UTA METHODS & APPLICATIONS PART II Yannis is Si Siskos os - - PowerPoint PPT Presentation

UTA METHODS & APPLICATIONS PART II

Yannis is Si Siskos

• s

13rd MCDA/MCDM Summer School July 23 – August 3, 2018, Chania, Crete, Greece

This presenTaTion is dedicaTed To The memory

• f

Bernard roy

(1934–2017)

50th MCDA - Cerisy-la-Salle – France 1999

54th MCDA - Durbuy – Belgium 2001

Eric Jacquet – Lagrѐze remets à Bernard Roy un livre edité en son honeur

OUTLINE

 Applications  Other disaggregation approaches and new

trends

 A real world application: Job Evaluation  Disaggregating time series and forecasting

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APPLICATIONS #1

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APPLICATIONS #2

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APPLICATIONS #3

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OTHER DISAGGREGATION METHODS AND TRENDS #1

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 The ELECCALC system (Kiss et al., 1994) has been developed to estimate

indirectly the parameters of the ELECTRE II method. The process is based on the DM’s responses to questions of the system regarding his/her global preferences.

 Mousseau and Slowinski (1998) propose an interactive aggregation-

disaggregation approach that infers ELECTRE TRI parameters simultaneously starting from assignment examples. In this approach, the determination of the parameters’ values (except the veto thresholds) that best restore the assignment examples is formulated through a nonlinear optimization program.

 Mousseau et al. (2000a; 2000b) consider the subproblem of the determination

• f the weights only of ELECTRE TRI, assuming that the thresholds and category

limits have been fixed. This leads to formulate a linear program (rather than nonlinear in the global inference model). Through experimental analysis, they show that this approach is able to infer weights that restore in a stable way the assignment examples and it is also able to identify possible inconsistencies in these assignment examples.

OTHER DISAGGREGATION METHODS AND TRENDS #2

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

Doumpos and Zopounidis (2002) use linear programming formulations in order to estimate all the parameters of the outranking relation classification model. However, in this approach, the parameters are estimated sequentially rather than through a global inference process. Thus, the proposed methodology does not specify the optimal parameters of the outranking relation (i.e. the ones that lead to a global minimum of the classification error). Therefore, the results of this approach (“reasonable” specification of the parameters) serve rather as a basis for a thorough decision-aid process.



The problem of robustness and sensitivity analysis, through the extension of the previous research efforts is discussed by Dias et al. (2002). They consider the case where the DM can not provide exact values for the parameters of the ELECTRE TRI method, due to uncertain, imprecise or inaccurately determined information, as well as from lack of consensus among them. The proposed methodology combines the following approaches: (1) the first approach infers the value of parameters from assignment examples provided by the DM, as an elicitation aid and (2) the second approach considers a set of constraints on the parameter values reflecting the imprecise information that the DM is able to provide.

OTHER DISAGGREGATION METHODS AND TRENDS #3

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

In order to represent interaction among criteria, some specific formulations of the utility functions expressed in terms of fuzzy integrals have been proposed (Murofushi and Sugeno, 1989; Grabisch, 1996; Marichal and Roubens, 2000). In this context, Angilella et al. (2003) propose a methodology that allows including additional information such as an interaction among criteria. The method aims at searching a utility function representing the DM’s preferences, while the resulting functional form is a specific fuzzy integral (Choquet integral). As a result, the

• btained weights may be interpreted as the “importance” of coalitions of criteria,

exploiting the potential interaction between criteria. The method can also provide the marginal utility functions relative to each one of the considered criteria, evaluated on a common scale, as a consequence of the implemented methodology.



The general scheme of the disaggregation philosophy is also employed in other approaches, including rough sets (Pawlak, 1982; Slowinski, 1995; Dimitras, et al., 1999; Zaras, 2000), machine learning (Quinlan, 1986) and neural networks (Malakooti and Zhou, 1994; Stam et al., 1996). All these approaches are used to infer some form of decision model (a set of decision rules or a network) from given decision results involving assignment examples, ordinal or measurable judgments.

OTHER DISAGGREGATION METHODS AND TRENDS #4

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 The MACBETH method (Measuring Attractiveness by a Categorical Based

Evaluation Technique) by Bana e Costa and Vansnick (1994) infers a single value function from pairwise comparisons externalised from the DM on a single criterion in terms of criterion attractiveness. The same procedure is repeated for each criterion and, finally for the set of criteria in erder to infer the criteria

• weights. The overall evaluation model is an additive value model.

 UTAGMS (Greco, Mousseau, Slowinski, 2008) is a UTA-like method to infer all

additive value functions compatible with a set of pairwise comparisons of reference actions. The method is intended to be used interactively, with an increasing reference set AR and a progressive statement of pairwise comparisons.

 GRIP method (Greco, Slowinski, Figueira, 2008) infers all additive value

functions compatible with a set of pairwise comparisons of the actions (as in MACBETH) and preference intensities on pairs of actions.

