influencing Economic Restructuring?
Financial
Sector
(FS)
Defense
Posture
(DS)
Global
Competition (GC)
FS
DP
GC
Vector
Weights
1
1/5
1/3
0.105
5
1
3
0.637
3
1/3
1
0.258
CI = 0.037
39
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 A: Relative likelihood of the strength of recovery if
consumption drives the expansion
V
S
M
W
Vec. Wts.
Very Strong (V)
Strong (S)
Moderate (M)
Weak (W)
1
1
1/5
1/7
1
1
1/5
1/7
5
5
1
1/3
7
7
3
1
.423
.423
.104
.051
Panel B: Relative likelihood of the strength of recovery if
exports drives the expansion
V
Very Strong (V)
Strong (S)
Moderate (M)
Weak (W)
1
1
3
5
S
1
1
3
5
CI = 0.028
M
W
1/3
1/3
1
3
1/5
1/5
1/3
1
Vec. Wts.
.095
.095
.249
.560
CI = 0.016
Panel C: Relative likelihood of the strength of recovery if
investment drives the expansion
V
S
M
W
Vec. Wts.
Panel D: Relative likelihood of the strength of recovery if
confidence drives the expansion
V
S
M
W
Vec. Wts.
Very Strong (V)
Strong (S)
Moderate (M)
Weak (W)
Very Strong (V)
Strong (S)
Moderate (M)
Weak (W)
1
1
3
1/2
1
1
3
1/2
1/3
1/3
1
1/6
2
2
6
1
.182
.182
.545
.091
1
1
1/3
1/5
1
1
1/3
1/5
CI = 0.0
3
3
1/3
1/7
5
5
7
1
.376
.376
.193
.054
CI = 0.101
Panel E: Relative likelihood of the strength of recovery if
fiscal policy drive the expansion
V
S
M
W
Vec. Wts.
Panel F: Relative likelihood of the strength of recovery if
monetary policy drives the expansion
V
S
M
W
Vec. Wts.
Very Strong (V)
Strong (S)
Moderate (M)
Weak (W)
Very Strong (V)
Strong (S)
Moderate (M)
Weak (W)
1
1
5
1
1
1
5
1
1/5
1/5
1
1/5
CI = 0.0
1
1
5
1
.125
.125
.625
.125
1
1
5
3
1
1
5
3
1/5
1/5
1
1/7
1/3
1/3
7
1
.084
.084
.649
.183
CI = 0.101
40
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 A: Relative likelihood of the strength of recovery if
financial sector drives the expansion
V
S
M
W
Vec. Wts.
Very Strong (V)
Strong (S)
Moderate (M)
Weak (W)
1
1
3
5
1
1
3
5
1/3
1/3
1
1/3
1/5
1/5
1/3
1
Panel B: Relative likelihood of the strength of recovery if
defense posture drives the expansion
V
S
M
W
Vec. Wts.
.095
.095
.249
.560
Very Strong (V)
Strong (S)
Moderate (M)
Weak (W)
1
3
5
7
CI = 0.016
1/3
1
3
5
1/5
1/3
1
3
1/7
1/5
1/3
1
.055
.118
.262
.565
CI = 0.044
Panel C: Relative likelihood of the strength of recovery if
global competition drives the expansion
V
S
M
W
Vec. Wts.
Very Strong (V)
Strong (S)
Moderate (M)
Weak (W)
1
1
3
5
1
1
3
5
1/3
1/3
1
1
1/5
1/5
1
1
.101
.101
.348
.449
CI = 0.012
Table 10: Overall Results for Strength of Recovery
% GNP Growth
Very Strong
Strong
Moderate
Weak
(5.5-6.5)
(4.5-.5)
(3-4.5)
(2-3)
% GNP Recovery Rate*
0.108
0.141
0.290
0.461
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.
41
Hamburger Model
Estimating Market Share of Wendy’s, Burger King and McDonald’s
with respect to the single economic control criterion
42
How to Pose the Question to
Make Paired Comparisons
• One must answer questions of the following kind: given
McDonald’s (in the Alternatives cluster) is its economic
strength derived more from Creativity or from Frequency
(both in the Advertising cluster)? Conversely, given
Creativity in the Advertising cluster who is more
dominant, McDonald’s or Burger King?
• Then, again, by comparing the dominance impact of the
clusters of Advertising and Quality of Food on the
economic success of McDonald by weighting and
normalizing we can relate the relative effect of elements in
these different clusters.
