1 / 58

A Multi-Criterion Decision Making Approach to Problem Solving

A Multi-Criterion Decision Making Approach to Problem Solving. M. HERMAN, Ir. Royal Defense College (Brussels - Belgium). MCDM, Quality and Productivity. Actions : Alternative Strategies, Procedures for improvement Criteria : impact on Productivity (% process time adding value ) Quality

mikko
Download Presentation

A Multi-Criterion Decision Making Approach to Problem Solving

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. A Multi-CriterionDecision MakingApproach toProblem Solving M. HERMAN, Ir Royal Defense College (Brussels - Belgium)

  2. MCDM, Quality and Productivity • Actions :Alternative Strategies, Procedures for improvement • Criteria :impact on • Productivity (% process time adding value) • Quality • Customer satisfaction • Timeliness of the production/service • Accuracy of results • Efficiency of the process (reduce rework) • Cost-effectiveness

  3. MCDM, Quality and Productivity • Data :Assessment of Actions on Criteria • Measurements : numerical data • Ranking of qualitative assessments : ordinal data • Problem :Rank or Select alternative strategies or procedures for improvement

  4. Some Typical MCDM Applications • Selection of high-tech industrial development zones • A multi-attribute decision making approach for industrial prioritisation • Selection of a thermal power plant location • An approach to industrial locations

  5. Some MCDM Applications (cont.) • Selecting oil and gas wells for exploration • Multi-attribute decision modelling for tactical and operations management planning in a batch processing environment • New campus selection by an MCDM approach • Selection of an automated inspection system • Selection of an incident management procedure in a computer center

  6. Some MCDM Applications (cont.) • Acquisition of equipment (vehicles, helicopters, computers,...) • Personnel selection and ranking • Personnel assignment to jobs • Ranking and selection of investment plans • Ranking of loan requests by banks • Burden sharing allocation in international organisations (EU, ASEAN,…) • …...

  7. Early Literature (1) • B. Roy, “Méthodologie multicritère d’aide à la décision”, Economica, Paris, 423 p, 1985 - translated into English • B. Roy and D. Bouyssou, “Aide multicritère à la Décision : Méthodes et Cas”, Economica, Paris, 700 p, 1993

  8. Early Literature (2) • J.P. Brans, B. Maréschal and Ph. Vincke, “How to select and how to rank projects : the Prométhée Method”, EJOR (European Journal of O.R.), 24, pp. 228-238, 1986 • B. Maréschal and J.P. Brans, “Geometrical Representation for MCDM, the GAIA procedure”, EJOR (European Journal of O.R.), 34, pp. 69-77, 1988

  9. Early Literature (3) • M. Roubens, “Analyse et agrégation des préférences : modélisation, ajustement et résumé de données relationnelles”, Revue Belge Stat. Inf. O.R. (JORBEL) 20(2), pp. 36-67, 1980 • M. Roubens, “Preference Relations on Actions and Criteria in Multicriteria Decision Making”, EJOR 10, pp. 51-55, 1982

  10. Early Literature (4) • R. Van den Berghe and G. Van Velthoven, “Sélection multicritère en matière de rééquipement”, Revue X (Belgium), Vol. 4, pp. 1-8, 1982 • H. Pastijn and J. Leysen, “Constructing an Outranking Relation with Oreste”, Mathematical Computation and Modelling, Vol. 12, No. 10/11, pp. 1255-1268, 1989

  11. First approach to solve MCDM Problems

  12. Ranking of criteria

  13. Combining criteria

  14. Drawbacks of this method * The problem of assigning weights * The problem of compensation

  15. * The problem of incomparability * The problem of indifference • Interactive compromises

  16. Feature of MCDM Problems Actions Quality Productivity a 15 500 b 30 400 c50 200 d30 350 Majority Principle a b d c a b d c a b d c

