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

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

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

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

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

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

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 11/20/2018

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 11/20/2018

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 11/20/2018

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 11/20/2018

First approach to solve MCDM Problems 11/20/2018

Ranking of criteria 11/20/2018

Combining criteria 11/20/2018

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

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

Feature of MCDM Problems Actions Quality Productivity a 15 500 b 30 400 c 50 200 d 30 350 Majority Principle a b d c a b d c a b d c 11/20/2018

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

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 11/20/2018

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 11/20/2018

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 11/20/2018

Scaling Effect on the Average Criteria Average 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 11/20/2018

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

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

The PROMETHEE METHOD 11/20/2018

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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

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

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“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

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

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

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

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

The outranking relationship 11/20/2018

Evaluating preferences 11/20/2018

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

a1 I a2 " a1" and " a2" are indifferent if: a1 I+ a2 and a1 I- a2 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 11/20/2018

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

Example : 11/20/2018

Selecting the generalized criteria 11/20/2018

The data 11/20/2018

Devising the flow table 11/20/2018

Devising the flow table 11/20/2018

Devising the flow table 11/20/2018

Devising the flow table 11/20/2018

Devising the flow table 11/20/2018

Devising the flow table 11/20/2018

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

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

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

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

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