43
Hamburger Model Supermatrix
Other
O
t
h
e
r
Q
Ad
C
o
m
p
Quality
Advertising
Competition
Local:
Menu
Cleanli
ness
Speed
Service
Location
Price
Reputa
tion
Take
Out
Portion
Taste
Nutri
tion
Freq
uency
Promo
tion
Creativ
ity
Wendy’s
Burger
King
McDonald’s
Menu Item
Cleanliness
Speed
Service
Location
Price
Reputation
Take-Out
Portion
Taste
Nutrition
Frequency
Promotion
Creativity
Wendy's
Burger King
McDonald’s
0.0000
0.6370
0.1940
0.0000
0.0530
0.1170
0.0000
0.0000
0.2290
0.6960
0.0750
0.7500
0.1710
0.0780
0.3110
0.1960
0.4930
0.0000
0.0000
0.7500
0.0780
0.1710
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.5000
0.2500
0.2500
0.0000
0.0000
0.0000
0.1880
0.0000
0.0000
0.0810
0.7310
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0990
0.3640
0.5370
0.0000
0.5190
0.2850
0.0000
0.0980
0.0000
0.0980
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.5280
0.1400
0.3330
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0950
0.2500
0.6550
0.0000
0.0000
0.0000
0.0000
0.5000
0.0000
0.0000
0.5000
0.8330
0.0000
0.1670
0.1670
0.8330
0.0000
0.0950
0.2500
0.6550
0.1930
0.2390
0.0830
0.0450
0.2640
0.0620
0.0570
0.0570
0.2800
0.6270
0.0940
0.5500
0.3680
0.0820
0.1010
0.2260
0.6740
0.0000
0.0000
0.2900
0.0550
0.6550
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.1960
0.3110
0.4940
0.0000
0.0000
0.0000
0.0000
0.0000
0.8570
0.0000
0.1430
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.2760
0.1280
0.5950
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.6050
0.1050
0.2910
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.5940
0.1570
0.2490
0.3110
0.0000
0.0000
0.0000
0.1960
0.0000
0.4930
0.0000
0.0000
0.0000
0.0000
0.0000
0.5000
0.5000
0.0880
0.1950
0.7170
0.1670
0.0000
0.0000
0.0000
0.0000
0.8330
0.0000
0.0000
0.0000
0.0000
0.0000
0.6670
0.0000
0.3330
0.0880
0.1950
0.7170
0.1350
0.0000
0.0000
0.0000
0.7100
0.0000
0.1550
0.0000
0.0000
0.0000
0.0000
0.8750
0.1250
0.0000
0.1170
0.2680
0.6140
0.1570
0.2760
0.0640
0.0650
0.1420
0.0300
0.2070
0.0590
0.0940
0.2800
0.6270
0.6490
0.0720
0.2790
0.0000
0.2500
0.7500
0.0510
0.1100
0.1400
0.1430
0.2240
0.2390
0.0420
0.0510
0.6490
0.0720
0.2790
0.7090
0.1130
0.1790
0.1670
0.0000
0.8330
0.1590
0.3330
0.0480
0.0240
0.1070
0.0330
0.2230
0.0740
0.5280
0.1400
0.3320
0.6610
0.1310
0.2080
0.2000
0.8000
0.0000
Cluster Priorities Matrix
Cluster:
Other
Quality
Advertising
Competition
Other
0.198
0.066
0.607
0.129
Quality
0.500
0.000
0.000
0.500
Advertising
0.131
0.000
0.622
0.247
Competition
0.187
0.066
0.533
0.215
44
Weighted Supermatrix
Weighted:
Menu
Cleanli
ness
Speed
Service
Location
Price
Reputa
tion
Take
Out
Portion
Taste
Nutri
tion
Freq
uency
Promo
tion
Creativ
ity
Wendy’s
Burger
King
McDonald’s
Menu Item
Cleanliness
Speed
Service
Location
Price
Reputation
Take-Out
Portion
Taste
Nutrition
Frequency
Promotion
Creativity
Wendy's
Burger King
McDonald ‘s
0.0000
0.1262
0.0384
0.0000
0.0105
0.0232
0.0000
0.0000
0.0151
0.0460
0.0050
0.4554
0.1038
0.0474
0.0401
0.0253
0.0636
0.0000
0.0000
0.4544
0.0473
0.1036
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.1974
0.0987
0.0987
0.0000
0.0000
0.0000
0.1138
0.0000
0.0000
0.0490
0.4426
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0391
0.1436
0.2118
0.0000
0.3141
0.1725
0.0000
0.0593
0.0000
0.0593
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.2082
0.0552
0.1313
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0950
0.2500
0.6550
0.0000
0.0000
0.0000
0.0000
0.0990
0.0000
0.0000
0.0990
0.0550
0.0000
0.0110
0.1014
0.5056
0.0000
0.0123
0.0323
0.0845
0.0382
0.0473
0.0164
0.0089
0.0523
0.0123
0.0113
0.0113
0.0185
0.0414
0.0062
0.3338
0.2233
0.0498
0.0130
0.0291
0.0869
0.0000
0.0000
0.1755
0.0333
0.3964
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0773
0.1226
0.1948
0.0000
0.0000
0.0000
0.0000
0.0000
0.4287
0.0000
0.0715