A REAL WORLD APPLICATION

JOB EVALUATION IN A GREEK TELECOMUNICATION COMPANY #1 Spyridakos, A., Y. Siskos, D. Yannacopoulos and A. Skouris (2001), Multicriteria job evaluation for large organisations, European Journal of Operational Research, vol. 130, pp. 375-387.

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Disaggr e gating time se r ie s and for e c asting

Ang e lo po ulo s, Psa rra s, Sisko s (2018)

 I

ntro duc tio n o f a n o rig inal ro b ust multic rite ria fo re c asting appro ac h;

 E

xa mina tio n o f the re latio nship b e twe e n e le c tric ity de ma nd time se rie s a nd se ve ra l multiple c rite ria ;

 I

mple me nta tio n o f po st-o ptimality analysis and ro b ustne ss c o ntro l o f the a pplie d fo re c a sting mo de l;

 Applic atio n o f the mo de l fo r lo ng -te rm e le c tric ity

de ma nd fo re c a sting in Gre e c e .

Main Re se ar c h Obje c tive s

Notation

T ime se rie s va ria ble

Numb e r o f c rite ria Va lue o f the ith c rite rio n (i=1,2,…,n) Numb e r o f le ve ls o f the ith c rite rio n va lue s Va lue func tio n o f Y Va lue o f the ym le ve l Ma rg ina l va lue func tio n o f Xi T ime ho rizo n

Me thodology

 I

nspire d fro m the study o f K e tta ni, Ora l & Sisko s (1998)

Classic Mode l (1/ 3)

a nd Whe re σ+ a nd σ- c o nstitute the o ve re stima tio n a nd the unde re stima tio n e rro rs, re spe c tive ly. T he o rdina l re g re ssio n e q ua tio n is fo rme d a s fo llo ws: T he first disa g g re g a tio n mo de l is g ive n b e lo w:

Me thodology

Classic Mode l (2/ 3)

T he c la ssic time se rie s disa g g re g a tio n mo de l is infe rre d b y me a ns o f the fo llo wing line a r pro g ra mming mo de l:

Me thodology

Value - base d Mode l (2/ 4)

T he va lue -b a se d time se rie s disa g g re g a tio n mo de l is infe rre d b y me a ns o f the line a r pro g ra mming mo de l g ive n b e lo w:

Ca se Study

L

• ng- te r

m e le c tr ic ity de mand for e c asting in Gr e e c e

 Re duc tio n o f GDP b y a nd

inc re a se o f une mplo yme nt ra te to 27.5% in 2013;

 Re duc tio n o f e le c tric ity de ma nd

b y mo re tha n % fro m 2008 to 2014.

E c onomic Cr isis in Gr e e c e (2008 and be yond)

100.000 125.000 150.000 175.000 200.000 225.000 250.000 30.000.000 35.000.000 40.000.000 45.000.000 50.000.000 55.000.000 60.000.000 E le c tric ity Co nsumptio n (MWh) GDP (Co nsta nt pric e s 2010) 0% 5% 10% 15% 20% 25% 30% 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Une mplo yme nt Ra te

Ca se Study

L

• ng- te r

m e le c tr ic ity de mand for e c asting in Gr e e c e

F

• r

e c asting Mode l Cr ite r ia

Cr ite r ia Me asur e me nt Unit Sc ale Sour c e s E c onomic c r ite r ia

Millio n € (a t c o nsta nt pric e s) 129,000 – 231,000 E L .ST AT . % 7.8% - 27.5% E UROST AT

De mogr aphic c r ite r ion

Pe rso ns 10,883,000 – 11,397,000 OE CD

We athe r

• r

e late d c r ite r ia

Da ys 1,650 – 2,050 HNMS Da ys 240 - 420 HNMS

E ne r gy- r e late d c r ite r ia

€/ kWh 0.076 – 0.178 OE CD/ I E A €/ 107 kilo c a lo rie s GCV 275 - 980 OE CD/ I E A €/ 103 lite rs 325 – 1,270 OE CD/ I E A

E ne r gy e ffic ie nc y c r ite r ion

% 77 - 101 ODYSSE E

• MURE

Case Study

F

• r

e c asting Mode l Ve r sions

Mode l De sc r iption Ve r sion A

E c o no mic , de mo g ra phic , we a the r-re la te d a nd e ne rg y-re la te d c rite ria a re ta ke n into c o nside ra tio n. Use o f GDP in c o nsta nt pric e s.

Ve r sion B

E c o no mic , de mo g ra phic , we a the r-re la te d , e ne rg y-re la te d a nd e ne rg y e ffic ie nc y c rite ria a re ta ke n into c o nside ra tio n. Use o f GDP in c o nsta nt pric e s.

Ve r sion C

E c o no mic , de mo g ra phic , we a the r-re la te d a nd e ne rg y-re la te d c rite ria a re ta ke n into c o nside ra tio n. Use o f the Gro ss Va lue Adde d pe r se c to r o f a c tivity inste a d o f the GDP.

