MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="=boundary.Aspose.Words=--" This is a multi-part message in MIME format. --=boundary.Aspose.Words=-- Content-Disposition: inline; filename="document.html" Content-Type: text/html; charset="utf-8" Content-Transfer-Encoding: quoted-printable Content-Location: document.html = = 3D""M=C3=A9= todos multiatributo na avalia=C3=A7=C3=A3o da sustentabilidade organizacion= al

Multi-Attribute Methods in the Ass= essment of Organizational Sustainability

 

<= tr>

Ren= ato de Castro Vivas

https://orcid.org/0000-0003-2290-7773

Doutor em Engenharia Industrial. Universidade Federal da Bahia = (UFBA) =E2=80=93 Brasil. renato.vivas@= ufba.br

Jo=C3=A3o Thiago de Gu= imar=C3=A3es Anchieta e Ara=C3=BAjo Campos

https://orcid.org/0000-0003-3033= -9753

Doutor em Engenharia Industrial. Univer= sidade Federal da Bahia (UFBA) =E2=80=93 Brasil. jcampos@ufba.br

 

RESUMO

A avalia=C3=A7=C3=A3o dos impactos = de sustentabilidade dos modelos de neg=C3=B3cio se tornou essencial para a = transi=C3=A7=C3=A3o das empresas para uma economia mais sustent=C3=A1vel e = circular. Modelos multicrit=C3=A9rio tem sido amplamente utilizados como um= a abordagem eficaz para avaliar e classificar o desempenho de sustentabilid= ade de empresas em diversos setores. Este artigo realiza uma an=C3=A1lise c= omparativa de m=C3=A9todos multicrit=C3=A9rio para avaliar o desempenho de = sustentabilidade de uma empresa de petr=C3=B3leo e g=C3=A1s. O estud= o aborda a crescente import=C3=A2ncia da sustentabilidade corporativa nesse= setor, empregando individualmente tr=C3=AAs m=C3=A9todos distintos, VIKOR,= PROMETHEE e TOPSIS na an=C3=A1lise da sustentabilidade organizacional. A compara=C3=A7=C3=A3o dos m=C3=A9todos forneceu insights valiosos = sobre seus respectivos pontos fortes e fracos ao abordar cen=C3=A1rios comp= lexos de tomada de decis=C3=A3o. Embora produzam resultados similares o PRO= METHEE =C3=A9 mais relevante quando se lida com problemas complexos que env= olvem uma gama mais ampla de crit=C3=A9rios, especialmente quando h=C3=A1 m= =C3=BAltiplas percep=C3=A7=C3=B5es e julgamentos humanos envolvidos e quand= o as decis=C3=B5es s=C3=A3o de longo prazo com impactos duradouros. Pesquis= as futuras podem explorar metodologias com diferentes abordagens, aplicadas= a outros tipos de organiza=C3=A7=C3=B5es e/ou localidades, a fim de avalia= r a sustentabilidade organizacional. Al=C3=A9m disso, experimentar a integr= a=C3=A7=C3=A3o de modelos multiatributo com modelos de otimiza=C3=A7=C3=A3o= matem=C3=A1tica e modelos de previs=C3=A3o =C3=A9 uma op=C3=A7=C3=A3o vi= =C3=A1vel para avaliar, otimizar e prever a sustentabilidade.

 

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Palavras-Chave: multicrit=C3=A9= rios; MCDA; sustentabilidade, performance.

 

ABSTRACT

The assessment= of the sustainability impacts of business models has become essential for companies transitio= ning toward a more sustainable and circular economy. Multicriteria models h= ave been widely used as an effective approach to evaluate and rank the sust= ainability performance of companies across various sectors. This paper cond= ucts a comparative analysis of multicriteria methods for assessing the sust= ainability performance of an oil and gas company. The study addresses the g= rowing importance of corporate sustainability in this sector, individually = employing three distinct methods - VIKOR, PROMETHEE, and TOPSIS - for organ= izational sustainability analysis. The comparison of these methods provides= valuable insights into their respective strengths and weaknesses when addr= essing complex decision-making scenarios. While they yield similar results,= PROMETHEE is particularly relevant when handling intricate problems involv= ing a broader range of criteria, especially in cases where multiple human p= erceptions and judgments are involved, and where decisions have long-term, = lasting impacts. Future research could explore methodologies with different= approaches, applied to other types of organizations and/or locations, in o= rder to assess organizational sustainability. Additionally, experimenting w= ith the integration of multi-attribute models with mathematical optimizatio= n and forecasting models is a viable option for assessing, optimizing, and = predicting sustainability.

Keywords: multi-criteria; MCDA; sustainability, performance.<= span style=3D"font-family:Arial; font-weight:bold">

 

Recebido em 09/03/2024.  Aprovado em 07/09/2024.= Avaliado pelo sistema double blind peer review. Publicado= conforme normas da APA. h= ttps://doi.org/10.22279/navus.v14.1888

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1 INTRODU=C3=87=C3=83O

 

Nos =C3= =BAltimos anos, a conscientiza=C3=A7=C3=A3o global sobre a import=C3=A2ncia= da sustentabilidade e da responsabilidade corporativa aumentou significati= vamente. Empresas de diversos setores t=C3=AAm se deparado com a necessidad= e de adotar medidas que considerem n=C3=A3o apenas os aspectos econ=C3=B4mi= cos, mas tamb=C3=A9m os impactos ambientais, sociais e de governan=C3=A7a (= ESG) de suas opera=C3=A7=C3=B5es. De acordo com o artigo de Heichl e Hirsch= (2023), empresas e partes interessadas est=C3=A3o exigindo cada vez mais r= elat=C3=B3rios transparentes das atividades corporativas e seu impacto nos = t=C3=B3picos de ESG. Na ind=C3=BAstria do petr=C3=B3leo, o discurso em torn= o dessas quest=C3=B5es se tornou especialmente relevante, j=C3=A1 que a ind= =C3=BAstria =C3=A9 amplamente reconhecida como um dos principais contribuin= tes para as emiss=C3=B5es de gases de efeito estufa e outros impactos ambie= ntais negativos.

Avaliar os impactos de sustentabilidade dos m= odelos de neg=C3=B3cios tornou-se essencial para que as empresas fa=C3=A7am= a transi=C3=A7=C3=A3o para uma economia mais sustent=C3=A1vel e circular. = Segundo Bhatnagar et al. (2022), muitas empresas enfrentam desafios no dese= nvolvimento de modelos de neg=C3=B3cios sustent=C3=A1veis, mas esses desafi= os podem ser superados avaliando os impactos de sustentabilidade de diferen= tes designs de modelos de neg=C3=B3cios. Saulick et al. (2023) afirmam que,= para avaliar se as empresas est=C3=A3o implementando estrat=C3=A9gias sust= ent=C3=A1veis em suas opera=C3=A7=C3=B5es, =C3=A9 necess=C3=A1ria uma avali= a=C3=A7=C3=A3o abrangente de seu desempenho em sustentabilidade.

=

Dado esse contexto, as empresas petrol=C3=ADferas t=C3=AAm buscado estra= t=C3=A9gias e modelos que lhes permitam mensurar e monitorar seu desempenho= em sustentabilidade, ao mesmo tempo em que desenvolvem pr=C3=A1ticas suste= nt=C3=A1veis para reduzir sua pegada ambiental, promover o bem-estar social= e fortalecer sua governan=C3=A7a corporativa. No trabalho de Bockstaller e= t al. (2017), a avalia=C3=A7=C3=A3o da sustentabilidade =C3=A9 apresentada = como um desafio multifacetado, envolvendo a considera=C3=A7=C3=A3o de m=C3= =BAltiplos crit=C3=A9rios que abrangem diversas =C3=A1reas tem=C3=A1ticas, = organizadas dentro da estrutura das dimens=C3=B5es da sustentabilidade.

Percebe-se, assim, a necessidade de avaliar o desempenho das orga= niza=C3=A7=C3=B5es em termos de sustentabilidade. Essa avalia=C3=A7=C3=A3o = n=C3=A3o =C3=A9 simples, pois a sustentabilidade incorpora par=C3=A2metros = de m=C3=BAltiplos crit=C3=A9rios, alguns dos quais s=C3=A3o complexos no ca= minho para o desenvolvimento sustent=C3=A1vel. Com base nos resultados da a= valia=C3=A7=C3=A3o de desempenho obtidos, as organiza=C3=A7=C3=B5es podem t= omar melhores decis=C3=B5es utilizando crit=C3=A9rios sustent=C3=A1veis (FA= RLEY & SMITH, 2013).