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.1381
0.0640
0.2976
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.6044
0.1049
0.2907
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.5940
0.1570
0.2490
0.0407
0.0000
0.0000
0.0000
0.0257
0.0000
0.0646
0.0000
0.0000
0.0000
0.0000
0.0000
0.3110
0.3110
0.0217
0.0482
0.1771
0.0219
0.0000
0.0000
0.0000
0.0000
0.1091
0.0000
0.0000
0.0000
0.0000
0.0000
0.4149
0.0000
0.2071
0.0217
0.0482
0.1771
0.0177
0.0000
0.0000
0.0000
0.0930
0.0000
0.0203
0.0000
0.0000
0.0000
0.0000
0.5444
0.0778
0.0000
0.0289
0.0662
0.1517
0.0293
0.0516
0.0120
0.0121
0.0265
0.0056
0.0387
0.0110
0.0062
0.0185
0.0413
0.3455
0.0383
0.1485
0.0000
0.0537
0.1611
0.0095
0.0205
0.0261
0.0267
0.0418
0.0446
0.0078
0.0095
0.0428
0.0047
0.0184
0.3773
0.0601
0.0953
0.0359
0.0000
0.1788
0.0297
0.0622
0.0090
0.0045
0.0200
0.0062
0.0417
0.0138
0.0348
0.0092
0.0219
0.3519
0.0697
0.1107
0.0429
0.1718
0.0000
Synthesized:
Global
Menu
Cleanli
ness
Speed
Service
Location
Price
Reputa
tion
Take
Out
Portion
Taste
Nutri
tion
Freq
uency
Promo
tion
Creativ
ity
Wendy’s
Burger
King
McDonald’s
Menu Item
Cleanliness
Speed
Service
Location
Price
Reputation
Take-Out
Portion
Taste
Nutrition
Frequency
Promotion
Creativity
Wendy's
Burger King
McDonald’s
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
0.0234
0.0203
0.0185
0.0072
0.0397
0.0244
0.0296
0.0152
0.0114
0.0049
0.0073
0.2518
0.1279
0.1388
0.0435
0.0784
0.1579
Limiting Supermatrix
{
Relative local weights: Wendy’s= 0.156, Burger King =0.281, and McDonald’s=0.566
45
Validation
The same problem worked as a simple and
a complex hierarchy and as a feedback network.
46
Hamburger Model
Synthesized Local Cont’d:
Synthesized Local:
Other
Quality
Menu Item
Cleanliness
Speed
Service
Location
Price
Reputation
Take-Out
Portion
Taste
Nutrition
Simple Hierarchy
(Three Level)
0.132
0.115
0.104
0.040
0.224
0.138
0.167
0.086
0.494
0.214
0.316
Advertising
Competition
Complex Hierarchy
(Several Levels)
Frequency
Promotion
Creativity
Wendy’s
Burger King
McDonald’s
Feedback
Network
0.485
0.246
0.267
0.156
0.281
0.566
Wendy’s
0.3055
0.1884
0.156
Actual
Market
Share
0.1320
Burger King
0.2305
0.2689
0.281
0.2857
McDonald’s
0.4640
0.5427
0.566
0.5823
47
48
Strategic Planning
for the Future of the
University of Pittsburgh Medical Center
Using the Analytic Network Process(ANP)
49
Evaluate Strategies for the University Health Network to Compete in a Managed Care Environment
Benefits Control Model
Costs Control Model
Benefits
Costs
Social
Social
Benefits
Network
Submodel
Economic Political
Economic
Benefits
Network
Submodel
Political
Benefits
Network
Submodel
Social
Social
Costs
Network
Submodel
Risks
Economic Political
Economic
Costs
Network
Submodel
Risks Control Model
Political
Costs
Network
Submodel
Social
Economic Political
Social
Risks
Network
Submodel
Economic
Risks
Network
Submodel
Political
Risks
Network
Submodel
50
List of Clusters and Elements (Not all the Clusters appear in all 9 of the sub-models.)
Cluster Names
Clients
Cluster Elements
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
51
*Strategies apperar in every sub-moadel as alternatives of choice
Clusters and Elements in the Economic Benefits Sub-model
52
Benefits & Costs
Predicting the Superbowl Winner ‘96 & ‘97
53
Pre-start (early December 1995)
Wild Card Games
All predictions correct except for two games below.
Team
Benefits
Costs
B/C
Miami vs.
Buffalo
0.701
0.745
0.612
0.590
1.145
1.263
Indianapolis vs.
San Diego
0.687
0.660
0.622
0.650
1.105
1.015
Detroit vs.
Philadelphia
0.625
0.695
0.636
0.580
0.983
1.198
Atlanta vs.
Green Bay
0.590
0.785
0.612
0.515
0.964
1.524
Second Round
Pittsburgh vs.
Buffalo
0.740
0.704
0.581
0.605
1.274
1.164
Indianapolis vs.
Kansas City
0.695
0.750
0.590
0.575
1.178
1.304
Kansas kicker missed 3 field goals & ruined them.
