MULTICRITERION DECISION MODELS MCDM

1
MULTICRITERION DECISION MODELS(MCDM)
2
COURSE CONTENT

• Chapter 1 Introduction
• MCDM overview
• MCDM fundamentals efficiency
• MCDM fundamentals methodology
• Preference / weights
• Chapter 2 MADM methods
• Analytic Hierarchy Process
• Multi-attribute Value/Utility Theory
• ELECTRE and PROMETHEE Methods
• Aspiration Level Interactive Method
• Other Outranking Methods
• Chapter 3 MODM Methods
• Global Criterion Method
• Maximum Effectiveness Method
• Goal Programming
• Compromise Programming and Compromise Constraint
  Method
• Interactive Models Step Method and Game
  Theoretic Method
• Parametric Method
• Chapter 4 MCDM applications and case studies

3
EVALUATION

• MIDTERM EXAM 30
• FINAL EXAM 50
• TERM PROJECT (GROUP WORK) 20
• TOTAL 100

4
Text books

• Lecture notes
• Tabucanon, M.T., Multiple Criteria Decision
  Making in Industry, Elsevier, 1988.
• Reference books
• Vincke, P., Gassner, M. and Roy, B.,
  Multicriteria Decision-aid, John Wiley, 1989.
• Zeleny, M., Multiple Criteria Decision Making,
  McGraw-Hill Book Co., 1982.
• Chankong, V. and Haimes, Y.Y., Multiobjective
  Decision Making Theory and Methodology,
  North-Holland, 1983.
• Vincke, P., Gassner, M. and Roy, B.,
  Multicriteria Decision-aid, John Wiley, 1989.
• Steuer, R.E., Multiple Criteria Optimization
  Theory, computation, and Application, Joth Wiley,
  1986.
• Szidanovszky, F., Gershon, M.E. and Duckstein,
  L., Techniques for Multiobjective Decision Making
  in Systems Management, Elsvier, 1986.

5
AN MCDM TREE
6

DM INCREASES
IMPLEMENTATIONAL TASK INCREASES
ORGANIZATION
7
Decision Making

• Process of selection
• Set of alternatives
• Criteria

8
DECISION MAKING
IMPLEMENTATION
9
DECISION MAKER
ANALYST
10
DECISION MAKER
ANALYST
IMPLEMENTOR
11
C
B
A
PROFIT / SALES
12
C
B
QUALITY
A
13
C
LONGEVITY
B
A
14
LONGEVITY
QUALITY
PROFIT
15
TRADITIONAL MONO-CRITERION APPROACH

• A well-defined set of feasible alternatives
• A real valued function defines on the feasible
  set precisely reflecting the preferences of the
  decision maker

16
A WELL FORMULATED MONO-CRITERION MATHMATICAL
PROBLEM

• Find x in X such that
• f(x) f (x) ? x ?X

17
PREFERENCE

• DM prefer x over x iff f(x) gt f(x)
• DM is indifferent between x and x iff
• f(x) f(x)

18
HIERARCHY OF OBJECTIVES
Socio- economic purpose
mission
Overall objectives of the organization
(long-range, strategic)
More specific overall objectives
Division objectives
Department and unit objectives
Individual objectives Performance Personal
development objectives
19
MULTIPLE OBJECTIVES ARE ALL AROUND US

• To manage an organization is to balance a
  variety of needs and goals. And this
  requires multiple objectives
• - PETER F. DRUCKER -

20
EXAMPLES OF DECISION MAKING INVOLVING
MULTIPLE CRITERIA

• A company may wish to find the optimal
  allocation of products to the different
  markets that simultaneously provides for high
  profit and big market share
• Decide the material allocations to the different
  major production facilities for a least
  manufacturing cost and high facility utilization.
• A consumer buying a car will pay attention to a
  series of attributes of a car such as price,
  safety, capacity, size, status and fuel
  consumption

21
Examples (cont.)

• A family look for a house will strive for
  a favorable combination of variables like
  distance to schools, ones works place and
  market, comfort of the dwelling, and
  presence of a pleasant envionment
• An unemployed person seeking work will take
  into consideration many job characteristics
  such as salary, working place, career
  prospects, etc.
• A government may be interested in promoting
  what - industry in which reging in order
  to have favorable balance of payments,
  create employment opportunities, and for
  better income distribution among regions

22
Examples (cont.)

• A local community confronted with planning
  public investments will take into account
  various aspects of these investments
  including accessibility, costs, and social
  benefits
• Planning committees composed of different
  interest groups will have different
  priorities with respect to the elements of
  plans to be decided upon
• Charles Darwin, a well known mathematician
  in the 15th century used the principles
  of multicriterion optimization in choosing
  his wife they lived happily ever after.