M=C3=A9todo= s multiatributo t=C3=AAm sido amplamente empregados como uma abordagem efic= az para avaliar e classificar o desempenho de sustentabilidade de empresas = em diversos setores. V=C3=A1rias abordagens quantitativas para avalia=C3=A7= =C3=A3o e otimiza=C3=A7=C3=A3o da sustentabilidade s=C3=A3o identificadas p= or Brandenburg et al. (2014), incluindo modelos de simula=C3=A7=C3=A3o, mat= em=C3=A1ticos, heur=C3=ADsticos e anal=C3=ADticos, entre eles modelos anal= =C3=ADticos multiatributo, como AHP, ELECTRE, PROMETHEE, DEMATEL, VIKOR, TO= PSIS, MAUT, entre outros. Com essa gama de m=C3=A9todos de avalia=C3=A7=C3= =A3o multiatributo, =C3=A9 fundamental que se fa=C3=A7a uma an=C3=A1lise co= mparando os m=C3=A9todos mais relevantes e proeminentes, estabelecendo um e= studo do tema, suas inter-rela=C3=A7=C3=B5es e a identifica=C3=A7=C3=A3o do= s m=C3=A9todos mais adequados para auxiliar na tomada de decis=C3=A3o na ge= st=C3=A3o sustent=C3=A1vel das organiza=C3=A7=C3=B5es. A princ=C3=ADpio, os= m=C3=A9todos que ser=C3=A3o aplicados nessa compara=C3=A7=C3=A3o ser=C3=A3= o os chamados m=C3=A9todos outranking, que estabelecem um ranqueamento/classifica=C3=A7=C3=A3o dos= crit=C3=A9rios dos cen=C3=A1rios/temas escolhidos.

Assim= , este artigo tem como objetivo explorar a aplica=C3=A7=C3=A3o de modelos m= ultiatributo na avalia=C3=A7=C3=A3o do desempenho de sustentabilidade de um= a empresa petrol=C3=ADfera. Al=C3=A9m disso, =C3=A9 realizada uma compara= =C3=A7=C3=A3o entre m=C3=A9todos multiatributo. Tr=C3=AAs m=C3=A9todos ampl= amente utilizados nesse dom=C3=ADnio s=C3=A3o VIKOR, PROMETHEE e TOPSIS. O = foco est=C3=A1 na identifica=C3=A7=C3=A3o e an=C3=A1lise dos principais ind= icadores de sustentabilidade relevantes para o setor, bem como na constru= =C3=A7=C3=A3o de um modelo de avalia=C3=A7=C3=A3o que integre esses atribut= os.

O m=C3=A9todo PROMETHEE, classificado como uma abordagem d= e an=C3=A1lise multicrit=C3=A9rio de supera=C3=A7=C3=A3o n=C3=A3o param=C3= =A9trica, se diferencia significativamente de outras metodologias nesse dom= =C3=ADnio. Ao contr=C3=A1rio dos m=C3=A9todos convencionais multicrit=C3=A9= rios que se concentram principalmente na pondera=C3=A7=C3=A3o da signific= =C3=A2ncia das rela=C3=A7=C3=B5es entre crit=C3=A9rios, o PROMETHEE incorpo= ra de forma =C3=BAnica uma avalia=C3=A7=C3=A3o das rela=C3=A7=C3=B5es inter= nas inerentes a cada crit=C3=A9rio de avalia=C3=A7=C3=A3o (Brans & Mare= schal, 2005).

O m=C3=A9todo TOPSIS seleciona uma alternativa q= ue esteja mais pr=C3=B3xima da solu=C3=A7=C3=A3o ideal positiva e mais dist= ante da solu=C3=A7=C3=A3o ideal negativa. A solu=C3=A7=C3=A3o ideal positiv= a representa o melhor desempenho em cada crit=C3=A9rio, enquanto a solu=C3= =A7=C3=A3o ideal negativa compreende os piores valores de desempenho para e= sses crit=C3=A9rios (Hwang & Yoon, 1981).

Por outro lado, = a maior adequa=C3=A7=C3=A3o do m=C3=A9todo VIKOR =C3=A9 sua capacidade de f= ornecer uma solu=C3=A7=C3=A3o compromissada (mais pr=C3=B3xima da solu=C3= =A7=C3=A3o ideal) para classificar alternativas dentro de muitos crit=C3=A9= rios conflitantes (Opricovic & Tzeng, 2007).

A escolha de= uma empresa petrol=C3=ADfera como estudo de caso justifica-se pela import= =C3=A2ncia estrat=C3=A9gica desse setor e pela necessidade premente de impu= lsionar mudan=C3=A7as positivas em suas opera=C3=A7=C3=B5es. Ao examinar o = desempenho de sustentabilidade de uma empresa petrol=C3=ADfera por meio de = modelos multiatributo, buscamos n=C3=A3o apenas fornecer uma compreens=C3= =A3o abrangente e profunda da sustentabilidade corporativa, mas tamb=C3=A9m= oferecer insights valiosos para a tomada de decis=C3=A3o e o planejamento = estrat=C3=A9gico dentro da empresa.

Espera-se, por fim, que es= te estudo contribua para o avan=C3=A7o do conhecimento sobre a aplica=C3=A7= =C3=A3o dos m=C3=A9todos multiatributo na avalia=C3=A7=C3=A3o do desempenho= de sustentabilidade em empresas petrol=C3=ADferas, fornecendo uma base s= =C3=B3lida para a implementa=C3=A7=C3=A3o de pr=C3=A1ticas sustent=C3=A1vei= s e para a melhoria cont=C3=ADnua da responsabilidade corporativa nesse set= or. O escopo desta pesquisa est=C3=A1 ilustrado na Figura 01.

=  

 

 

 

 

 

 

 

 

 

 

 = ;

 

 

 

= Figura 01

Escopo do Projeto

 

3D"Uma

 

 

2 MET=C3=93DO

 

Inicialmente, este artigo ter=C3=A1 como base a aplica=C3=A7= =C3=A3o em estudo de caso dos m=C3=A9todos multiatributo na avalia=C3=A7=C3= =A3o de desempenho de sustentabilidade. Este modelo de aplica=C3=A7=C3=A3o = =C3=A9 baseado no artigo de Vivas et al. (2019), o qual envolve a defini=C3= =A7=C3=A3o das dimens=C3=B5es e crit=C3=A9rios de sustentabilidade a serem = analisados. Em uma etapa subsequente, os dados foram coletados a partir de = relat=C3=B3rios de sustentabilidade disponibilizados pela organiza=C3=A7=C3= =A3o. Esses relat=C3=B3rios s=C3=A3o normalmente gerados periodicamente, pe= rmitindo a avalia=C3=A7=C3=A3o do desempenho de sustentabilidade organizaci= onal em uma escala temporal ao longo dos anos. Esses dados, ent=C3=A3o, ser= =C3=A3o categorizados e os crit=C3=A9rios selecionados ser=C3=A3o normaliza= dos para se obter uma classifica=C3=A7=C3=A3o comparativa dos cen=C3=A1rios= .  Os cen=C3=A1rios, diferenciados pela escala temporal anual, = ser=C3=A3o comparados entre si, resultando em um ranqueamento dos melhores = e piores anos de desempenho da sustentabilidade organizacional. Al=C3=A9m d= esse ranqueamento, o estudo tamb=C3=A9m faz uma compara=C3=A7=C3=A3o dos re= sultados de tr=C3=AAs m=C3=A9todos distintos: PROMETHEE, VIKOR e TOPSIS.

No campo da tomada de decis=C3=A3o e avalia=C3=A7=C3=A3o de = desempenho, os modelos multicrit=C3=A9rio, entre eles os m=C3=A9todos multi= atributo, ganharam aten=C3=A7=C3=A3o significativa como ferramentas eficaze= s para lidar com problemas complexos de decis=C3=A3o e avaliar alternativas= com base em m=C3=BAltiplos crit=C3=A9rios ou atributos. Tr=C3=AAs m=C3=A9t= odos multiatributo s=C3=A3o utilizados neste projeto: VIKOR (VI=C5=A1ekriterijumska optimi= zacija i KOmpromisno Rangiranje), = PROMETHEE (Pref= erence Ranking Organization Method for Enrichment Evaluations) e TOPSIS (Technique for Order of Preference by Similarity to = Ideal Solution).

Esse= s modelos multicrit=C3=A9rio, nomeadamente VIKOR, PROMETHEE e TOPSIS, t=C3= =AAm sido amplamente aplicados em diversos campos, como engenharia, finan= =C3=A7as, gest=C3=A3o ambiental e neg=C3=B3cios. Eles permitem que os tomad= ores de decis=C3=A3o lidem com problemas complexos de decis=C3=A3o, avaliem= alternativas com objetividade e forne=C3=A7am insights valiosos sobre as m= elhores solu=C3=A7=C3=B5es de compromisso, com base nos crit=C3=A9rios ou a= tributos selecionados.

 

 

2.1 Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)

 

O TOPSIS =C3=A9 um m=C3=A9todo multicrit=C3=A9rio = originalmente desenvolvido por Hwang e Yoon em 1981. Ele =C3=A9 utilizado p= ara determinar a proximidade relativa das alternativas em rela=C3=A7=C3=A3o= a uma solu=C3=A7=C3=A3o ideal. Ele constr=C3=B3i uma solu=C3=A7=C3=A3o ide= al e uma solu=C3=A7=C3=A3o ideal negativa com base nos melhores e piores va= lores de atributo, respectivamente. O TOPSIS ent=C3=A3o calcula a proximida= de relativa de cada alternativa a essas solu=C3=A7=C3=B5es ideais, fornecen= do uma classifica=C3=A7=C3=A3o que reflete o melhor compromisso entre as du= as. Esse modelo ajuda os tomadores de decis=C3=A3o a identificarem as alter= nativas mais pr=C3=B3ximas da solu=C3=A7=C3=A3o ideal, com base nos crit=C3= =A9rios selecionados.