No way to know his ailments that day.
Green Bay vs.
San Francisco
0.755
0.751
0.590
0.585
1.280
1.284
Was too close to determine the winner.
Green Bay won.
Philadelphia vs.
Dallas
0.732
0.759
0.641
0.576
1.142
1.318
Divisional Playoffs
Dallas vs.
Green Bay
0.742
0.756
0.540
0.561
1.370
1.350
Pittsburgh vs.
Indianapolis
0.699
0.741
0.555
0.598
1.260
1.240
The Super Bowl
Dallas vs.
Pittsburgh
0.761
0.748
0.728
0.735
1.045
1.018
54
Pre-start (early December 1996)
The first predictions were wrong
on three games which then
required revision.
Playoff Predictions
Pre-Start
Predicted Outcomes
AFC
Team
Benefits
Costs
B/C
Winner
Las Vegas
Wild Cards
Indianapolis
Pittsburgh
0.588
0.592
0.489
0.477
1.2
1.24
Pittsburgh
Jacksonville
Buffalo
0.601
0.594
0.501
0.487
1.2
1.22
Buffalo
Wrong prediction.
Pittsburgh
New England
0.609
0.516
0.479
0.419
1.27
1.23
Pittsburgh
Wrong prediction.
Buffalo
Denver
0.551
0.62
0.488
0.447
1.13
1.39
Denver
Wrong prediction.
Pittsburgh
Denver
0.633
0.686
0.523
0.5318
1.21
1.29
Denver
Philadelphia
San Francisco
0.557
0.621
0.467
0.444
1.19
1.4
San Francisco
Minnesota
Dallas
0.545
0.571
0.488
0.476
1.12
1.2
Dallas
San Francisco
Green Bay
0.585
0.685
0.5
0.46
1.17
1.49
Green Bay
Dallas
Carolina
0.522
0.51
0.494
0.448
1.06
1.14
Carolina
Carolina
Green Bay
0.511
0.643
0.498
0.521
1.03
1.23
Green Bay
0.618
0.556
0.457
0.476
1.35
1.17
Green Bay
Conference Finals
NFC
Wild Cards
Conference Finals
Super Bowl
Green Bay
Denver
55
Post-start (before Conference Finals)
Playoff Predictions
A gains error in one game.
Predicted Outcomes
AFC
Team
Benefits
Costs
B/C
Winner
Actual
Conference Finals
Jacksonville
Denver
0.545
0.612
0.488
0.447
1.12 Denver
1.37
Jacksonville
New England
0.576
0.645
0.515
0.519
1.12 New Eng
1.24
NE
0.627
0.653
0.554
0.506
1.13
1.29 Green Bay
Jax
Super Bowl
New England
Green Bay
56
The Benefits
The Costs
57
Benefits Supermatrix
Local Weights
Offense
QB Ability
Running
Emotions Play Above
Ability
Coaching
Emotional State
Outside Home Field
Road Ahead
Teams
Dallas
Green Bay
Offensive
Global
0.0297
0.3140
Local
0.0864
0.9136
0.0037
0.0235
0.0923
0.0433
0.3670
0.1227
0.0039
0.0309
0.1962
0.7724
0.1055
0.8945
0.9693
0.0308
QB Ability
Emotions
Running
Play Above
1.0000
Outside
Coaching
0.8000
0.2000
Emotions
1.0000
Home Field
.8000
.2000
Road Ahead
Teams
Dallas
1.0000
Green Bay
0.8000
0.2000
1.0000
0.7500
0.2500
1.0000
1.0000
1.0000
1.0000
0.7500
0.2500
1.0000
1.0000
1.0000
0.2000
0.8000
1.0000
CLUSTER WEIGHTS
Offense
Offense
0.0000
Emotions 0.2176
Outside
0.0914
Team
0.6910
Emotions
0.2449
0.0000
0.0902
0.6648
Outside
0.6442
0.0852
0.0000
0.2706
Teams
0.7172
0.1947
0.0881
0.0000
58
Weighted Supermatrix
Cluster Weights
Offense
QB Ability
Running
Emotions Play Above
Ability
Coaching
Emotional State
Outside Home Field
Road Ahead
Teams
Dallas
Green Bay
Offensive
Global
0.0297
0.3140
Local
0.0864
0.9136
0.0037
0.0235
0.0923
0.0433
0.3670
0.1227
0.0039
0.0309
0.1962
0.7724
0.1055
0.8945
0.9693
0.0308
QB Ability
Emotions
Running
Play Above
0.7308
Coaching
0.1959
0.0490
Outside
Emotions
0.7308
Home Field
0.5154
0.1288
Teams
Road Ahead
Dallas
Green Bay
0.7125
0.1781
0.6442
0.0852
0.0639
0.0213
1.0000
1.0000
0.2692
0.0902
0.4986
0.1662
0.6885
0.3115
0.0538
0.2153
0.2706
0.0219
0.0875
0.2706
Limiting Benefits Supermatrix
Offensive
Offense
Emotions
Outside
Teams
QB Ability
Running
Play Above
Ability
Coaching
Emotional State
Home Field
Road Ahead
Dallas
Green Bay
Emotions
Global
0.0297
0.3140
Local
0.0297
0.3140
QB Ability
0.0297
0.3140
0.0037
0.0235
0.0923
0.0433
0.3670
0.1227
