1 / 17

Index

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

elaine
Download Presentation

Index

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Index • Introduction • Analytic Framework • Illustrative Example • Conclusions End

  2. 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.

  3. (t1, t2) Feasible set Introduction Weighted Minmax Lexicographic

  4. Analytic Framework • where: • all functions gj are convex, • all functions fi are concave, • all goals derive from attributes “more is better”

  5. Weighted: • Minmax: • Lexicographic. Levels 1,..., l Analytic Framework Classical GP variants:

  6. 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

  7. Type 3. The percentage of unachieved goals cannot surpass a certain bound Q3 Analytic Framework META-GOALS

  8. Type 1 goal on a set • Type 3 goal on a set • Type 2 goal on a set Analytic Framework

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. Illustrative Example INFEASIBLE

  15. Illustrative Example (GP)2 Model

  16. 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)

  17. 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

More Related