23
MULTIPLE CRITERIA DECISION MAKING (MCDM)

• The process of selecting an act or
  courses of
• action among alternative acts or course of
  actions
• such that it will produce optimal results
  under some
• criteria of optimization.
• Optimal implies satisficing
• To satisfy to sacrifice
• Multicriteria decision making (MCDM)
  Multicriteria decision analysis (MCDA)

24
Elements of MCDM
25
CATEGORIES OF MCDM

• MULTIPLE OBJECTIVE DECISION MAKING (MODM)
• MULTIPLE ATTRIBUTE DECISION MAKING (MADM)

26
Classification of MCDM Problems
27
MODM

• For large set of alternatives
• E.g. If the problem is that of a product
  mix in a manufacturing firm - that is, the
  question of what and how much to produce in
  a multi-product firm and management aspires
  for both profit and market share.
• Number of alternatives infinite.
• MODM is a problem of design and mathematical
  techniques of optimization are used.

X
28
MADM

• For selecting an alternative from among a
  small explicit list of alternatives.
• E.g. Selecting the best production system-
  Such as the type of production technology
  to be used from among a realistically
  small number of alternatives.
• MADM is a problem of choice and classical
  mathematical programming tools need not be
  used

29
Comparison of MODM and MADM
30
CONFLICTING CRITERIA /OBJECTIVES
A problem can be considered as that of
MCDM if and only if there appears at
least two conflicting criteria/objectives.
Criteria/objectives are said to be in
conflict if the full satisfaction of one
will result in impairing the full
satisfaction of the other(s).
Criteria/objectives are considered to be
strictly conflicting if the increase in
satisfaction of one will result in a
decreasing satisfaction of the other(s).
MCDM, however does not necessarily stipulate
strict conflict of criteria/objectives.
31
CONFLICTING CRITERIA /OBJECTIVES

• Conflict due to intrapersonal reasons
• E.g. A consumer faced with multiple criteria
  in purchasing a car is an example of
  conflicting criteria caused intra-personally.
• Conflict due to interpersonal reasons
• E.g. A family is looking for a house to
  reside in is a typical example of conflicts
  of criteria due to inter-personal reasons.

32
Objective Functions Nonconflicting
33
(No Transcript)
34
Conflicting Objective Functions
35
(No Transcript)
36
GENERAL MODM FORMULATION
MAX (MIN) Zl fl(x), l 1, 2,, k
S.t. gi (x) bi , i 1,2,, m
x 0
37
MAX (MIN) Z CX S.t. A X B X
0
WHERE, Z IS k BY 1 MATRIX X
IS n BY 1 MATRIX B IS m BY
1 MATRIX C IS k BY n MATRIX A
IS m BY n MATRIX
38
A WELL FORMULATED MULTICRITERON MATHEMATICAL
PROBLEM
Find x in X such that U(x) U (x)
?x ? X (U works like a unique function)
39
Payoff Matrix
40
TRADITIONAL APPROACH

• Individual/organizational aspirations expressed
  in single criterion/objective
• Simplification is usually done by ignoring
  secondary criteria/objectives (those with
  lesser degrees of importance) and come up
  with single criterion situation

41
MODERN APPROACH

• Individual/ organizational aspirations
  expressed
• in multiple criteria/objectives
• Modern techniques of multi-criterion
  optimization
• are used

42
MAIN FEATURES OF MODM

• A well defined set of feasible
  alternatives
• (Nothing changes compared to traditional OR)
• A model of preferences rationally
  structured from a set of attributes
• A real valued function u, called utility
  function defined
• x P x iff U(x) gt U(x)
• x I x iff U(x) U(x)