0.0039
0.0037
0.0235
0.0923
0.0433
0.3670
0.1227
0.0039
0.0037
0.0235
0.0923
0.0433
0.3670
0.1227
0.0039
Running
0.0297
0.3140
0.0037
0.0235
0.0923
0.0433
0.3670
0.1227
0.0039
Play Above
0.0297
0.3140
0.0037
0.0235
0.0923
0.0433
0.3670
0.1227
0.0039
Outside
Teams
Coaching
0.0297
0.3140
Emotions
0.0297
0.3140
Home Field
0.0297
0.3140
0.0037
0.0235
0.0923
0.0433
0.3670
0.1227
0.0039
0.0037
0.0235
0.0923
0.0433
0.3670
0.1227
0.0039
0.0037
0.0235
0.0923
0.0433
0.3670
0.1227
0.0039
Road Ahead
0.0297
0.3140
0.0037
0.0235
0.0923
0.0433
0.3670
0.1227
0.0039
Dallas
0.0297
0.3140
Green Bay
0.0297
0.3140
0.0037
0.0235
0.0923
0.0433
0.3670
0.1227
0.0039
59
0.0037
0.0235
0.0923
0.0433
0.3670
0.1227
0.0039
Costs Supermatrix
Local Weights
Offense
History
Outside
Teams
Road Ahead
Immature Players
Not Full Strength
Cinderella
Play Bey Ability
Past Failures
Mental State
Weather
Dallas
Green Bay
Offensive
Global
0.1529
0.0000
0.2261
0.0011
0.2002
0.0738
0.0121
0.1683
0.1653
0.0000
Local
0.4034
0.0000
0.5966
0.0041
0.7278
0.2683
0.0673
0.9332
1.0002
0.0000
Emotions
Immature Not Full
Road Ahead Players Strength
Outside
Cinderella
1.0000
Play
beyond
Past
Mental
Ability Failures State
0.8000
0.8000
0.2000
1.0000 0.2000
1.0000
0.8333
0.1667
0.8571
0.1429
1.0000
Teams
Weather
1.0000
0.7500
0.2500
1.0000
1.0000
1.0000
Dallas Green Bay
0.7500
0.2000
0.2500 0.8000
0.7500
0.2500
1.0000
0.8333 1.000
0.1667
1.0000
CLUSTER WEIGHTS
Offense
Offense
0.0000
Emotions 0.0877
Outside
0.1392
Team
0.7731
Emotions
0.3614
0.0000
0.0650
0.5736
Outside
0.6267
0.0936
0.0000
0.2797
Teams
0.7172
0.1947
0.0881
0.0000
60
Weighted Supermatrix
Cluster Weighted
Offense
History
Outside
Teams
Road Ahead
Immature Players
Not Full Strength
Cinderella
Play Bey Ability
Past Failures
Mental State
Weather
Dallas
Green Bay
Offensive
Global
0.1529
0.0000
0.2261
0.0011
0.2002
0.0738
0.0121
0.1683
0.1653
0.0000
Local
0.4034
0.0000
0.5966
0.0041
0.7278
0.2683
0.0673
0.9332
1.0002
0.0000
Emotions
Immature Not Full
Road Ahead Players Strength
Outside
Cinderella
1.0000
Play
beyond
Past
Mental
Ability Failures State
0.2891
0.5014
0.0723
1.0000 0.1253
0.0936
0.8333
0.1667
1.0000
Teams
Weather
0.6267
0.0702
0.0234
0.8571
0.1429
0.2797
Dallas Green Bay
0.5379
0.1434
0.1793 0.5738
0.1947
0.0734
0.0147
0.1460
0.0487
0.0881
0.2797
Limiting Costs Supermatrix
Offensive
Offense
History
Outside
Teams
Road Ahead
Immature Players
Not Full Strength
Cinderella
Play Bey Ability
Past Failures
Mental State
Weather
Dallas
Green Bay
Emotions
Global
Local
0.1529 0.1529
Immature Not Full
Road Ahead Players Strength
0.1529
0.1529 0.1529
0.0000 0.0000
0.0000
0.0000 0.0000
0.2261
0.0011
0.2002
0.0738
0.0212
0.1683
0.1653
0.0000
0.2261
0.0011
0.2002
0.0738
0.0212
0.1683
0.1653
0.0000
0.2261
0.0011
0.2002
0.0738
0.0212
0.1683
0.1653
0.0000
0.2261
0.0011
0.2002
0.0738
0.0212
0.1683
0.1653
0.0000
0.2261
0.0011
0.2002
0.0738
0.0212
0.1683
0.1653
0.0000
Outside
Cinderella
0.1529
Play
beyond
Ability
0.1529
Past
Mental
Failures State
0.1529 0.1529
Teams
Weather
0.1529
Dallas
0.1529
Green Bay
0.1529
0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0000
0.2261
0.0011
0.2002
0.0738
0.0212
0.1683
0.1653
0.0000
0.2261
0.0011
0.2002
0.0738
0.0212
0.1683
0.1653
0.0000
0.2261
0.0011
0.2002
0.0738
0.0212
0.1683
0.1653
0.0000
0.2261
0.0011
0.2002
0.0738
0.0212
0.1683
0.1653
0.0000
0.2261
0.0011
0.2002
0.0738
0.0212
0.1683
0.1653
0.0000
0.2261
0.0011
0.2002
0.0738
0.0212
0.1683
0.1653
0.0000
0.2261
0.0011
0.2002
0.0738
0.0212
0.1683
0.1653
0.0000
61
Benefits Intensity Priorities
Quarterback (0.030):
