DECISION THEORY
Preference Programming
Ratio-based Efficiency Analysis
incomplete information
in value tree analysis
Add new / revise
preference statements
n
j
no
comparison of DMUs under incomplete information
about the output and input weights
N
value of outputs
Efficiency of DMUk Ek
value of inputs
j
V ( x ) vi ( xi )
i 1
E1
E2
yes
Recommendations
by decision rules
Overall value and
ranking intervals
u y
(0,0,1)
Display of results and
recommendations
E3 / E0 = 1.6
n nk
n 1
M
x2
v
x2
x
m mk
yes
Decision
3 4 12
, ,
19 19 19
w3 w2
interval methods:
Preference Assessment by Imprecise
Ratio Statements (PAIRS)
Interval AHP
Preference Ratios in Multiattribute Evaluation (PRIME)
Interval SMART/SWING
w2
S
0.5
DMU2
E1 / E*=0.6
DMU3
ranking 1
x1
ranking 2
DMU1
ranking 3
ranking 4
DMU4
DMU1 DMU2 DMU3 DMU4
x1
new flexibility in dynamic problems
x
1
dominance relations
attainable rankings
3 2 6
, ,
11 11 11
1 2 2
, ,
5 5 5
(0,1,0)
E0
efficiency bounds
S
w3 3w2
1 4 4
, ,
9 9 9
w3 2w1
u1/u2
x*
x*
S
E1 / E*[0.6,1.0]
E2 / E*[0.9,1.0]
...
E3 / E0[1.2,1.6]
E4 / E0[1.0,1.3]
w3
w3 4w1
Goal set (intervals): ([l1,u1],[l2,u2])
E3 / E0 = 1.2
E4
Interpretation
of results
Goal point: (g1,g2)
E*
E1 / E*=1
E3
no
Adequate ?
extension of a goal point to a goal set
m 1
Consistent ?
Dominance
relations
Interval goal programming
w1 0.25w2
sensitivity of university rankings
w1
(1,0,0)
w1 1.5w2
(0,0,1)
- what if slightly different weigths were applied?
w3
w3 w1
Robust rankings
w3 w2
incomplete ordinal information:
w1
r (3,1, 2)
r (1,2,3)
r (2,1,3)
(1,0,0)
Different weighting would
likely yield a better ranking
t2
Alternative
Utility
20 % interval
Strategy 0
0.474
Strategy 1
0.697
Strategy 2
0.694
Strategy 3
0.748
Strategy 4
0.628
incomplete ordinal
no information
t3
tk
time
global sensitivity analysis
exact weights
30 % interval
r (1,3,2)
Rank Inclusion in Criteria Hierarchies (RICH)
RICHER = RICH with Extended Rankings
t1
Costs
Other cancers
Political cost
Soc.-Psych Negative
Soc.-Psych Positive
Thyroid cancer
(0,1,0)
w2
origins of procedural and behavioral biases
Number of attribute
levels effect in
conjoint analysis
Hierarchical
weighting leads to
steeper weigths
Range effect
Systems
Analysis Laboratory
Updated 17.05.2010
Weighting methods
yield different
weights
Weights
derived
from
ordinal
infromation
Averages over a
group yield even
weights
Normalization
Division of
attributes changes
weights
Rank reversal in
AHP
Splitting bias
10th
442nd
web-sites and selected publications
http://www.decisionarium.hut.fi
A. Salo and A. Punkka: Ranking intervals and dominance relations for Ratio-based Efficiency Analysis, manuscript, 2010
A. Punkka and A. Salo: Preference Programming with incomplete ordinal information, manuscript, 2010
A. Salo and R. P. Hmlinen: Preference Programming - multicriteria weighting models under incomplete information,
in: Zopounidis and Pardalos (eds.): Handbook of Multicriteria Decision Analysis, Springer, New York, 2010
J. Liesi, P. Mild and A. Salo: Preference programming for robust multi-criteria portfolio modeling and project selection,
Eur. J. Oper. Res. (EJOR), 2007
J. Mustajoki, R. P. Hmlinen and M. R. K. Lindstedt: Using intervals for global sensitivity and worst case analyses in multiattribute value trees, EJOR, 2006
A. Salo and A. Punkka: Rank inclusion in criteria hierarchies, EJOR, 2005
J. Mustajoki, R. P. Hmlinen and A. Salo: Decision Support by Interval SMART/SWING - Incorporating Imprecision in the SMART and SWING Methods,
Decision Sciences, 2005
A. Salo and R. P. Hmlinen: Preference ratios in multiattribute evaluation (PRIME), IEEE Syst. Man Cybernetics, 2001
R. P. Hmlinen and J. Mntysaari: A dynamic interval goal programming approach to the regulation of a lake-river system, J. Multi-Crit. Dec. Anal., 2001
A. Salo and R. P. Hmlinen: Preference programming through approximate ratio comparisons, EJOR, 1995
A. Salo and R. P. Hmlinen: Preference assessment by imprecise ratio statements, Operations Research, 1992