1. A Multi-Criterion Decision Making Approach to Problem Solving
M. HERMAN, Ir
Royal Defense College (Brussels - Belgium)
11/20/2018

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
11/20/2018

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
11/20/2018

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
11/20/2018

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
11/20/2018

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,…)
…...
11/20/2018

7. Early Literature (1)
B. Roy, “Méthodologie multicritère d’aide à la décision”, Economica, Paris, 423 p, translated into English
B. Roy and D. Bouyssou, “Aide multicritère à la Décision : Méthodes et Cas”, Economica, Paris, 700 p, 1993
11/20/2018

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 , 1986
B. Maréschal and J.P. Brans, “Geometrical Representation for MCDM, the GAIA procedure”, EJOR (European Journal of O.R.), 34, pp , 1988
11/20/2018

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 , 1980
M. Roubens, “Preference Relations on Actions and Criteria in Multicriteria Decision Making”, EJOR 10, pp , 1982
11/20/2018

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 , 1989
11/20/2018

11. First approach to solve MCDM Problems
11/20/2018

12. Ranking of criteria
11/20/2018

13. Combining criteria
11/20/2018

14. Drawbacks of this method * The problem of assigning weights
* The problem of compensation
11/20/2018

15. 11/20/2018

16. 11/20/2018

17. Interactive compromises
* The problem of incomparability
* The problem of indifference
Interactive compromises
11/20/2018

18. Feature of MCDM Problems
Actions Quality Productivity a b c d
Majority Principle
a b
d c
a b
d c
a b
d c
11/20/2018

19. 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
11/20/2018

20. Requirements for MCDM methods
Actions Criteria
a P b a b
Actions Criteria
a R b a b
11/20/2018

21. Requirements for MCDM methods
Actions Criteria
a P b a b
Actions Criteria
a I b a b
11/20/2018

22. Requirements for MCDM methods
Actions Criteria
a I b a b
Actions Criteria
a I b a b
11/20/2018

23. Scaling Effect on the Average
Criteria Average a
a P b b a
a P b b a
b P a
b ,
11/20/2018

24. 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
11/20/2018

25. Some MCDM Methods Complete & Partial Ranking
Prométhée : numerical data
Oreste : ordinal data
Electre : Pairwise comparisons - outranking with Incomparabilities
AHP : Pairwise comparisons No Incomparabilities ….
11/20/2018

26. The PROMETHEE METHOD
11/20/2018

27. 11/20/2018

28. 11/20/2018

29. 11/20/2018

30. The foundations of the PROMETHEE method
The three steps of the method
(1) Selecting generalized criteria
(2) Determining an outranking relationship
(3) Evaluating preferences
11/20/2018

31. The concept of generalized criteria
Where Ci(a) is a criterion to be optimized
We consider a preference function
d = Ci(a1) - Ci(a2)
11/20/2018

32. 11/20/2018

33. “Diskrete gebeurtenis-gestuurd” is de vrije vertaling van “discrete event oriented”. In deze simulatie-methode wordt de tijd gediscretiseerd. Het model wordt aan wijzigingen onderworpen wanneer een “gebeurtenis” plaats grijpt, terwijl de “simulatieklok” een diskrete sprong maakt.
Een gebeurtenis kan bv. de aankomst van een telefonische oproep zijn in een callcenter, of de aanvraag naar een wisselstuk in een logistiek depot.
11/20/2018

34. 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
11/20/2018

35. Parameter settings Indifference threshold : q Preference threshold : p
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
11/20/2018

36. 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)
11/20/2018

37. 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"
11/20/2018

38. The outranking relationship
11/20/2018

39. Evaluating preferences
11/20/2018

40. 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)
11/20/2018

41. a1 I a2 " a1" and " a2" are indifferent if: a1 I+ a2 and a1 I- a2
a1 P a "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
11/20/2018

42. The PROMETHEE II method
a1 PII a2 "a1" outranks "a2"
if (a1) > (a2)
a1 III a2 "a1" and "a2" are indifferent
if (a1) = (a2)
11/20/2018

43. Example :
11/20/2018

44. Selecting the generalized criteria
11/20/2018

45. The data
11/20/2018

46. Devising the flow table
11/20/2018

47. Devising the flow table
11/20/2018

48. Devising the flow table
11/20/2018

49. Devising the flow table
11/20/2018

50. Devising the flow table
11/20/2018

51. Devising the flow table
11/20/2018

52. 11/20/2018

53. 11/20/2018

54. The ranking obtained using the Promethee I method
11/20/2018

55. The ranking obtained using the Promethee II method
11/20/2018

56. Flexibility of Prométhée
Weights
Transformation functions = generalised criteria
Parameter settings
11/20/2018

57. Thanks for your attention
MCDM
Questions ?
Suggestions ?
11/20/2018

58. AREOPA MOBIUS RUG RMA H.Pastijn
Questions ?
11/20/2018
AREOPA MOBIUS RUG RMA H.Pastijn