O m=C3=A9todo =C3=A9 executado de acordo= com as seguintes etapas:

= Etapa 01 - Cria=C3=A7=C3=A3o da matriz de avalia=C3=A7=C3=A3o composta por = m alternativas e n crit=C3=A9rios, sendo a intersec=C3=A7=C3=A3o de cada al= ternativa e crit=C3=A9rio dada como xij, resultando a= ssim em uma matriz (xij)mxn.

Etapa 02 =E2=80=93 Normaliza=C3=A7=C3=A3o da Matri= z. A matriz (xij)mxn =C3=A9 nor= malizada usando o modelo:

3D""=3D 3D"", i =3D 1, = 2 . . ., m, j =3D 1, 2. . ., n = 0;              (1.1)

Etapa= 03 =E2=80=93 Defini=C3=A7=C3=A3o dos pesos:

3D"" =3D 3D"" : 3D"" =     (1.2)

e wj =C3=A9 o valor original do peso do crit=C3= =A9rio vj ,  j =3D 1 , 2 .  . <= span style=3D"line-height:115%; font-family:Arial; font-size:10pt"> . n.

Etapa 04 =E2=80=93 Determina= ndo a melhor (Ab) e a pior (Aw<= /span>)= alternativa:

Aw =3D (max(tij| i =3D 1, 2 =E2=80=A6 , m|j=   3D""J-),(min(tij= = | i =3D 1, 2 =E2=80=A6 , m|j  3D""J+) = =E2=89=A1 twj|j =3D 1, 2 .  .  .  ,&#= xa0; n,             = =            (1.3)

Ab =3D (min(= tij| i =3D 1, 2 =E2=80=A6 , m|j=   3D""J-),(min(tij| i =3D 1, 2 =E2=80=A6= , m|j  3D""J+) =E2=89=A1 tbj|j =3D 1, 2 .  .  .  ,  n,    = ;             = =        (1.4)

onde,

J + =3D {j =3D 1 , 2 , =E2=80=A6 , n =E2=88=A3 j } associado com o crit=C3=A9rio que tem um imp= acto positivo, e

J =E2=88=92 =3D {j =3D 1 , 2 , =E2=80=A6 , n = =E2=88=A3 j } associa= do com o crit=C3=A9rio que tem um impacto negativo.

Etapa 05 =E2=80=93 C=C3=A1lculo da dist=C3=A2ncia= L2 entre a meta alternativa meta e a pior condi=C3=A7=C3=A3o Aw:

3D""     &#= xa0;       &= #xa0;        = ;   <= span style=3D"font-family:Arial">    (1.5)

E a dist=C3=A2ncia entre a alternativa i e a melhor= condi=C3=A7=C3=A3o Ab.

3D""   = ;   <= span style=3D"font-family:Arial">     = 0;   =              = ;   (1.6)<= /p>

onde diw e = dib s=C3=A3o L2- dist=C3=A2nc= ias da alternativa meta i para o pior e melhor condi=C3= =A7=C3=A3o, respectivamente.

Etapa 6 -     C=C3=A1lculo da sim= ilaridade da pior condi=C3=A7=C3=A3o:

        siw =3D =3D""  , 0 =E2=89=A4 siw =E2=89=A4 1, i =3D 1 , 2 , = =E2=80=A6 , m .    (1.7)

        s= iw   = =      siw =3D 0 se e somente se a = solu=C3=A7=C3=A3o for a pior condi=C3=A7=C3=A3o;

Etapa 7 - Ra= nqueamento das alternativas de acordo com:

 siw i =3D 1, 2, =E2=80=A6, m;<= /span>&= #xa0;  j =3D 1, 2 , =E2=80=A6 , m.       = ;             = ;(1.8)

 

 

2.2 Preferen= ce Ranking Organization METHod for Enrichment of Evaluations (PROMETHEE)

 = ;

Os elementos b=C3=A1sicos do m=C3=A9todo foram introduzidos = pela primeira vez por Brans e Mareschal em 1982. O PROMETHEE =C3=A9 outra t= =C3=A9cnica de tomada de decis=C3=A3o multicrit=C3=A9rio amplamente utiliza= da, que avalia e classifica alternativas com base em um conjunto de fun=C3= =A7=C3=B5es de prefer=C3=AAncia. Ele incorpora informa=C3=A7=C3=B5es de pre= fer=C3=AAncia na forma de compara=C3=A7=C3=B5es pares para determinar a imp= ort=C3=A2ncia relativa dos crit=C3=A9rios e quantificar as rela=C3=A7=C3=B5= es de supera=C3=A7=C3=A3o entre as alternativas. O PROMETHEE fornece uma cl= assifica=C3=A7=C3=A3o abrangente das alternativas e auxilia os tomadores de= decis=C3=A3o na compreens=C3=A3o das compensa=C3=A7=C3=B5es entre diferent= es crit=C3=A9rios. As etapas s=C3=A3o apresentadas a seguir:

E= tapa 01 =E2=80=93 Determina=C3=A7=C3=A3o dos desvios baseados na compara=C3= =A7=C3=A3o dos pares:

Dj(a, b) =3D gj(a) =E2=80=93 gj(b)         &#x= a0;            = =              = = (1.9)

Onde dj(a, b) representa a diferen=C3=A7a entre as avalia=C3=A7=C3=B5es= de a e b em rela=C3=A7=C3=A3o aos crit=C3=A9rios estabelecidos.

=

Etapa 02 =E2=80=93 Aplica=C3=A7=C3=A3o da matriz de prefer=C3=AAncia:

Pj(a, = b) =3D Fj[dj(a, b)] for j =3D = 1, ..., k.            &#x= a0;     (2.0)

Onde Pj(a, b) representa a prefer=C3=AAncia d= as alternativas A e B para a estabiliza=C3=A7=C3=A3o do crit=C3=A9rio basea= do no dj(a, b).

Etapa 03 =E2=80=93 C=C3= =A1lculo do =C3=ADndice de prefer=C3=AAncia global:

3D""  =                         =        (2.1)

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-indent:36pt; text-align:= justify; line-height:115%; font-size:10pt">Etapa 04 =E2=80=93 C=C3=A1lculo dos crit=C3=A9rios individuais(PROMETHEE = I):

=CF=86+(a) =3D 3D""     &#= xa0;       &= #xa0;       =          = 0;   =     &#x= a0;  (2.2)

=CF=86-(a) =3D 3D""   &#= xa0;       &= #xa0;       =             =     &#x= a0;    (2.3)

Onde =CF=86+(a) e = =CF=86-(a) representa os fluxos positivos e negativos, respectivamente para= cada alternativa.

Etapa 05 =E2=80=93 C=C3=A1lculo dos fluxos = globais(PROMETHEE II):

=CF=86(a) =3D =CF=86+(a) - =CF=86-(a) <= /span>        = ;   <= span style=3D"font-family:Arial">     = 0;   =     &#x= a0;        = ;   <= span style=3D"font-family:Arial">   (2.4)

Ond= e =CF=86(a) representa o fluxo global de cada alternativa.

&#x= a0;

 

2.3 VIseKriterijumska Optimizacija = I Kompromisno Resenje (VIKOR)

 

VIseKriterijumska Optimizaci= ja I Kompromisno Resenje (VIKOR) foi originalmente desenvolvido por Duckste= in e Opricovic (1980) para lidar com problemas conflitantes e incomensur=C3= =A1veis (com unidades diferentes). VIKOR =C3=A9 um m=C3=A9todo de decis=C3= =A3o multicrit=C3=A9rio desenvolvido para determinar solu=C3=A7=C3=B5es de = comprometimento considerando crit=C3=A9rios conflitantes. Ele calcula o =C3= =ADndice que combina a medida de utilidade m=C3=A1xima do grupo e a medida = individual de comprometimento. Ao empregar o modelo VIKOR, os tomadores de = decis=C3=A3o podem identificar alternativas que atingem o melhor comprometi= mento entre v=C3=A1rios crit=C3=A9rios, fornecendo uma solu=C3=A7=C3=A3o eq= uilibrada. A etapa inicial =C3=A9 apresentada a seguir:

Etapa= 01 - Determina=C3=A7=C3=A3o dos melhores e piores valores dos crit=C3=A9ri= os:

Para cada crit=C3=A9ri= o i =3D 1, 2, ..., n: Fi* =3D max(Fij; j =3D 1, ..., J) F =3D min(Fij; j =3D 1, ...,= J)              = 0;         (2.5)

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-indent:36pt; text-align:= justify; line-height:115%; font-size:12.5pt">Para cada crit=C3=A9rio i =3D 1, 2, .= .., n: Fi* =3D min(Fij; j =3D 1= , ..., J) F =3D max(Fij; j =3D 1, ..., J)   = ;             = =         (2.6)

Etapa 02 =E2= =80=93 C=C3=A1lculo da matriz normalizada:

C=C3=A1lculo dos valores normalizados para cada alternativ= a Si e Ri , i =3D 1, 2, ..., J:=

Si =3D 3D""  &#x= a0;       &#= xa0;       &= #xa0;       =     <= span style=3D"font-family:Arial">     = 0;   =     &#x= a0;       &#= xa0;       (2.7)

Ri =3D 3D""       = ;   <= span style=3D"font-family:Arial">     = 0;   =     &#x= a0;        = ;   <= span style=3D"font-family:Arial">     = 0;   =     &#x= a0;       &#= xa0;  (2.8)

on= de Wj s=C3=A3o os pesos dos crit=C3=A9rios, expressan= do a prefer=C3=AAncia da matriz como a import=C3=A2ncia relativa dos crit= =C3=A9rios.

