Index

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# Index - PowerPoint PPT Presentation

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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Presentation Transcript
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
• 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”
Weighted:
• 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 1 goal on a set
• 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)
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