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Quantitative model for impact measurement system
National Technical University of Athens
Identification of impact factors & their relationship
Effect of a factor on impact: Direct (vertical) effect Indirect (horizontal) effect Self-interaction effect
Structuring the factors hierarchically
Cognitive map Cause & effect diagram Tree diagram
Quantifying the effect of the factors on impact
Comparing factors Ai, which one does have stronger impact and how strong?
Analytic Hierarchy Processsee Saaty, T.L., 1980, “The Analytic Hierarchy Process”,
McGraw-Hill, New York
Output: Indicators Prioritization
Further Indicator Analysis
For the most influential factors: Paasche’s Index Laspeyres’ Index Decomposition Analysis
Pilot Implementation: Tourism Factors identified:
Hotel rooms available (A) Hotel rooms occupied (B) Tourists Arrivals (C) Touristic currency (D)
StructureAll are one-level sub factors
Criteria of factors selection Importance Acquisition Difficulty
Analytic Hierarchy Process (I) Create pair wise comparison matrixes for
each criteria, for example:
Importance A B C D
A 1 a1 a2 a3
B a1-1 1 a4 a5
C a2-1 a4
-1 1 a6
D a3-1 a5
-1 a6-1 1
where ai [1,…,9] ( Z) and declare importance (preference level)
Analytic Hierarchy Process (II)
Sum all the values in each column Divide the values in each column by
the corresponding column sum Find the average of each row
(decimal)
Analytic Hierarchy Process (III)
The following matrix (M1) is now available:
Tourism Importance Difficulty
A x11 x12
B x21 x22
C x31 x32
D x41 x42
Analytic Hierarchy Process (IV)
Create same-structured pair wise comparison matrix for the criteria for factors selection:
Tourism Importance Difficulty
Importance 1 b1
Difficulty b1-1 1
Analytic Hierarchy Process (V) After following the same process (AHP
II), the following matrix M2 would be available:
Tourism Row average
Importance y1
Difficulty y2
Analytic Hierarchy Process (VI)
The product M=M1xM2 quantifies the prioritization of the factors (indicators)…
Tourism Ranking
A ra
B rb
C rc
D rd
Further Indicator Analysis
Assume that the AHP suggested the indicators Hotel rooms occupied (B) Tourists Arrivals (C) Touristic currency (D)
Now we can move on to further analysis
Paasche’s Index
Paasche’s Index of touristic movement:
where S(t): touristic currency at year t, CPI: consumer price index
CPIStS
CPI
tSPV
)0()(
)()(
Laspeyres’ Index
Laspeyres’ index of price changes:
Where Vj(t)T: Arrivals at year t, tourist category j σj(t)T: Touristic currency per arrival at year t
(tourist category j) : Touristic currency per arrival at year
t (tourist category j) with prices of year ‘0’
n
jTjTj
n
jTjTj
V
tV
1
1
)0()0(
)(ˆ)0(
Tj t)(̂
Philosophy of Deconstruction (Jacques Derrida)…
n
jTTj
n
jTjTj
T
n
jTjTj
n
jTjTj
Tn
jTjTj
n
jTjTj
tV
tV
tV
tV
ttV
tVV
tV
tS
1
11
1
1
1
)()0(
)()0(
)(
)()0(
)()(
)()0()0(
)(ˆ)0(
)(
Decomposition Analysis (I) Which is the overall change of the
composition of night stays from year 0 to year t, broken into hotel category, country of origin and month?
An objective meter is:
where H: hotel, C: country & M: month
H C M HCM
HCMHCMHCM
ttA
)0(
)(ln)(
Decomposition Analysis (II) number of night stays in
hotel category H, tourists from country C, for all months
cell’s ‘HC●’ participation in total night stays
participation of month ‘M’ in the night stays of cell ‘HC●’
M
HCMHC NN
N
NHCHC
HC
HCMHCHCM N
N
Decomposition Analysis (III)
Quantifies the change in the composition of the total night stays in hotel categories and countries of origin
Quantifies the change in the composition of each ‘HC●’ cell in months
H C HC
HCHCHC
ttA
)0(
)(ln)(
MHCHCO
HCHCOHC
HCMHCHCM
ttA
)0(
)(ln)(
Summary
Finally, the measurement of Olympic impact on each system is modelled through:
Identification of the main impact factors & their relationship structure
Determinable quantification (prioritization) of the factors impact on the system through Analytic Hierarchy Process
Advanced analysis of the most influential indicators
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