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Index. Introduction Analytic Framework Illustrative Example Conclusions. End. Introduction. GP is the most widely used MCDM approach Realistic Satisficing Philosophy Variant used: (Tamiz et al., 1995) 64\%, lexicographic 21\%, weighted Rest, minmax

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index
Index
  • Introduction
  • Analytic Framework
  • Illustrative Example
  • Conclusions

End

introduction
Introduction
  • GP is the most widely used MCDM approach
  • Realistic Satisficing Philosophy
  • Variant used: (Tamiz et al., 1995)
    • 64%, lexicographic
    • 21%, weighted
    • Rest, minmax
  • The variant chosen critically affects the final solution.
slide3
(t1, t2)

Feasible set

Introduction

Weighted

Minmax

Lexicographic

slide4
Analytic Framework
  • where:
  • all functions gj are convex,
  • all functions fi are concave,
  • all goals derive from attributes “more is better”
slide5
Weighted:
  • Minmax:
  • Lexicographic. Levels 1,..., l

Analytic Framework

Classical GP variants:

slide6
Type 1. The percentage sum of unwanted deviation variables cannot surpass a certain bound Q1.
  • Type 2. The maximum percentage deviation cannot surpass a certain bound Q2.

Q1

Meta-Satisfying

Set

Q2

Feasible set

Analytic Framework

Meta-Goal

type 2

Meta-Goal

type 1

META-GOALS

slide7
Type 3. The percentage of unachieved goals cannot surpass a certain bound Q3

Analytic Framework

META-GOALS

slide8
Type 1 goal on a set
  • Type 3 goal on a set
  • Type 2 goal on a set

Analytic Framework

slide9
Analytic Framework
  • General Formulation of the Meta-Goal
  • Programming model, with:
  • m1 type 1 meta-goals,
  • m2 type 2 meta-goals,
  • m3 type 3 meta-goals
slide10
Environmental Impact

Gross margin-break-even point

g5: x1 + n5 - p5 = 300

Unwanted deviation variables

Production capacities

g6: x2 + n6 - p6 = 200

Employment

Gross margin

Illustrative Example

Hypothetical Production Planning Problem

g1: x1 + 2x2 + n1 - p1 = 300

g2: 100x1 + 300x2 + n2 - p2 = 50000

g3: 100x1 + 300x2 + n3 - p3 = 90000

g4: x1 + x2 + n4 - p4 = 500

slide11
Illustrative Example

min f ( p1, n2, n3, n4, p5, p6)

  • Lexicographic Variant
  • Level 1: Goals 2, 5 and 6
  • Level 2: Goals 1, 3 and 4
slide12
Illustrative Example

SOLUTION:

  • Decision Variables:
  • x1 = 300; x2 = 66,66
  • Level 1:
  • n2 = 0; p5 = 0; p6 = 0
  • Level 2:
  • p1 = 133,33; n3 = 40000; n4 = 133,33
slide13
Illustrative Example
  • D.M. says:
  • With respect to the number of satisfied goals:
  • - Satisfy goals 2, 5 and 6;
  • - Maximize the number of satisfied goals among 1, 3 and 4;
  • Aggregate percentage deviation of not more than a 100% in the second level;
  • Maximum percentage disagreement of not more than a 75% in the second level
slide16
Illustrative Example

SOLUTION:

  • Level 1: ( n2 = p5 = p6 = 0 )
  • 1 = 0;
  • Level 2: ( p1 = 400; n3 = n4 = 0 )
  • - 2 = 1/3; (1 unsatisfied goal)
  • - 3 = 0.33; (133% aggregate disagreement)
  • - 4 = 0.58; (133% maximum disagreement)
slide17
Using a mixture of variants instead of a single one
  • Target values for several achievement functions

META-GP MODEL

Conclusions

  • Choosing a single GP variant can be a too mechanistic way of incorporating the DM’s preferences into the model
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