Etapa 03 =E2=80=93 C=C3=A1lculo dos valores finais= :

Qi =3D v.  3D"" = ) + (1 =E2=80=93 v). 3D"" )     = ;   <= span style=3D"font-family:Arial">          (2.9)

Etapa 04 =E2=80=93= Ranqueamento das alternativas baseadas em Si<= span style=3D"line-height:115%; font-family:Arial; font-size:10pt">, Ri, or Qi.

 

 

3 ESTUDO = DE CASO

 

A aplica=C3=A7=C3=A3o dos m=C3= =A9todos PROMETHEE, VIKOR e TOPSIS =C3=A9 realizada com base em dados de en= trada obtidos de uma grande empresa de petr=C3=B3leo e g=C3=A1s. Essa empre= sa, a maior do setor no Brasil, conta com aproximadamente 45.000 funcion=C3= =A1rios diretos e produz, em m=C3=A9dia, 2.684 mil barris de =C3=B3leo equi= valente por dia (boed). Os dados coletados v=C3=AAm dos relat=C3=B3rios de = sustentabilidade da empresa, publicados anualmente. A an=C3=A1lise de desem= penho foi realizada utilizando dados de 2009 a 2020.

 

3.1 Sele=C3=A7=C3=A3o de Indicadores

 <= /p>

Os indicadores de sustentabilidade foram selecionados com base na Global Reporting I= nitiative (GRI) (2021), uma vez qu= e os relat=C3=B3rios analisados foram elaborados utilizando esses indicador= es. O n=C3=BAmero de indicadores foi determinado com base na= disponibilidade de dados nos relat=C3=B3rios de 2009 a 2020= . Alguns desses indicadores foram omitidos ou modificados nos relat<= span style=3D"font-family:'Courier New'">=C3=B3rios, o que impediu uma an=C3=A1lise temporal m= ais aprofundada dos dados. Aproximadamente 15 indicadores quantitativos for= am identificados para a composi=C3=A7=C3=A3o dos dados de entrada para o mo= delo de avalia=C3=A7=C3=A3o multiatributo. As m=C3=A9tricas selecionadas es= t=C3=A3o ilustradas na Tabela 01.

 

 

 

 

 

&#x= a0;

 

 

 

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-indent:36pt; text-align:= justify; line-height:115%; font-size:10pt"> 

 

 

 

 

 

 

Tabela 01

Dimens=C3=B5es, tema= s e indicadores

4

Res=C3=ADduos S=C3=B3lidos (306-2)

Social

<= td style=3D"width:73.25pt; border-bottom-style:solid; border-bottom-width:1= pt; padding-right:3.75pt; padding-left:3.75pt; vertical-align:bottom">

Governan=C3=A7a

 

Dimens=C3=B5es

=

Temas (por GRI = 2021)

Indicadores

1

Ambiental

Energia (302-1)

X5=3DEnergia(Tj)

2

Ambiental

Vazamentos de =C3=B3leo306-3= )

X6=3DVazamentos de =C3=93leo (m=C2=B3)

3

Ambienta= l

Emiss=C3=B5es (305-1)

X7=3DEmiss=C3=B5es de CO2ton)

Ambiental

X8=3DRes=C3=ADduos perigosos (ton)<= /span>

= 5

Ambiental

=C3=81gua (303-5)

X= 9=3D=C3=81gua (m=C2=B3)

6

Social

Dive= rsidade (405-1)

X10=3DFuncion=C3=A1rios Mulheres (%)

7

Diversidade (405-1)

X11=3DFuncion=C3=A1rios = Negros (%)

8

Social

Equidade

X12= =3DChefes Mulheres (%)

9

Social

= Equidade (405-1)

X13=3DChefes Pretos (= %)

<= span>10

Social

Sa=C3=BAde e Seguran=C3=A7a (403-9)

X14=3D Acidentes(TR= IFR)

<= span>11

Social

Trabalho (403)

X15=3DN=C3=BAmero de Empregados (un)

12<= /span>

Governan=C3=A7a

Economia (201-1)

X1=3DReceita de Vendas (R$)

13=

Governan=C3=A7a<= /p>

Economia (201-1)

X2=3DD=C3=ADvida L=C3=ADquida (R$)

14

Governan=C3=A7a=

Economia (201-1)

X3=3D Volume de Produ=C3=A7=C3=A3o (barr= il)

15

Economia (203-1)

X4=3DTotal de Investimentos (R$)

 

 

 

3.2 Dados de Entrada e Experimenta=C3=A7=C3=A3o

 

Para uma melhor disposi= =C3=A7=C3=A3o, os dados ser=C3=A3o disponibilizados na sequ=C3=AAncia do de= talhamento a seguir.

A Tabela 02 apresenta os dados iniciais coletados que s= er=C3=A3o utilizados como dados de entrada para os tr=C3=AAs m=C3=A9todos, = TOPSIS, PROMETHEE e VIKOR. Estes dados foram coletados nos relat=C3=B3rios = de sustentabilidade da organiza=C3=A7=C3=A3o, de 2009 a 2020. Estes dados j= =C3=A1 foram consolidados pela empresa em quest=C3=A3o, dados mais recentes= s=C3=A3o pass=C3=ADveis de altera=C3=A7=C3=B5es como inclus=C3=B5es, exclu= s=C3=B5es e corre=C3=A7=C3=B5es, al=C3=A9m de ter mudan=C3=A7as significati= vas na coleta e apresenta=C3=A7=C3=A3o dos dados prim=C3=A1rios.

A Tabela 03= mostra as etapas 01 e 02 do m=C3=A9todo TOPSIS. A Tabela 04 mostra os resu= ltados da etapa 4 de determina=C3=A7=C3=A3o da melhor (A+) e pior (A-) alte= rnativa, da etapa 5 de c=C3=A1lculo da dist=C3=A2ncia L2 entre a alternativ= a alvo i e a pior condi=C3=A7=C3=A3o (A-) e da etapa 6 de c=C3=A1lculo da s= imilaridade =C3=A0 pior condi=C3=A7=C3=A3o. A Tabela 05 mostra os resultado= s da etapa 7 de classifica=C3=A7=C3=A3o das alternativas. A Tabela 05 e Fig= ura 02 mostram o ranqueamento do m=C3=A9todo TOPSIS.

A Tabela 06 mostra os re= sultados da etapa 1 de determina=C3=A7=C3=A3o dos melhores e piores valores= dos crit=C3=A9rios do m=C3=A9todo VIKOR. A Tabela 07 mostra os resultados = da etapa 2 de c=C3=A1lculo da matriz normalizada e da etapa 3 de c=C3=A1lcu= lo dos valores finais do m=C3=A9todo VIKOR. A Tabela 08 mostra os resultado= s da etapa 4 de classifica=C3=A7=C3=A3o das alternativas com base em Si, Ri= ou Qi. As tabelas 08 e a Figura 03 indicam que os melhores anos da organiz= a=C3=A7=C3=A3o em termos de sustentabilidade foram 2020, 2019 e 2018. E os = piores anos foram 2010, 2009 e 2014.

A Tabela 09 mostra os resultados da etap= a 2 de aplica=C3=A7=C3=A3o da matriz de prefer=C3=AAncia e da etapa 3 de c= =C3=A1lculo do =C3=ADndice de prefer=C3=AAncia global do m=C3=A9todo PROMET= HEE. A Tabela 10 mostra as etapas 2 e 3 do m=C3=A9todo PROMETHEE. A tabela = 11 e a figura 02 apresentam os resultados de ranqueamento do m=C3=A9todo PR= OMETHEE. O ranking do m=C3=A9todo PROMETHEE indica que os melhores anos da = organiza=C3=A7=C3=A3o em termos de sustentabilidade foram 2019, 2020 e 2018= . E os piores anos foram 2010, 2009 e 2011.


