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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. - PowerPoint PPT Presentation
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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
9 July 2010 Case Study - Student Selection 2
Criteria
• Grades– 3rd and 4th year– Rescaled to 1-5
• Motivation• Maturity/Personality• Professional Project • Knowledge of IE
9 July 2010 Case Study - Student Selection 3
From interview, numbers 1-5
Post analysis of the 2009 selection
9 July 2010 Case Study - Student Selection 4
• 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
9 July 2010 Case Study - Student Selection 7
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
9 July 2010 Case Study - Student Selection 8
Approach - Step 1
9 July 2010 Case Study - Student Selection 9
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
9 July 2010 Case Study - Student Selection 10
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
9 July 2010 Case Study - Student Selection 12
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
9 July 2010 Case Study - Student Selection 14