Average (0.091)
Running Game (0.314):
Average (0.084)
Good (0.281)
Good
(0.211)GB
Play Above Potential (0.004):
Average (0.075)
Good (0.229)D
Coaching Ability
to Inspire (0.023):
Not A lot (0.078)
Emotional State (0.092):
Apathy (0.082)
Home Field
Advantage (0.043):
Neutral (0.105)
The Road Ahead (0.367):
No Effect (0.082)
Somewhat
(0.205)D
Mediocre (0.236)
High Ability
(0.691)GB,D
High Ability
(0.705)D
High Play Level (0.696)GB
Heroic
(0.717)GB
Excitement
(0.682)GB,D
Some Effect
(0.258)GB
Significant
Effect (0.637)D
Some Effect
(0.236)D
Very
Confident (0.682)GB
Dallas’ Effect on the Ultimate
Outcome (0.123):
Medium (0.280)
Low Effect (0.094)
Greatly
Influenced (0.627)GB,D
Green Bay’s Effect on the Ultimate
Outcome (0.004):
Medium (0.258)
Not Much (0.105)
Greatly
Influenced (0.637)GB,D
Costs Intensity Priorities
The Road Ahead (0.153):
Low Effect (0.085)
Somewhat (0.271) GB,D High Effect (0.644)
Not at Full Strength
(0.226):
Few Injuries (0.091)
Some
Injuries (0.218)
Big Injury
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):
Good History (0.082) GB
Mixed Past (0.236)D
Can’t get
it Gone (0.682)
Mental State
of Preparedness (0.012):
Ready (0.122)GB
May be
Hurt (0.230)D
Unready (0.648)
Cinderalla Team (0.001): Good Team
Not Cinderalla (0.082) GB,D Lucky (0.236)
It’s Midnight (0.682)
Weather Sensitivity (0.168): Small
High
Anything 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)
Veterans (0.082)D
Young
Players (0.682)
Some
Experience (0.236)GB
Each of the two teams obtained a total score from the intensities.
62
Illustrative Considerations in the Evaluation
of 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.
63
For the Costs Model:
- 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.
Conclusion
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.
64
Prediction of the 1997 Australian Tennis Open
Two models were used to predict the matches for the top 16 ranked players in the tournament. In the first
model, a feedback network modeled past performance. Here, we examined performances of players in
previous 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 ratings
module to rate the players. Past Performance from the network model in the first stage was the first
criterion 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 final
between Sampras and Chang. In reality, the final was a match between Moya and Sampras, with the top
seed winning the outcome. As Moya was ranked 58th in the world prior to the start of the tournament, he
was not even included in the model.
65
Sampras
Chang
Becker
Agassi
Ivanisevic
Krajicek
Muster
Courier
Kafelnikov
Martin
Washington
Enqvist
Ferreira
Rios
Costa
mantilla
0.658
0.638
0.516
0.512
0.483
0.460
0.468
0.462
0.438
0.422
0.421
0.398
0.374
0.366
0.334
0.329
66
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).
67
The Purpose
The 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?
68
The Approach
These 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.
69
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 business
professionals.
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 international
organizations (GATT.WTO).
H).Political- Opportunities:
1. Political credit.
2. Investment.
3. Membership of international
organization (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.
70
The Set of Four Control Hierarchies
Benefits Control Model
Opportunities Control Model
*
Risks Control Model
Costs Control Model
*
71
72
73
Economic Benefits Sub-Model
74
Results
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.
