MULTICRITERIA DECISION MAKING

1
MULTICRITERIA DECISION MAKING
MENU 1. Definition 2. Terms for Multicriteria
Decision Making Environment 3. Models for
Multicriteria Decision Making 4. Scaling
Problems 5. Normalisation 6. Simple Additive
Weighting Method 7. Promethee Methods
2

• Multicriteria decision making (MCDM) refers to
  makingdecisions in the presence of multiple,
  usually conflicting criteria.
• Multiple objectives/attributes
• Conflict among criteria
• Incommensurable units
• Design/selection
• Multiattribute decision making (MADM)
• Multiobjective decision making (MODM)

3

• MODM methods possess
• a set of quantifiable objectives
• a set of well defined constraints
• a process of obtaining some tradeoff
  information between the objectives
• MADM methods possess
• limited number of predetermined alternatives
• values of the attributes
• inter- and/or intra-attribute comparisons
• Preference of decision maker
• no preference
• preference on attributes (standard level,
  ordinal, cardinal, etc.)
• preference on alternatives

4

• Terms for MCDM environment
• Criterion measure of effectiveness.
• benefit criterion
• cost criterion
• Attribute means of evaluating the level of an
  objective.
• Objective something to be pursued to its
  fullest.
• Goal is a priori value or level of aspiration.
• Decision matrix
• A A1, A2,,AN
• C C1, C2,,CK

5
Numerical example. Fighter aircraft selection
problem. Attributes C1 maximum speed
(Mach) C2 ferry range (NM) C3 maximum payload
(pounds) C4 purchasing cost ( ? 106) C5
reliability (high - low) C6 maneuverability
(high - low)
6

• Optimal solution (ideal solution, superior
  solution) results in the maximum (minimum) value
  of each of the objective functions simultaneously
  .
• Nondominated solution (efficient solution,
  noninferior solution, Pareto-optimal solution)
  there exists no other solution that will yield
  an improvement in one objective/attribute without
  causing a degradation in at least one other
  objective/attribute.
• Preferred solution is nondominated solution
  selected as the final choice by the decision
  maker utilising his/her preference information.

7

• Models for MADM
• Noncompensatory models do not permit tradeoffs
  between attributes.
• Compensatory models permit tradeoffs between
  attributes.
• Classification
• 1. Multiattribute utility theory
• there exists function aggregates the criteria,
• decision maker wishes to maximise it
• 2. Outranking methods
• pairwise comparison of the alternatives
• 3. Interactive methods
• calculation stage selection of an alternative
• discussion stage decision maker provides
  supplementary information about his/her
  preferences

8
Scaling Problems
9

• Normalisation
• 1. Linear scale transformation
• benefit criterion

• 0 lt rnk ? 1
• cost criterion

10
(No Transcript)
11
2. Transformation which maps criteria values to
interval 0,1

• benefit criterion

• cost criterion

12
(No Transcript)
13
Simple Additive Weighting Method
A A1, A2,,AN C C1, C2,,CK W (w1,
w2,,wK)
14

• normalisation of weights

15
Example Fighter aircraft selection problem.
16
W 0.2, 0.1, 0.1, 0.1, 0.2, 0.3 A1 0.2 ? 0.8
0.1 ? 0.56 0.1 ? 0.95 0.1 ? 0.82 0.2 ?
0.71 0.3 ? 1.0 0.835 A2 0.2 ? 1.0 0.1 ?
1.0 0.1 ? 0.86 0.1 ? 0.69 0.2 ? 0.43 0.3
? 0.56 0.709 A3 0.2 ? 0.72 0.1 ? 0.74
0.1 ? 1.0 0.1 ? 1.0 0.2 ? 1.0 0.3 ? 0.78
0.852 A4 0.2 ? 0.88 0.1 ? 0.67 0.1 ? 0.95
0.1 ? 0.90 0.2 ? 0.71 0.3 ? 0.56
0.738 ? A3 is selected
17
Promethee Methods
alternatives A a,b,c,d, attributes C
f1, f2,,fK weights W (w1, w2,,wK)
18

• ex. I a should be recommended
• ex. II a and b are incomparable
• ex. III a should be recommended
• ex. IV a and b are indifferent
• ex. V a and b are indifferent

19

• The amplitudes of the deviations between the
  criteria values should be considered.
• The scaling effects should be eliminated.
• Incomparability should not be excluded in case
  of pairwise comparisons.
• An appropriate methods should include no
  technical parameters having no economical
  significance.
• An appropriate methods should be simple
  understandable by the decision maker.

20

• Promethee methods
• Step 1. Generalised Criteria
• f is benefit criterion
• dominance relation
• f(a) gt f(b) ? a is preferred to b
• f(a) f(b) ? a is indifferent to b
• P(a,b) preference function
• a is not better than b with respect to criterion
  ? P(a, b) 0
• a is "slightly" better than b with respect to
  criterion ? P(a, b) ? 0
• a is "strongly" better than b with respect to
  criterion ? P(a, b) ? 1
• a is "strictly" better than b with respect to
  criterion ? P(a, b) 1

P(a,b)
1
d f(a) - f(b)
21
Type I Usual criterion

• Type II Quasi criterion
• q - is a parameter defining an indifference area

P(a,b)
1
d f(a) - f(b)
q
22

• Type III Criterion with linear preference
• p - is a parameter defining a strict preference
  area

Type IV Level criterion
23
Type V Criterion with linear preference and
indifference interval
P(a,b)
1
d f(a) - f(b)
p
q

• Type VI Gaussian criterion
• s - is a parameter of Gaussian distribution
  (q lt s lt p )

P(a,b)
1
d f(a) - f(b)
p
24

• Step 2. Outranking Graph
• for each pair of alternatives a and b and for
  each criterion k calculate
• dk fk(a) - fk(b), Pk(a,b)
• P(a,b) w1P1(a,b) w2P2(a,b) ... wKPK(a,b)

• if weights of all criteria are the same

25
(No Transcript)
26
Step 3. Decision Aid 1. Positive outranking flow
2. Negative outranking flow
A
A
c
c
d
d
b
b
...
...
a
?(a)
a
?-(a)
27

• Promethee I gives partial rank (preference,
  indifference and incomparability)
• Promethee II gives complete rank
• (preference, indifference)
• Net outranking flow
• ?(a) ?(a) - ?-(a)
• ? (a) gt ?(b) ? a outranks b
• ? (a) ?(b) ? a indifferent b

28
Example. Location of an electric power
plant. Alternatives a1 Italy a2 Belgium a3
Germany a4 UK a5 Portugal a6
France Attributes C1 Manpower for running the
plant C2 Power (in Megawatt) C3 Construction
costs (in million ) C4 Annual maintenance costs
(in million ) C5 Ecology number of villages to
evacuate C6 Safety level
29
(No Transcript)
30
? A5 is selected
31
Literature 1. Multiple Attribute Decision
Making, Methods and Applications, A
state-of-the-Art Survey, C-L. Hwang and
K.Yoon, Springer-Verlag, 1981. 2. The Promethee
Methods for MCDM, J.P.Brans, B.Mareschal, Vrije
Universitet, Brussel, 1989. 3. "How to Select
and How to Rank Projects The Promethee
Method", European Journal of Operational
Research, 24, 228-238. J.P.Brans, Ph. Vincke,
B.Mareschal,