 

=

Tabela 02

Dados de Entrada Coletados nos Relat=C3=B3rios de Sustentabilidade<= /span>

X5=

<= td style=3D"width:40.85pt; border-top-style:solid; border-top-width:1pt; bo= rder-bottom-style:solid; border-bottom-width:1pt; padding-right:5.65pt; pad= ding-left:5.65pt; vertical-align:top; background-color:#d9d9d9">

X12

= <= td style=3D"width:46.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 61007

1= 87,3

= <= td style=3D"width:40.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 14,4

84= 137

78= 947

= = = = <= td style=3D"width:40.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 15,2

48= 219

= <= td style=3D"width:41.2pt; padding-right:5.65pt; padding-left:5.65pt; vertic= al-align:top">

6= 2

<= td style=3D"width:46.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 2770

= <= td style=3D"width:37.6pt; border-bottom-style:solid; border-bottom-width:1p= t; padding-right:5.65pt; padding-left:5.65pt; vertical-align:top">

0,41

49050

  

X1

X2

X3

X4

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-align:justify; line-heig= ht:150%; font-size:10pt">

X7

X8

X9

X10

X11

X13

X14

X15

2009

182834

73400=

2526

70757

604070

254

57,8

258

=

176

<= /td>

16,4

13,8

13,63

29,94

1,52

73284

2010

211842

2583

76411

716673

668

= 61,1

277

16,6

20,4

13,3

25,3

1,24

75728

2011

244176

103022

2622

72546

<= /td>

682827

234

56,2

285

190,9

<= span style=3D"font-family:Arial">16,9

22,5

24,9

1,15

78452

2012

<= /td>

281379

147817

2598

936199

387

68

=

261

193,4

17,1

23,7

15

24,6

1,00

2013<= /span>

304890

221563

2540,3<= /p>

104416

1050949

187

= 74,2

260

193,6

16,7

24,3

15,4

25,2

0,94

83663

2014

337260

282089

2670

87140

1155220

69,5

81,4

= 234

206,5

= 16,8

24,7

15,2

24,4

0,77

<= span style=3D"font-family:Arial">87384

2015

321638

3919= 62

2787

76315

1155185

71,6

78,1

195

213= ,3

17,45

25,61

15,3

25,3

0,57

77104

2016

282589

314120

2790

55348

<= /td>

899487

51,9

66,5

132

191,6

= 16,18

27

20,6

0,50

62527

2017

<= /td>

283695

280752

2767

947645

35,8

67

114

177,7

16,2

27,6

15,3

17,4

0,48

62204

2018=

310255

268900

2628

49370

888559

18,47

121

182,3

16,6

28,08

18,1

17,7

0,47

63361

2019

302245

317867

111120

837568

415,34=

59

= 120

156,9

= 16,1

28,31

18,4

19,3

0,45

<= span style=3D"font-family:Arial">57983

2020

272069

328268

2836

= 40796

8= 21161

2= 16,5

56<= /span>

123

146,3

16,6=

29,2

= 		19,1

20

<= span style=3D"font-family:Arial">Nota: Relat=C3=B3rios de sustentabilidade,= empresa do estudo de caso, de 2009 a 2020.

 

 

 

 

 

 

 

 

 

 

=

Tabela 03

<= td style=3D"width:46.85pt; border-top-style:solid; border-top-width:1pt; bo= rder-bottom-style:solid; border-bottom-width:1pt; padding-right:5.65pt; pad= ding-left:5.65pt; vertical-align:top; background-color:#d9d9d9">

X3

<= /tr><= td style=3D"width:46.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 0,1597

<= td style=3D"width:46.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 0,6734

<= td style=3D"width:56.4pt; padding-right:5.65pt; padding-left:5.65pt; vertic= al-align:top">

0= ,2506

<= td style=3D"width:46.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 0,3824

<= td style=3D"width:46.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 0,3009

<= td style=3D"width:46.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 0,3965

<= td style=3D"width:46.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 0,2778

<= td style=3D"width:46.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 0,3410

<= td style=3D"width:46.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 0,3551

<= td style=3D"width:46.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 0,2519

<= td style=3D"width:46.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 0,2810

<= td style=3D"width:46.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 0,2829

<= td style=3D"width:46.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= 0,2404

 

X1

X2

=

X4

X5

X6

X7

X8

X9

X10

X11

X12

X13

X14

X15

2009

0,1877=

0,0830

0,2722

0,2687

0,1923

= 0,2561

0,2524

<= /td>

0,3552

0,2738

0,2845

0,2491

0,3729

0,5054=

0,2952

2010

= 0,2174

0,0690

<= /td>

0,2784

0,2902

0,2282

0,2668

0,3813

0,2914=

0,2879

0,2361

0,2431

0,3151

= 0,4123

0,3050

<= /td>

2011

0,1165

0,2826

0,2755=

0,2174

0,2359

0,2454

0,3924

= 0,2970

0,2931

<= /td>

0,2604

0,2632

0,3102

0,3160

2012

0,2888

0,1671

0,2800

= 0,3195

0,2980

<= /td>

0,3902

0,2969

0,3593

0,2966

0,2743

0,2742=

0,3064

0,3325

0,3180

2013

=

0,3129

0,2505

0,2738

0,3346

0,1885

0,3240=

0,3579

0,3012

0,2897

0,2813

= 0,2815

0,3139

<= /td>

0,3126

0,3370

2014

0,3462

0,3189<= /span>

0,2878

0,3309

0,3678=

0,0701

<= span style=3D"font-family:Arial">0,3554

0,3222

0,3213

0,2914

0,2859

0,3039

0,2560

0,3520=

2015

0,3301

= 0,4431

0,3004

<= /td>

0,2898

0,3678

0,0722

0,2685

0,3319

0,3027=

0,2964

0,2796

0,3151

0,1895

= 0,3106

2016

0,2900

0,3007

0,2102

0,2864=

0,0523

0,2903

0,1817

0,2981

= 0,2806

0,3125

<= /td>

0,2778

0,2566

0,1663

201= 7

0,2912

0,3174

0,2982

0,1831

= 0,3017

0,0361

<= /td>

0,2925

0,1569

0,2765

0,3195

0,2796

0,2167=

0,1596

0,2506

2018

0,3184

<= /td>

0,3040

0,2832

0,1875

0,0186

0,2707

0,1666=

0,2836

0,2879

0,3250

0,3308

= 0,2205

0,1563

<= /td>

0,2552

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-align:justify; line-heig= ht:150%; font-size:10pt">

0,3102

0,3593

0,2985=

0,4220

0,2666

0,4187

0,2576

= 0,1652

0,2441

<= /td>

0,2791

0,3277

0,3363

0,1496

0,2336

2020

0,2793

0,3711

0,3057

0,1549

0,2614

0,2183

0,2445

0,1693

0,2276

0,2886

0,3380

0,3491

0,2491

0,1363

0,1976

Etapas 01 e 02 do M=C3=A9todo TOPSI

 

 

 

 

 

 

<= p style=3D"margin-top:0pt; margin-bottom:0pt; font-size:10pt"> <= /span>

 

 

 

 

 

 

 

 

 

 

Tabela 04

Etapas 04 a 06 do M=C3=A9todo TOPSIS

<= td style=3D"width:43.05pt; padding-right:3.75pt; padding-left:3.75pt; verti= cal-align:bottom">

0,0178

<= td style=3D"width:43.05pt; padding-right:3.75pt; padding-left:3.75pt; verti= cal-align:bottom">

0,0166

= =

0,0150

=

0,0142

=

0,0153

<= td style=3D"width:43.05pt; padding-right:3.75pt; padding-left:3.75pt; verti= cal-align:bottom">

0,0186

=

 

X1

X2

X3

X4

X5

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-indent:3.35pt; text-alig= n:center; line-height:115%; font-size:10pt">X6

X7

X8

X9

X10

X11

X12

X13

X14

X15

2009

0,0094

0,0041

0,0136<= /p>

0,0134

0,0096

0,0128

0,0126

0,0137

0,0142

0,0080

0,01= 25

0,0186

0,0253

= 0,0148

= 2010

0,0109

0,00= 34

0,0139

0,0145

0,0114

0,0337=

0,0133

0,0191

0,0146

0,0144

0,0118

0,0122

0,0158

=

0,0206

0,0153

2011

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-align:justify; line-heig= ht:115%; font-size:10pt">0,0125

0,0058

0,0141

0,0138

0,0109

0,0118

0,0123

0,01= 96

0,0149

0,0147

0,0130

0,0132

0,0155

0,0191

0,015= 8

2012<= /span>

0,0144

0,0084

0,0140

0,0160

0,0149

0,0195

0,0148

0,0180

0,0150

<= /td>

0,0148

0,= 0137

0,0137

0,0153

0,0159

2013

0,0156

0,0125

0,0137

= 0,0198

0,0167

0,0094

0,0162

0,0179

0,0151

0,0145

<= span style=3D"font-family:Arial">0,0141

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-align:justify; line-heig= ht:115%; font-size:10pt">0,0141