75
The output from the first Financial Center model
We assume that all the situation will remain the same after 1997. In other words, the
main land China government will adopt a set of feasible policies toward Hong Kong. Based on
this assumption, we made the judgments. After synthesis, we got the results below:
Opportunities
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
Economic
0.4096
0.2874
0.303
Political
0.3813
0.2935
0.3252
Social
0.4511
0.2227
0.3261
Economic Political
0.3086
0.4278
0.2186
0.4387
0.4728
0.1335
Social
0.4387
0.2365
0.3248
Risks
Costs
Hong Kong
Singapore
Tokyo
Hong Kong
Singapore
Tokyo
Economic Political
0.2393
0.1922
0.2804
0.3625
0.4803
0.4453
Social
0.2519
0.1803
0.5678
Hong Kong
Singapore
Tokyo
The overall result is listed below:
Alternatives
Hong Kong
Singapore
Tokyo
Rank
(B*O)/(C*R)
1
1.6498
2
0.906
3
0.5338
It is clear that Hong Kong has the highest priority, which means if mainland China
government adopt all the policies described above toward Hong Kong, it will remain to be the
financial center in the Asia-Pacific region.
76
Likely Policies Followed by China
Affecting 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.
77
Sample Hierarchy for Assessing Benefit Intensities
78
Policy Rating
79
The output from the Chinese policies model
We picked 18 different factors (in the Financial Center model) which are highly
dependent on the policies of the mainland China government. For each of the factors, we divided
it into three situations(positive +, mutual 0, negative -), which denote the different Chinese
policies toward it. And then, we put them into the China government model(absolute hierarchy
model, including four sub-model: benefits, costs, opportunities and risks). After synthesis, we
got the overall score for each policy. Based on the scores, we draw the optimal and most likely
policies package(it is shown below).
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Optimal and most likely policies
free flow of information 0
free flow of people 0
educated workforce +
convertible currency +
deregulated market 0
assistance from government +
inflation +
independent legal system 0
political restrcitions 0
instability of local society +
availability of business professionals +
public insecurity +
corruption +
tax +
protectionist barrier 0
investment +
political credit +
access to potential market +
80
The output from the second Financial Center model
Based on the optimal and most likely policies package we got, we made another set of
judgments for the Financial Center model. This is, with the assumptions we have made, an
estimation of the location of the financial center in the Asian-Pacific region. The results are
listed below:
Benefits
Hong Kong
Singapore
Tokyo
Opportunities
Economic Political
0.3814
0.4435
0.2992
0.2187
0.3194
0.3378
Social
0.4238
0.2306
0.3456
Costs
Hong Kong
Singapore
Tokyo
Hong Kong
Singapore
Tokyo
Economic
Political
0.4096
0.3813
0.2874
0.2935
0.303
0.3252
Social
0.4511
0.2227
0.3261
Economic
Political
0.4278
0.4278
0.4387
0.4387
0.1335
0.1335
Social
0.4387
0.2365
0.3248
Risks
Economic
Political
0.2966
0.2814
0.2561
0.3161
0.4475
0.4025
Social
0.3045
0.1657
0.5298
Hong Kong
Singapore
Tokyo
The overall result is as below
Alternatives
Hong Kong
Singapore
Tokyo
Rank
(B*O)/(C*R)
1
1.1822
2
1.1093
3
0.5949
We can see that Hong Kong can still maintain the financial center status after 1997, but
the gap between Hong Kong and other cities is much smaller. Especially, Singapore becomes
very competitive.
81
Original Economic Benefits Sub-Model Supermatrix
(Truncated to save space)
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
0.0538
0.0459
0.0501
0
0
0
0
0
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
assistance from government
free flow of people
82
Weighted Economic Benefits Sub-Model Supermatrix
(Truncated to save space)
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
0.0538
0.0459
0.0501
0
0
0
0
0
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
assistance from government
free flow of people
83
Limiting Economic Benefits Sub-Model Supermatrix
(Truncated to save space)
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
84
Normalized by Cluster - Results from Limiting
Economic Benefits Sub-Model Supermatrix
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
85
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.
86
Conclusions
1) 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.
87
Feedback Measurement as the Limiting Power of the Supermatrix
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:
II(jI-W)
Wk =
n

i=1

k
i
ji
II(j-i)
ji
if the eigenvalues are distinct, or if they are not then by:
m
Wk =

i=1
1
d mi-1
(mi-1)! d mi-1
ki (I-W)-1
n
II (- i)
i=1
n
II (- i)
i=mi+1
 = i
One is the largest eigenvalue of a stochastic matrix. This follows from
n
 max  max
i
a
ij
j=1
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.
88
Irreducible Stochastic (  = 1 is a simple root)
W =
No other roots with modulus equal to one
(primitive)
Case A
Primitive if trace is positive.
Raise W to powers.
All columns the same and any column can also be
obtained as the solution of the eigenvalue
problem Ww = w.
Other roots with modulus equal to one
(imprimitive with cyclicity c).