43
CONCEPT OF OPTIMALITY

• An optimal solution is one which attains
  the maximum value of all the objectives
  simultaneously. The solution x is optimal to
  the problem if and only if x? S and
  fl(x) fl(x) for all l and for all x ? S, where
  S is the feasible region.
• Single objective problems optimality? Yes
• Multi-objective problem Optimality?
• Yes (for non-conflicting) objectives
• No (for conflicting) objectives (MCDM)

44
(No Transcript)
45
EFFICIENCY
x is efficiency in X (We say also pareto
optimal) if it is impossible to find x
such that fj (x) fj(x) ?j and fj
(x) gt fj (x) for at least one j.
46
CONCEPT OF EFFICIENCY
An efficient (noninferior, nondomianted,
pareto optimal) solution is one in which no
increase can be obtained in any of the
objectives without causing a simultaneous
decrease in at least one of the
objectives. The solution x is efficiency
to the problem with bi-objective f1 f2 ,
iff there does not exist any x ? X such
that fl(x) fl (x) for all l and fl (x) gt
fl(x) for at least one l. This solution is
obviously not unique
47
Objective function Z2 f2(x)
48
Objective function Z1 f1(x)
Set of Efficient Solutions
Feasible region X
Z2 f2(x)
49
SOME LIMITATIONS ON OBJECTIVITY

• The frontier of feasible region is often
  fuzzy
• In many real world problems, the DM as a
  person truly able to make the decision,
  does not really exist
• Even when the DM is not a mythical
  person, his/her preferences very seldom
  well-stated.
• Data, in many cases, are imprecise and/or
  defined in an arbitrary way.
• In general, it is impossible to say that
  a decision is good or bad by referring
  only to a mathematical model

50
Definition of Basic Concepts

• Attributes characteristics
• Objective traits
• E.g. height, weight, age, wealth, number
  of employees, etc.
• Subjective traits
• E.g. beauty, goodwill, etc.
• Objectives directions of improvement of
  selected attributes.
• Maximize or minimize
• Goals a priori levels of attributes/
  objective
• desired.
• Criteria measures, rules, and standards that
  guide decision making.
• All those attributes, objective or goals,
  which have been judged relevant in a given
  decision situation.

51
MEASUREMENT OF PREFERENCES

• Ordinal
• Purely relational
• Objectives are rank-ordered
• No other meaningful numerical properties can
  be assigned to them
• E.g.
• A is preferred to B
• Objectives are ranked as 1, 2, 3, 4, etc.
• Or as bad, average, good ,
  excellent
• Cardinal
• Assign meaningful numerical values (Nos.,
  Intervals, ratios, etc.)
• Suggests the degree (by how much?) of
  preference of one over others weight, priority,
  tradeoff

52
APPROACHES TO MCDM

• (Ref. HWANG et. al., Mathematical
  programming with multiple objectives a
  tutorial, C O.R.,Vol. 7, 1980.)
• No articulation of preference information.
• A priori articulation of cardinal
  information.
• A priori articulation of cardinal and
  cardinal information.
• Progressive articulation of explicit trade-off
  information.
• 5. Progressive articulation of implicit
  trade-off information.
• A posteriori articulation of preference
  information.

53
CLASSES OF MCDM TECHNIQUES

• Value or utility
• Outranking
• Distance-based
• Direction-based
• Mixed

54
VALUE OR UTILITY TYPE

• Deterministic MAVT
• Probabilistic MAUT
• Based on preference order of DM, which is
  assumed to be known, and on the hypothesis
  that the preference structure can be formally
  and mathematically represented.
• E.g.
• Method of Zionts Wallenius
• Delphic GP
• Keeney Method
• etc.

55
OUTRANKING METHODS

• Uses outranking relationships to select most
  satisfying alternative.
• E.g.
• ELECTRE (Roy)
• AHP (Saaty)
• PROMETHEE (Bran)
• etc.

56
DISTANCE BASED METHODS

• Proxy measure human preference
• E.g. GP, Compromise programming, Game
• theory
• Direction - based methods interactive schemes
• E.g. Zionts Wallenius approach, STEM
• Pareto Race, SWT, Game Theory.
• Mixed type
• Others
• Generating techniques
• Parametric MOSM(Zeleny), VMA (Steuer)