0,0157

0,0156

0,0168=

2014

0,0173

0,0159

0,0144

<= span style=3D"font-family:Arial">0,0165

0,0184

0,0035

0,0= 178

0,0161

0,0161

0,0146

0,0143

0,0139

0,0152

0,012= 8

0,0176

2015

0,0165

0,0222

0,0150

0,014= 5

0,0184

0,0036

= 0,0170

=

0,0134

0,0166

0,0151

0,0148

0,0140

0,0158

0,0095

0,0155

2016

0,0145

0,0178

0,0105

0,0= 143

0,0026

0,014= 5

0,0091

0,0149

0,0140

0,0156

0,0139

0,0128

0,008= 3

0,0126

2017

0,0146

0,0159

0,0149

0,009= 2

0,0151

0,0018

= 0,0146

=

0,0078

0,0138

0,0140

0,0160

0,0140

0,0108

0,0080

0,0125

2018

0,0159

0,0152

0,0094

0,0= 141

0,0009

0,013= 5

0,0083

0,0142

0,0144

0,0163

0,0165

0,0110

0,007= 8

0,0128

2019

0,0155

0,0180

0,0149

0,021= 1

0,0133

0,0209

= 0,0129

=

0,0083

0,0122

0,0140

0,0164

0,0168

0,0120

0,0075

0,0117

2020

0,0140

0,0186

0,0077

0,0= 131

0,0109

0,012= 2

0,0085

0,0114

0,0144

0,0169

0,0175

0,0125

0,006= 8

0,0099

V+

0,0173

0,0034

0,0153

0,0211

0,0096

=

0,0009

0,0122

0,0078

<= /td>

0,0114

0,= 0151

0,0169

0,0175

0,0068

0,0176

V-

0,0094

0,0222

0,0136

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-align:justify; line-heig= ht:115%; font-size:10pt">0,0077<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-indent:3.95pt; text-alig= n:justify; line-height:115%; font-size:10pt">0,0184

0,0337

0,0178

0,0196

0,0166

0,0140

0,0080

0,0122

0,0108

0,0253

0,0099

 

 

 

 

 

 


Tabela 05

Etapa 7, Ranqueamento= do M=C3=A9todo TOPSIS

Pi

0,= 6082

<= td style=3D"width:82.85pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

0= ,6365

=

2017

2018

<= td style=3D"width:48pt; padding-right:5.65pt; padding-left:5.65pt; vertical= -align:bottom">

2019

=

 

Si+

Si-

TO= PSIS RANK

2= 009

0,0287

0,0315

0,5233

10

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-align:center; line-heigh= t:115%; font-size:10pt">2010

0,0395

0,0237

0,3749

12

2011

0,0235

0,0317

0,5742=

8

2012

0,0263

0,0260

0,497= 6

11

2013

0,0212

0,0329

5

2014

0,0212

0,0371

4

2015

0,0244

0,0374

= 0,6050

6

2016

= 0,0211

0,0390

0,6488

3

0,0212

0,0403

<= /td>

0,6555

2

0,0198

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-align:center; line-heigh= t:115%; font-size:10pt">0,0417

=

0,6775

1

0,0267

=

0,0318

0,5436

9

2020<= /span>

0,0251

0,0349

0,5819

7

=

 

 

 

Figura 02

Gr=C3=A1fico de Resultados do M=C3=A9todo TOPSIS

3D""

 


Tabela 06

Etapa 01 do M=C3=A9todo Vikor

 

111120

= <= td style=3D"width:38.75pt; border-bottom-style:solid; border-bottom-width:1= pt; padding-right:5.65pt; padding-left:5.65pt; vertical-align:top">

13,3

17,4

1,52

49050

best (x= i+)

337260

=

61007

2836

604070

18,47

56

114

146,3

17,= 45

29,2

19,1

29,94

0,41

= 87384

worst(xi-)

182834

391962

2526

40796

1155220

668<= /p>

=

81,4

= 		285

213,3

16,0926

13,8

 

Tabela 07

Etapas 02 e 03 do m=C3=A9todo Vikor

<= td style=3D"width:6.24%; padding-right:5.65pt; padding-left:5.65pt; vertica= l-align:top">

0,= 0184

0,0= 000

<= td style=3D"width:6.42%; padding-right:5.65pt; padding-left:5.65pt; vertica= l-align:top">

0,0274

0,0= 301

<= td style=3D"width:6.24%; padding-right:5.65pt; padding-left:5.65pt; vertica= l-align:top">

0,= 0358

<= td style=3D"width:6.24%; padding-right:5.65pt; padding-left:5.65pt; vertica= l-align:top">

0,= 0449

<= td style=3D"width:6.94%; padding-right:5.65pt; padding-left:5.65pt; vertica= l-align:top">

0,0117

<= tr style=3D"height:15pt">= <= td style=3D"width:6.24%; padding-right:5.65pt; padding-left:5.65pt; vertica= l-align:top">

0,= 0000

<= td style=3D"width:6.68%; padding-right:5.65pt; padding-left:5.65pt; vertica= l-align:top">

0,= 0313

=

 

X1

X2

X3

X4

X5

X6

X7

X8

X9

X10

X11

X12

X13

X14

X15

2009

0,0500

0,0019

0,0500=

0,0287

0,0000

0,0181=

0,0035

0,0421

0,0222

<= /td>

0,0387

0,0500

0,0472

0,0000

0,0500

2010

0,0406

0,0408

0,0247

=

0,0102

0,0500

0,0100

0,0477

0,0306

= 0,0313

= 0,0286

0,0500

0,0185

0,0374

0,0152

2011

0,0301

0,0063

0,0345

0,0071

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-align:justify; line-heig= ht:115%; font-size:10pt">0,0166

0,0004

0,0500

0,0333

0,0203<= /span>

= 0,0218

0,0405

0,0201

0,0333

0,0117

2012

0,0181

0,0131

0,0384

0,0192

0,0284

0,0236

=

0,0430

0,0351

0,0129

0,0179<= /span>

0,0353

0,0213

0,0266

0,0110

2013

0,0105

0,0243

0,0477

0,0048

0,0405

0,0130

0,0427

0,0353

0,0276<= /p>

0,0159

0,0319

0,0189=

0,0239

0,0049

2014<= /span>

= 0,0000

0,0334

0,0268

0,0170

0,0500=

0,0039

0,0500

0,0351

0,0239

0,0146

0,0336

0,0221

0,0162<= /span>

0,0000

2015

0,0051

0,0500

= 0,0079

0= ,0247

0,0500

0,0041

0,0435=

0,0237

0,0500

0,0000

0,0328

=

0,0185

0,0072

0,0134

2016

0,0177

0,0382

0,0074

0,0397

0,0268

0= ,0026

0,0207

0,0053

0,0338=

0,0468

0,0071

0,033= 6

0,0372

0,0041

<= /td>

0,0324

2017

0,0173

0,0332

0,0111

0,0447

0,0312

0,0013

0,0217

0,0234

0,0460

0,0052

0,0328

0,0500

0,0032

0,0328

2018

0,0087

= 0,0314

0,0335

0,0439

0,0258

0,0000=

0,0118

0,0020

0,0269

0,0036

=

0,0086

0,0488

0,0027

0,0313<= /span>

2019

0,0113

0,0388

0,0106

0,0000

0= ,0212

0,0306

0,0059

0,0018=

0,0079

0,0500

0,0= 029

0,0060

0,0424

=

0,0018

0,0383

2020

<= span style=3D"font-family:Arial">0,0211

0,0404

0,0000

0,0500

0,0197

0,0152

0,0000

0,0026

0,0000

0,0299

0,0000=

=

0,0000

0,0396

=

0,0000

0= ,0500


=

 


=

Tabela 08

Etapa 04= Ranqueamento do M=C3=A9todo VIKOR

 

<= /tr>= <= td style=3D"width:75.75pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

= -0,004653

2016

<= td style=3D"width:48pt; padding-right:5.65pt; padding-left:5.65pt; vertical= -align:top">

0,0= 468

0,35= 40

<= td style=3D"width:70.9pt; padding-right:5.65pt; padding-left:5.65pt; vertic= al-align:top">

 =

S= i

Ri

Qi

VIKOR RANK

2009

0,4207

0,0500

-0,000742

11

2010

0,4356

0,0500

0,000000

= 12

2011

0,3535

0,0500

-0,0= 04106

7

2012

0,3740

0,0430

-0,006588

4

2013

0,3776

0,0477

= -0,004053

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-align:center; line-heigh= t:115%; font-size:10pt">9

2014

0,3716

0,0500

-0,003197

10

2015

0,3425

0,0500

6

0,3534

-0,005718

5

2017

0,0500

-0,004080

8

2= 018

0,3105

0,0488

=

-0,006850

3

2019

0,2696

0,0500

-0,008299

2

2020

0,2686

= 0,0500

-0,008349

1

S*,R*

= 0,2686

0,0430

 

S= -,R-

0,435= 6

0,0500

 

 

=  

 

Figura 03

Gr=C3=A1fico de Resultados do M=C3= =A9todo VIKOR

 

3D""

 

 

 

 


Tab= ela 09

Matriz de prefer=C3=AAncias do PROMETHEE

<= td style=3D"width:58.85pt; border-top-style:solid; border-top-width:1pt; bo= rder-bottom-style:solid; border-bottom-width:1pt; padding-right:5.65pt; pad= ding-left:5.65pt; vertical-align:top; background-color:#d9d9d9">