Case A
1
( I  W c )( I  W ) 1 (W c ) c  2
c
89
Reducible Stochastic
W =
No other roots with modulus equal to one
=1
Simple
Case B
( I W ) 1 (1)  Adjoint(I  W ) normalized
(1)
(1)
=1
multiple
Case C
n1
n1  ( 1) k
k 0
n1! ( n1  k ) ( )
(I  W )  k 1 | 1
( n1 )
( n1  k )  ( )
Other roots with modulus equal to one (cyclic
with cyclicity c).
Case B
1
( I  W c )( I  W ) 1 (W c ) c  2
c
Case C
1
c2
( I  W c )( I  W ) 1 (W c ) 
c
The desired outcome for Case C can often be obtained by introducing loops at all sinks and raising the
matrix to limiting powers.
90
Computationally, the foregoing classification may be simplified along the following lines. Define
1. We have:
Proper
| i | < 1 i > 1
1 = 1 simple root
A primitive stochastic matrix is proper
(1)
Fully Regular
The index k=1 in the diagonal primitive block
matrices of the normal form
max =
Improper
| i |  1 (for several i)
Roots of unity of cyclicity c.
(2)
1
( I  W c )( I  W ) 1 (W c ) 
c
( I  W ) 1 (1) Adjoint(I  W )

(1)
(1)
Normalize the columns of the adjoint to get W.
When W is primitive one can simply raise W to
very large powers on a personal computer.
(3)
1 = 1 multiple root If and only if matrices A1,…, Ak in upper part of
of multiplicity n1
diagonal of normal form are primitive
n1
n1  (1) k
k 0
(4)
1
( I  W c )( I  W ) 1 (W c ) 
c
n1! ( n1  k ) ( )
(I  W )  k 1 | 1
(n1  k )! ( n1 ) ( )
A simple practical rule for obtaining a limiting matrix for a given n by n nonnegative and stochastic
supermatrix W is first to test it for irreducibility with the condition (I+W)n-1 > 0. If it is irreducible, then
max = 1 is simple and one of the two formulas applies. It is then tested for cyclicity and the answer is
obtained using the above.
When alternatives do not feed back into the criteria, it is best not to include them in the supermatrix. The
reason is that if the supermatrix cycles, then the average value would first have to be calculated. The
average weights of the criteria are then used to weight the alternatives in a separate hierarchy.
91
ANP PROJECTS
1996 United States Presidential Election
A Day at the Races: Predicting a Harness Race at the Meadows: An Application of the ANP
A Prediction of Opportunities for Job Growth by U.S. Region
Alternative Fuels for Automobiles
An ANP Approach for Commodity Markets Demand/Supply Ratio Model
Analysis of the Market for 32-Bit Operating Systems
Bridge Management Decision
Choosing the Best Location for Permanent Storage of High-Level Nuclear Waste
Commodity Markets
Convocation Center
Corporate Market Value in the Computer Industry
Corporate Restructuring at Chrysler
Corporate Strategies for Competitors
Crime and Punishment
Disney America: Should Disney Build a Theme Park?
Given $10 Million, What Would be the Best Allocation to Each of the Proposed Programs that
Contribute to Decreasing Gang Activity?
Health Insurance Systems
How to Implement Flex Time
Justify the Existence of the Economic Black Market
Lake Levels and Flow Releases
Management Consulting Model
Market Share Predictions for Aqueous Intra-Nasal Steroids
Medical Center: Strategic Planning with the ANP
Mergers and Acquisitions
Mode of Transportation to School
Modeling a Reservoir Operations for Managing of Ecological Interests
Multi-Objective Decision Making Analysis with Engineering and Business Applications
92
ANP REFERENCES cont’d
NBA Playoffs for 1991
Net Dollar Value for IBM, Apple, Intel and Microsoft
Network Analysis of Illegal Drug Marketing in the United States
Planning Strategies for Incubator Space using the ANP
Predicting the Outcome of Legislative Debate over Superfund Reauthorization
Predicting the Winner of the 1995-1996 NHL Stanley Cup
Predicting the Winner of the 1996 Chase Championship with the ANP
Prediction of 1997 Australian Tennis Open
Prediction of the 1997 Wimbledon Tennis Championships
Prediction of the CPU Market
Prioritizing Flow Alternatives for Social Objectives
Ranking Countries in Telecommunications as a Subset of Locating a Business Problem
Stadium Placement and Optimal Funding
Strategic Staffing – Extra Care Providers
Strategies for Improvement at the Joseph M. Katz Graduate School of Business
Teenage Pregnancy
Telecommunications Network Design and Performance
The 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 Industries
The Future of East Central Europe
The Future of Major League Baseball in Pittsburgh: Strategic Planning with the ANP
The Future of the University of Pittsburgh’s Medical Center
The Middle East
The Optimal MBA Program Structure
The Teenage Smoking Problem
Transportation to Work
Understanding the Tiananmen Massacre in China
What will be the worth? (Predicting Average Starting Salaries for MBA Graduates)
Where to Invest in Capital Markets
93