  17. MCDM methods for richer dominance relations • Aggregation by majority principles yields VERY POOR DOMINANCE RELATION: • A lot of Incomparabilities (R) • Some Indifferencies (I) and Preferences (P) • MCDM methods should make the dominance relation richer (take into account more information than majority principles do) • Less R (making decisions easier) • More I and P

  18. Requirements for MCDM methods Actions Criteria a P b a 100 100 b 30 20 Actions Criteria a R b a 100 20 b 30 100

  19. Requirements for MCDM methods Actions Criteria a P b a 100 99 b 20 100 Actions Criteria a I b a 100 99 b 99 100

  20. Requirements for MCDM methods Actions Criteria a I b a 100 100 b 99 99 Actions Criteria a I b a 100 99 b 99 100

  21. Scaling Effect on the Average CriteriaAverage a 100 99 99.5 a P b b 20 100 60 a 100 990 545 a P b b 20 1000 510 a 100 9900 5000 b P a b 20 10,000 5010

  22. Requirements for an MCDM Method • Deviations have to be considered • Elimination of scale effects • Pairwise comparison must lead to partial ranking (incomparabilities) or to complete ranking • Methods must be transparant (“simple”) • Technical parameters must have an interpretation by the decision maker • Weights allocated to criteria must have a clear interpretation • Conflict analysis of the criteria

  23. Some MCDM Methods Complete & Partial Ranking • Prométhée : numerical data • Oreste : ordinal data • Electre : Pairwise comparisons - outranking with Incomparabilities • AHP : Pairwise comparisons - No Incomparabilities • ….

  24. The PROMETHEE METHOD

  25. The foundations of the PROMETHEE method • The three steps of the method • (1) Selecting generalized criteria • (2) Determining an outranking relationship • (3) Evaluating preferences

  26. The concept of generalized criteria • Where Ci(a) is a criterion to be optimized • We consider a preference function d = Ci(a1) - Ci(a2)

  27. Choice of transformation functions • Operational criteria : type III • Financial short term, acquisition cost, construction cost : type V • Financial long term, maintenance cost, life cycle cost : type IV • Discrete resources, manpower (roughly estimated) : type II • Ecology, dramatic impact : type I • Security, Quality, Aesthetics : type VI

  28. Parameter settings • Indifference threshold : q • high if uncertainty, low accuracy of data • Preference threshold : p • close to maximum deviation if no loss of information is advisable (accurate data) • Interactive choice in Promcalc

  29. The outranking relationship • For each criterion Ci we will associate the preference function P. •  (a1, a2) =  wi * Pi (a1, a2) (Different weights)  (a1, a2) = (1/m) * Pi (a1, a2) (All weights are equal)

  30. We have: 0 ( a1, a2)  1 • Furthermore, • if ( a1, a2)  0 slight preference for "a1" over "a2" • if ( a1, a2)  1 strong preference for "a1" over "a2"

  31. The outranking relationship

  32. Evaluating preferences

  33. The PROMETHEE I method a1 P+ a2 if +(a1) > +(a2) a1 I+ a2 if +(a1) = +( a2) a1 P- a2 if -(a2) > -(a1) a1 I- a2 if -(a2) = -(a1)

  34. a1 P a2 "a1" outranks "a2" if: a1 P+ a2 and a1 P- a2 a1 P+ a2 and a1 I- a2 a1 I+ a2 and a1 P- a2 • a1 I a2 " a1" and " a2" are indifferent if: a1 I+ a2 and a1 I- a2 • a1 R a2 "a1" and "a2" are incomparable: in all other cases

  35. The PROMETHEE II method • a1 PII a2 "a1" outranks "a2" if (a1) > (a2) • a1 III a2 "a1" and "a2" are indifferent if (a1) = (a2)

  36. Example :

  37. Selecting the generalized criteria

  38. The data

  39. Devising the flow table

  40. Devising the flow table

  41. Devising the flow table

  42. Devising the flow table

  43. Devising the flow table

More Related