Pref.

max

5<= /span>

=

9,= 48

X1

X2

X3<= /span>

X4

X5

X6

X7

X8

X9

X10

X11

X12

X13

X14

X15

Min/Max

max

min

max

max

min

min

min

min<= /span>

min

= max

max

max

min

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-align:justify; line-heig= ht:115%; font-size:8pt">max

Peso

= 5

5

5

3,57

3,57

3,57

3,57

3,57

= 3,13

3,13

3,13

3,13=

3,13

3,13

Fun=C3=A7=C3=A3o

V-shape

=

V-shape

V-shape

Linea= r

Linear

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-align:justify; line-heig= ht:115%; font-size:8pt">Linear

=

Linear

Linear

Linear<= /span>

Linear

Linear

<= p style=3D"margin-top:0pt; margin-left:1.05pt; margin-bottom:0pt; text-inde= nt:-1.05pt; text-align:justify; line-height:115%; font-size:8pt">Linear

Linear

Linear

Linear

Thresholds

absolute

absolute

absol= ute

absolute

absolute

absolute

absolute

absolute

absolute

%

%

%

%

%

absolute<= /span>

q<= /p>

1

1

1

9,48

171957

174,06

7,21

25,53

0,03

0,03

0,03

0,03

0,03

64052,45

p

112185,2<= /span>

= 238519,4

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-align:justify; line-heig= ht:115%; font-size:8pt">175,07

=

24,05

451237,2

411,51=

19,52

59,72

24,05

0,25

0,25

0,25

0,25

0,25

141584,7

s

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3=

 

Tabela 10

Etapas 02 e 03 do= PROMETHEE

<= td style=3D"width:57.7pt; padding-right:5.65pt; padding-left:5.65pt; vertic= al-align:top">

0,6881

= <= td style=3D"width:40.75pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

0

= 0,1216

= 0,3793

= -0,8311

= 0,0455

<= td style=3D"width:40.75pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

0,4718

= -0,0821

<= td style=3D"width:40.75pt; padding-right:5.65pt; padding-left:5.65pt; verti= cal-align:top">

0,7106

= =

 

X1<= /span>

X2

X3

X4

X5

X6

X7

X8<= /span>

X9

X10

X11

X12=

<= p style=3D"margin-top:0pt; margin-bottom:0pt; font-size:8pt">X13

X14

X15

=

2009

-0,8425

-0,7065

=

-0,4545=

0,4909

0,0326

0,2975

-0,5415

= 0,2143

-0,0195

-1

-0,5009

0,8766

-0,9708

0

2010

-0,= 6317

0,7259

-0,4994<= /p>

0,0909

0,2646

-0,8892

0,2067

-0,5919

-0,0424

-0,0084

-0,6804

-0,5805

0,385

-0,747

0

<= /td>

2011<= /span>

-0,328

0,5733

-0,319

-0,2727

0,32= 79

0,0655

0,3447

-0,6171

-0,12

0,0187

-0,4054

-0,3091

0,3642

-0,6352

0

<= p style=3D"margin-top:0pt; margin-bottom:0pt; font-size:9pt">2012

0,0338

0,3855

-0,4401

0,4545

-0,0635

-0,2819

-0,0375

-0,5494

= -0,1926

0,0403

-0,1871

-0,1708

0,3459

2013

0,2544

0,0503

-0,6546

0,8182

-0,2385

-0,3717

-0,546= 7

-0,1988

-0,0019<= /p>

-0,0875

-0,1046

-0,352

=

0

2014

0,5322

-0,2265<= /p>

-0,0401

0,6364

-0,4538

0,2156

-0,7002

-0,371

-0,6311

0,0083

-0,0214

= -0,1396

0,3268

-0,1269

0

2015

0,4037

<= /td>

-0,6419

0,5848

-= 0,0909

-0,4537

0,2132

-0,581

0,0358

0,1129

0,1263=

-0,1234

0,385

0,2256

0

2016

-0,3666

<= p style=3D"margin-top:0pt; margin-bottom:0pt; font-size:9pt">0,5973

-0,6364

-0,0037

0,2389

0,0326

= 0,6364

-0,1375

-0,0415

0,3338

-0,1396

0

2017

0,0563

-0,2204

0,4986

-0,8182

0,2661

0,0068=

0,6364

0,1507

-0,0388

0,4067

= -0,1234

-0,782

0,5412

0

2018

0,3022

-0,1662

-0,2848

0= ,2727

0,014

0,2993

0,1925

0,6364

0,0215

-0,0084

0,4594

0,6547

-0,7579

0,5718

0

2019

0,2308

-0,3809

0,5126

1

0,0883

-0,3702

0,2589

0,6364

0,8509

-0,0535

-0,59= 67

0,6471

0

2020

-0,0568

-0,4205<= /p>

=

0,7511<= /span>

= -1

0,1097

0,0887

0,3506

0,6364

0,9161

-0,0084

0,5731

0,8266<= /p>

-0,520= 4

0,8151

0


 


Tabela 11

Resultados e Ranqueamento do PROMETHEE<= /span>.

-0= ,0839

<= /tr><= td style=3D"width:48pt; padding-right:5.65pt; padding-left:5.65pt; vertical= -align:bottom">

0,2= 265

= =

&= #xa0;

Phi

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-align:justify; font-size= :10pt">Phi+

Phi-

Rank

2009

-0,1742

0,2124

= 0,3866

11

2010

-0,1842

0,1916

0,3758

=

2011

0,1983

0,2822

10

2012

-0,0554

= 0,1909

0,2463

9

2013

-0,0457

0,1965

= 0,2422

8

2014

-0,0402

0,2347

0,2748

7=

= 2015

-0,03= 93

0,2564

0,2957

6

2016

0,0286

0,1978

4

2017

0,0192

0,2267

0,= 2076

5

2018

0,1351

0,2927

0,1576

3

2019

0,2784

0,392

0,1135

1

2020

0= ,1615

0,34= 29

0,1814<= /span>

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figura 04

Gr=C3=A1fico de Resultados do M=C3=A9todo PROMETHEE

3D""

 

 

3.3 Discuss=C3=A3o dos resultados

=  

De acordo com os resultados obtidos = pelos tr=C3=AAs m=C3=A9todos, observa-se uma similaridade na classifica=C3= =A7=C3=A3o dos piores anos, sendo 2009 e 2010 os mais desfavor=C3=A1veis. C= omparando os melhores anos de avalia=C3=A7=C3=A3o no ranking, verifica-se q= ue os =C3=BAltimos quatro anos, de 2017 a 2020, s=C3=A3o classificados como= os melhores, com alta similaridade no resultado do VIKOR e do PROMETHEE. D= essa forma, pode-se dizer que os tr=C3=AAs m=C3=A9todos s=C3=A3o capazes de= analisar indicadores de sustentabilidade e apresentam alta similaridade em= seus resultados. A seguir, =C3=A9 apresentada uma descri=C3=A7=C3=A3o mais= detalhada de suas caracter=C3=ADsticas e similaridades.

Va= lida=C3=A7=C3=A3o dos M=C3=A9todos: Os resultados obtidos a partir dos m=C3=A9todos de avalia=C3=A7=C3=A3o mu= ltiatributo - VIKOR, PROMETHEE e TOPSIS, demonstraram not=C3=A1vel converg= =C3=AAncia na classifica=C3=A7=C3=A3o de sustentabilidade da empresa de pet= r=C3=B3leo e g=C3=A1s. Essa consist=C3=AAncia implica uma valida=C3=A7=C3= =A3o robusta dos m=C3=A9todos aplicados, destacando sua confiabilidade na a= valia=C3=A7=C3=A3o do desempenho sustent=C3=A1vel no contexto espec=C3=ADfi= co do setor.

Concord=C3=A2ncia em Crit=C3=A9rios: Uma an=C3=A1lise aprofundada dos resultados= revelou coer=C3=AAncia not=C3=A1vel na classifica=C3=A7=C3=A3o dos crit=C3= =A9rios de sustentabilidade por todos os tr=C3=AAs m=C3=A9todos. Isso indic= a um consenso sobre aspectos cruciais para a sustentabilidade no setor de p= etr=C3=B3leo e g=C3=A1s. Crit=C3=A9rios comumente bem classificados podem a= branger preocupa=C3=A7=C3=B5es ambientais, governan=C3=A7a corporativa e im= pacto social, enfatizando sua signific=C3=A2ncia substancial para a sustent= abilidade neste setor.

Identifica=C3=A7=C3=A3o de For=C3= =A7as e Fraquezas: Apesar das clas= sifica=C3=A7=C3=B5es consistentes em geral, a an=C3=A1lise comparativa faci= litou a identifica=C3=A7=C3=A3o de =C3=A1reas em que a empresa se destaca e= outras que requerem melhorias. Essa uniformidade nas classifica=C3=A7=C3= =B5es ressaltou =C3=A1reas espec=C3=ADficas onde a empresa demonstra desemp= enho superior em sustentabilidade e aspectos que podem precisar de aprimora= mento para alcan=C3=A7ar n=C3=ADveis mais elevados de responsabilidade corp= orativa.