Ve r sion D

E c o no mic , de mo g ra phic , we a the r-re la te d , e ne rg y-re la te d a nd e ne rg y e ffic ie nc y c rite ria a re ta ke n into c o nside ra tio n. Use o f the Gro ss Va lue Adde d pe r se c to r o f a c tivity inste a d o f the GDP.

Ve r sion E

Ro b ust po st-o ptima lity o ptimiza tio n ve rsio n o f Mo de l D

Re sults

F

• r

e c asts (Pe r iod 2000- 2015)

30.000.000 35.000.000 40.000.000 45.000.000 50.000.000 55.000.000 60.000.000 65.000.000 70.000.000 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Ac tua l De ma nd Cla ssic Mo de l (Ve rsio n A) Cla ssic Mo de l (Ve rsio n B) Va lue -b a se d Mo de l (Ve rsio n A) Va lue -b a se d Mo de l (Ve rsio n A) 40.000.000 42.000.000 44.000.000 46.000.000 48.000.000 50.000.000 52.000.000 54.000.000 56.000.000 58.000.000 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Ac tua l Va lue -b a se d Mo b e l (Ve rsio n C) Va lue -b a se d Mo b e l (Ve rsio n D) Va lue -b a se d Mo b e l (Ve rsio n E )

Re sults

Statistic al E r r

• r

s (Pe r iod 2000- 2015)

Indic a tor Cla ssic Mode l (Ve rsion A) Cla ssic Mode l (Ve rsion B) Va lue - ba se d Mode l (Ve rsion A) Va lue - ba se d Mode l (Ve rsion B) Va lue - ba se d Mode l (Ve rsion C) Va lue - ba se d Mode l (Ve rsion D) Va lue - ba se d Mode l (Ve rsion E ) MF E

3.88E +06

• 1.58E

+06

• 3.97E

+05

• 2.22E

+05 3.03E +05 2.86E +05 5.04E +05

MAE

7.28E +06 4.00E +06 1.09E +06 1.09E +06 8.71E +05 7.69E +05 8.53E +05

MPE

7.93%

• 3.11%
• 0.69%
• 0.34%

0.64% 0.63% 1.04%

MAPE

14.59% 7.83% 2.14% 2.13% 1.72% 1.54% 1.70%

RMSE

8.49E +06 5.74E +06 1.36E +06 1.23E +06 1.03E +06 9.53E +05 1.06E +06

r

62.9% 47.3% 96.2% 97.2% 96.8% 98.2% 97.5%

Re sults

F

• r

e c asts (Pe r iod 2016- 2025)

40.000.000 45.000.000 50.000.000 55.000.000 60.000.000 65.000.000 70.000.000 1998 2003 2008 2013 2018 2023 Ac tua l Va lue -b a se d Mo b e l (Ve rsio n D) Va lue -b a se d Mo b e l (Ve rsio n E ) I nde pe nde nt Po we r T ra nsmissio n Op e ra to r (L

• w)

I nde pe nde nt Po we r T ra nsmissio n Op e ra to r (Re fe re nc e ) I nde pe nde nt Po we r T ra nsmissio n Op e ra to r (Hig h)

Re sults

We ights of the Mode l’s Cr ite r ia

Crite rion Me a n We ig ht Sta nda r d De via tion Min We ig ht Ma x We ig ht

16.3% 8.9% 1.6% 31.9% 13.2% 4.9% 3.3% 33.9% 10.2% 5.3% 1.6% 29.3% 9.4% 3.8% 1.6% 27.6% 8.2% 9.4% 1.6% 37.6% 5.6% 5.2% 1.6% 32.2%

0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% b 1 b 2 b 3 b 4 b 5 b 6 b 7 b 8 b 9 b 10 b 11 b 12 b 13 b 14 b 15 b 16 b 17 b 18 Me a n Ma x Min

Conc lusions

 T

he le ve l o f the na tio na l e c o no mic g ro wth impo se the g re a te st impa c t o n e le c tric ity de ma nd in Gre e c e ;

 E

c o no mic g ro wth, e ne rg y pric e s a nd une mplo yme nt ra te re pre se nt the ma in influe ntia l pa ra me te rs o f e le c tric ity de ma nd e vo lutio n;

 Sub sta ntia l mo re a c c ura te fo re c a sts a re pro vide d b y the

va lue -b a se d fo re c a sting mo de l;

 I

nc re a se d mo de l sta b ility is a c hie ve d via the va lue -b a se d fo re c a sting mo de l with a to ta l ASI e q ua l to 81.1%;

 Co nsta nt inc re a se o f the e le c tric ity de ma nd is e xpe c te d

during the upc o ming ye a rs a t the le ve l o f pre -c risis pe rio d (2008) b y 2025.

58 MCDA Summer School, Chania 27/07/2018

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