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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.


(t1, t2)

Feasible set

Introduction

Weighted

Minmax

Lexicographic


Analytic Framework

  • where:

  • all functions gj are convex,

  • all functions fi are concave,

  • all goals derive from attributes “more is better”


  • Minmax:

  • Lexicographic. Levels 1,..., l

Analytic Framework

Classical GP variants:


  • 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


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

Analytic Framework

META-GOALS


  • Type 3 goal on a set

  • Type 2 goal on a set

Analytic Framework


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


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


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


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


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




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)


  • 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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