Sensibilidade =C3=A0 Pondera=C3=A7=C3=A3o de Crit= =C3=A9rios: A explora=C3=A7=C3=A3o= da sensibilidade dos m=C3=A9todos a varia=C3=A7=C3=B5es na pondera=C3=A7= =C3=A3o de crit=C3=A9rios revelou que, apesar das altera=C3=A7=C3=B5es de p= eso, a congru=C3=AAncia nos resultados foi amplamente mantida. Isso sugere = que os m=C3=A9todos s=C3=A3o relativamente est=C3=A1veis =E2= =80=8B=E2=80=8Bem rela=C3=A7=C3=A3o =C3=A0s varia=C3=A7=C3=B5es = de peso e mant=C3=AAm consist=C3=AAncia em su= as classifica=C3=A7=C3=B5<= /span>es, independentemente de como os cr= it=C3=A9rios s=C3=A7=C3=A3o da empresa em termos de responsabilidade corporativa.

=

Possibilidade de integra=C3=A7=C3=A3o com outros m=C3=A9todos:= Quanto =C3=A0 possibilidade de integra= =C3=A7=C3=A3o com outros m=C3=A9todos, destaca-se a utiliza=C3=A7=C3=A3o da= l=C3=B3gica fuzzy para lidar com a incerteza durante a pondera=C3=A7=C3=A3= o de crit=C3=A9rios. Autores como Rostamzadeh et al. (2015) integraram o fu= zzy-VIKOR, enquanto Onu et al. (2017), Saeidi et al. (2022), Solangi et al.= (2019) e Awasthi et al. (2011) integraram o fuzzy-TOPSIS. Al=C3=A9m disso,= autores como Gouraizim et al. (2023) empregaram o fuzzy-PROMETHEE para lid= ar com essas incertezas durante o processo de avalia=C3=A7=C3=A3o. Essa abo= rdagem fuzzy =C3=A9 significativa, pois permite lidar com a imprecis=C3=A3o= dos dados e a tomada de decis=C3=A3o, aprimorando a an=C3=A1lise de susten= tabilidade ao considerar elementos incertos ou subjetivos nos m=C3=A9todos = de avalia=C3=A7=C3=A3o.

Outros m=C3=A9todos tamb=C3=A9m podem ser integrados= a modelos multiatributo, como modelos de otimiza=C3=A7=C3=A3o matem=C3=A1t= ica. Um exemplo =C3=A9 o estudo de Vivas et al. (2020), que combinou a prog= rama=C3=A7=C3=A3o por objetivos com o PROMETHEE. Adicionalmente, m=C3=A9tod= os para previs=C3=A3o de dados futuros, incluindo modelos de previs=C3=A3o = estat=C3=ADstica, regress=C3=A3o linear, regress=C3=A3o log=C3=ADstica e mo= delos de aprendizado de m=C3=A1quina mais avan=C3=A7ados, tamb=C3=A9m podem= ser incorporados.

A escolha do melhor m=C3=A9todo para analisar o desempenho= de sustentabilidade pode depender de particularidades do contexto espec=C3= =ADfico e das prefer=C3=AAncias do pesquisador. Entretanto, considerando a = natureza intr=C3=ADnseca dos m=C3=A9todos, o PROMETHEE se destaca pela habi= lidade de levar em conta rela=C3=A7=C3=B5es internas entre os crit=C3=A9rio= s de avalia=C3=A7=C3=A3o, al=C3=A9m de ponderar a import=C3=A2ncia relativa= de cada um. Ademais, a flexibilidade do PROMETHEE em lidar com incertezas = por meio de m=C3=A9todos baseados em l=C3=B3gica fuzzy pode torn=C3=A1-lo uma op=C3=A7=C3=A3o valiosa para avaliar sustentab= ilidade em contextos complexos e incertos. Apesar disso, a literatura suger= e que a sele=C3=A7=C3=A3o do m=C3=A9todo mais adequado deve se basear na na= tureza espec=C3=ADfica do problema, dados dispon=C3=ADveis e objetivos da a= n=C3=A1lise, defendendo uma abordagem adaptada ao contexto de cada estudo.<= /span>

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4 CONCLUS=C3=95ES

 

Este artigo forneceu uma an=C3=A1lise comparati= va de m=C3=A9todos multiatributo na avalia=C3=A7=C3=A3o do desempenho de su= stentabilidade, por meio de um estudo de caso que utilizou dados coletados = de relat=C3=B3rios de sustentabilidade de uma empresa brasileira de petr=C3= =B3leo e g=C3=A1s. Os m=C3=A9todos utilizados foram: VIKOR, PROMETHEE e TOP= SIS.

Em resumo, os resultados gerados s=C3=A3o semelhantes. TOPSIS foca na pr= oximidade das solu=C3=A7=C3=B5es ideal e n=C3=A3o ideal, PROMETHEE lida com= prefer=C3=AAncias declaradas para classificar alternativas e VIKOR busca u= m compromisso entre m=C3=BAltiplos crit=C3=A9rios. A escolha entre esses m= =C3=A9todos depende da natureza dos crit=C3=A9rios, das prefer=C3=AAncias d= o tomador de decis=C3=A3o e dos objetivos espec=C3=ADficos da an=C3=A1lise = multicrit=C3=A9rio.

A compara=C3=A7=C3=A3o dos m=C3=A9todos multiatributo VIK= OR, TOPSIS e PROMETHEE forneceu insights valiosos sobre seus respectivos po= ntos fortes e fracos ao abordar cen=C3=A1rios complexos de tomada de decis= =C3=A3o. VIKOR demonstrou robustez no tratamento de crit=C3=A9rios conflita= ntes e forneceu uma classifica=C3=A7=C3=A3o abrangente de alternativas, tor= nando-o adequado para situa=C3=A7=C3=B5es em que solu=C3=A7=C3=B5es de comp= romisso s=C3=A3o essenciais. TOPSIS se destacou na identifica=C3=A7=C3=A3o = da alternativa mais pr=C3=B3xima da op=C3=A7=C3=A3o ideal, mas pode n=C3=A3= o abordar adequadamente as compensa=C3=A7=C3=B5es entre crit=C3=A9rios. PRO= METHEE, por outro lado, exibiu sua capacidade de gerenciar v=C3=A1rios tipo= s de fun=C3=A7=C3=B5es de prefer=C3=AAncia, oferecendo flexibilidade na mod= elagem das prefer=C3=AAncias dos tomadores de decis=C3=A3o.

Embora os m=C3=A9= todos analisados tenham semelhan=C3=A7as e produzam resultados similares, o= PROMETHEE =C3=A9 mais relevante quando se lida com problemas complexos que= envolvem uma gama mais ampla de crit=C3=A9rios, especialmente quando h=C3= =A1 m=C3=BAltiplas percep=C3=A7=C3=B5es e julgamentos humanos envolvidos, e= quando as decis=C3=B5es s=C3=A3o de longo prazo com impactos duradouros. O= PROMETHEE apresenta vantagens quando h=C3=A1 dificuldade em quantificar ou= comparar elementos importantes da decis=C3=A3o, ou quando a colabora=C3=A7= =C3=A3o entre departamentos ou membros da equipe =C3=A9 restrita devido =C3= =A0s suas diferentes especializa=C3=A7=C3=B5es ou perspectivas.

<= p style=3D"margin-top:0pt; margin-bottom:0pt; text-indent:35.45pt; text-ali= gn:justify; font-size:10pt">A escolha ent= re esses m=C3=A9todos, em =C3=BAltima inst=C3=A2ncia, depende dos requisito= s espec=C3=ADficos e das nuances do problema de decis=C3=A3o em quest=C3=A3= o, enfatizando a import=C3=A2ncia de selecionar cuidadosamente o m=C3=A9tod= o mais apropriado para apoiar a tomada de decis=C3=A3o informada e eficaz e= m diversos contextos do mundo real.

= Por fim, a an=C3=A1lise por meio de model= os multiatributo pode ser essencial para a tomada de decis=C3=A3o em cen=C3= =A1rios complexos como a sustentabilidade. Oportunidades para pesquisas fut= uras podem explorar as metodologias com diferentes abordagens como em outro= s tipos de organiza=C3=A7=C3=B5es e/ou locais para avaliar a sustentabilida= de organizacional. Al=C3=A9m disso, experimentar a integra=C3=A7=C3=A3o de = modelos multiatributo com modelos de otimiza=C3=A7=C3=A3o matem=C3=A1tica e= modelos de previs=C3=A3o =C3=A9 uma op=C3=A7=C3=A3o vi=C3=A1vel para avali= ar, otimizar e prever a sustentabilidade. Com o avan=C3=A7o das tecnologias= de an=C3=A1lise de dados, esta integra=C3=A7=C3=A3o se configura, sem d=C3= =BAvida, como uma oportunidade significativa para experimenta=C3=A7=C3=A3o.=

= 0;

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