MCDA Summer School 2010

Case Study -Student selection for last year of Industrial Engineering at

Politecnico di Roma Nicolas Albarello, Akram Dehnokhalaji, Sanna

Hanhikoski, Lounes Mohamed Mammeri, Mathieu Rivallain, Céline Verly

Problem

• n applicants for the Industrial Engineering major (2009 n=71, 2010 n=51)

• Selection of best students (max 50)– 50 students in 2009, 36 in 2010– Dividing students in 4 Paths – A homogeneous distribution (gender, quality, also

in Paths)

• Ensure transparent and fair selection

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Criteria

• Grades– 3rd and 4th year– Rescaled to 1-5

• Motivation• Maturity/Personality• Professional Project • Knowledge of IE

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From interview, numbers 1-5

Post analysis of the 2009 selection

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• In 2009 data, one main inconsistency :

Gender seems to be taken into account in the selection

An additive value model (without sex) is not able to solve this inconsistency

Page 5Presentation title – file name

Preference model inference (1/2)• Monte-Carlo approach

– Random weights in weighted sum + optimal selection threshold– Many models but always 1 inconsistency (the one previously presented)

Min-Ave-Max weights

00.10.20.30.40.5

3rd

4th

Mot

ivatio

n

Perso

nality

Projec

tJo

bs Sex

Analysis of inferred models• Jobs are a quite important criteria• Sex is not an important criteria (considering individuals)• DMs give more weight to interviews results (in average)

Page 6 Presentation title – file name

Preference model inference (2/2)

• Dominance-based Rough Sets Approach– With sex: A set of 10 rules (sometimes discriminatory) permit to fully

describe the decision

– Without sex: A set of 8 rules permit to describe the decision at 96,7%

Sex should not be taken as a student value criteria but as a collective value criteria (at the Major/Paths level)

Approach• Step 0

– Analyse the current applicants• Step 1

– Pre-selection of students with RPM (Robust Portfolio Modelling)

• Step 2– Ranking the pre-selected students with PROMETHEE – Selecting the required number of students

• Step 3– Assigning students to different paths

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Approach - Step 1

• Selecting a portfolio of m students out of n applicants (in 2009 m=50, n=69)

• Criteria equally weighted• Number of women between 7 and 10• Results

– Several non-dominated portfolios– 8 students red → eliminated in this phase– Green and yellow students to next step

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Approach - Step 1

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Approach - Step 2

• Use of PROMETHEE to rank the selected students from RPM

• Equal weights • Usual functions for interview criteria• Linear function for grades (q=1, p=2)• m first students selected

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Page 11Presentation title – file name

Stochastic method for Paths formation

• Random attribution of students to Paths• Evaluation of an objective function (weighted sum)

– Minimize the normalized ECART in number of students/value/sex ratio between Paths

– Maximize the overall satisfaction of the group (sum of students satisfaction)

• Alternative : evolutionary algorithm (better)

Path allocation results in 2009

Number in group 1 14 Value 1 20.51544 M/F in 1 0.071429 Total satisfaction 6

Number in group 2 12 Value 2 19.80451 M/F in 2 0.041667 Relative satisfaction 0.3

Number in group 3 12 Value 3 20.82182 M/F in 3 0.055556

Number in group 4 12 Value 4 20.83608 M/F in 4 0.0625

Number selected 50 81.97786

Ecart 0.142857 Ecart 0.049509 Ecart 0.416667 Solution value 0.3090

Results- Selection 2009

• 49 students selected with our approach were really selected in 2009

• Exception: Difina really selected, our approach would select Quagliata instead

Student Grades Interview Sex Core index (RPM) Rank (PROM) Net flow (PROM)

DIFINA 3.7 3.4 2 3 2 2 M 0.687707641 52 -0.379

QUAGLIATA 2.3 3.1 3 3 3 3 M 0.780730897 41 -0.22

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Results – Selection 2010Student Grades Interview Sex Core index (RPM) Rank (PROM) Net flow (PROM) Path

ABBATANGELO 4.7 5.0 5 4 4 5 M 1 8 0.334 4

AMODEO 3.7 5.0 5 5 5 5 M 1 2 0.538 4

BRANCATO 2.7 4.0 5 3 3 4 M 0.87654321 26 -0.136 2

CANOSA 4.0 5.0 2 4 2 3 M 0.703703704 36 -0.421 2

CARLUCCI 3.5 5.0 5 5 5 5 F 1 3 0.533 2

CASCIO 4.3 5.0 4 4 3 4 M 1 21 -0.06 4

CONTE 4.4 5.0 3 4 3 2 M 0.740740741 34 -0.341 3

CORONATO 2.1 3.7 4 4 4 3 F 0.62962963 30 -0.226 1

DE MARE 2.8 3.0 4 4 4 5 M 1 18 0.028 2

DEPASCALE 4.0 4.3 4 4 3 4 M 1 23 -0.101 1

DI LASCIO 3.5 3.8 5 5 4 4 F 1 11 0.255 1

DI VIRGILIO 2.5 3.7 3 4 3 4 M 0.740740741 32 -0.281 3

D'IMPERIO 4.7 5.0 4 4 4 5 M 1 12 0.203 3

FALCE 3.3 4.3 5 5 5 4 M 1 5 0.374 1

GALLO 3.0 4.9 5 5 5 5 M 1 4 0.512 3

GAZZANEO 3.1 4.1 3 4 3 3 M 0.679012346 35 -0.369 1

GUARINI 3.1 3.1 5 4 5 5 M 1 9 0.282 1

INFANTINO 3.1 4.8 4 4 5 4 M 1 15 0.115 1

IORIO 3.3 4.8 5 5 5 3 M 1 10 0.262 1

LO TITO 4.1 4.5 3 4 3 4 M 1 29 -0.203 2

LULLO 2.5 2.7 4 4 4 4 M 0.851851852 25 -0.131 1

MANCUSI 3.5 4.0 3 4 4 3 M 1 31 -0.255 4

MARINO 4.7 3.7 3 4 4 4 M 1 22 -0.078 3

MARTOCCIA 3.0 4.1 4 4 4 3 M 1 28 -0.155 4

MAURO 3.0 3.7 5 5 5 4 M 1 7 0.347 2

MONTEMURRO 3.3 3.2 4 5 5 4 F 1 13 0.199 4

PANARIELLO 3.3 4.7 4 4 3 4 M 1 24 -0.104 4

PASTORE 3.5 4.2 4 4 4 3 F 1 27 -0.14 3

PIETRAGALLA 3.6 3.7 5 5 5 4 M 1 6 0.362 2

PODANO 3.3 3.3 4 4 4 4 M 1 20 -0.053 2

QUARATINO 3.1 3.7 4 5 4 4 F 1 16 0.111 3

RICCIARDI 4.3 2.9 4 5 4 4 F 1 17 0.089 3

ROMANAZZI 3.7 3.9 4 4 4 4 M 1 19 -0.013 2

ROMANO 4.1 4.4 4 4 5 4 M 1 14 0.122 4

SANCHEZ 4.0 5.0 5 5 5 5 F 1 1 0.545 4

TROGLIA 3.6 3.0 4 3 3 4 M 0.827160494 33 -0.294 39 July 2010 Case Study - Student Selection 13

Conclusions

• Transparent and fair approach• The homogenity of gender taken into account• Students’ wishes taken into account as much

as possible

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