A macro-level multi-objective model with uncertain data for sustainability studies Carla Oliveira a , Carlos Henggeler Antunes a,b , a INESC Coimbra, Rua Antero de Quental 199, 3030-030 Coimbra, Portugal b Department of Electrical Engineering and Computers, University of Coimbra, Polo II, 3030-030 Coimbra, Portugal, Abstract: * DLCK@$J<:KFI8C <:FEFDP$<E<I>P$<EM@IFED<EK DF;<C @J GIFGFJ<; KF G<I=FID 8 GIFJG<:K@M< 8E8CPJ@J F= K?< :?8E><J @E K?< <:FEFD@: JKIL:KLI< 8E; K?< <E<I>P JPJK<D I<JLCK@E> =IFD ;@==<I<EK GFC@:@<J# 8J N<CC 8J KF 8JJ<JJ K?< :FII<JGFE;@E> <EM@IFED<EK8C @DG8:KJ# GIFM@;@E> ;<:@J@FE JLGGFIK @E GFC@:P D8B@E>% 5?< DF;<C @J 8 KFG$;FNE D8:IF$<:FEFD@: DLCK@$F9A<:K@M< DF;<C# N?@:? 8CCFNJ K8B@E> @EKF 8::FLEK K?< <E<I>P :8II@<IJ 8JJF:@8K<; N@K? GI@D8IP JLGGC@<J# :FEM<IJ@FE 8E; KI8EJ=FID8K@FE GIF:<JJ<J% 5?< ;<D8E; =FI <E<I>P J<IM@:<J @J ;@J8>>I<>8K<; 9P <:FEFD@: J<:KFIJ 8E; D8P 9< ;@J8>>I<>8K<; 9P JG<:@=@: =LE:K@FEJ N@K?@E 8 J<:KFI% 5?< DF;<C 8CCFNJ KF <OGCFI< K?< <==<:KJ F= E<N C<JJ <E<I>P$@EK<EJ@M< FI :8I9FE$@EK<EJ@M< K<:?EFCF>@<J FE K?< KFK8C JPJK<D :FJKJ# :?8E><J @E =L<C 8E; K<:?EFCF>P D@O# 8E; K?< C<M<CJ F= >I<<E?FLJ< >8J<J 8E; FK?<I <D@JJ@FEJ% 5?@J @J ;FE< @E K?< DF;<C =I8D<NFIB 9P :FEJ@;<I@E> GFCCLK8EK&<E<I>P :F<==@:@<EKJ ;<=@E<; 8J @EK<IM8CJ# N?@:? :8GKLI< K?< LE:<IK8@EKP 8JJF:@8K<; N@K? E<N GIF:<JJ<J 8E;&FI K<:?EFCF>@<J% 5?@J KPG< F= 8E8CPJ@J @J F= FLKJK8E;@E> @DGFIK8E:< =FI LE;<IJK8E;@E> K?< IFC< F= K<:?EFCF>P @E :8I9FE D@K@>8K@FE <==FIKJ 8E; FK?<I <E<I>P JPJK<D GC8EE@E> JKL;@<J 8K 8 D8:IF C<M<C% Keywords: +:FEFDP$<E<I>P$<EM@IFED<EK @EK<I8:K@FEJ# 0LCK@$F9A<:K@M< C@E<8I GIF>I8DD@E># 0LCK@$J<:KFI8C DF;<CJ# LE:<IK8@EKP ?8E;C@E>% 1. Introduction 2FIKL>8C @J =8:<; N@K? >I<8K :?8CC<E><J I<>8I;@E> K?< GFC@:@<J KF 8:?@<M< K?< K8I><KJ K?8K ?8M< 9<<E @DGFJ<; 9FK? =FI K?< <E<I>P 8E; <EM@IFED<EK8C J<:KFIJ# N@K?FLK E<>C<:K@E> K?< <:FEFD@: 8E; JF:@8C @JJL<J 8JJF:@8K<; N@K? K?FJ< GFC@:@<J% 5?LJ# K?< LJ< F= 8;<HL8K< KFFCJ# N?@:? 8CCFN F9K8@E@E> JFLE; @E=FID8K@FE @E FI;<I KF =8:@C@K8K< ;<:@J@FE$ D8B@E># @J F= :8G@K8C @DGFIK8E:<% 0LCK@$J<:KFI8C <:FEFDP$<E<I>P$<EM@IFED<EK !0+(" DF;<CJ GIFM@;< K?< 89@C@KP KF G<I=FID 8 GIFJG<:K@M< 8E8CPJ@J F= K?< :?8E><J @E K?< <:FEFD@: JKIL:KLI< 8E; K?< <E<I>P JPJK<D# 8J N<CC 8J KF 8JJ<JJ K?< :FII<JGFE;@E> <EM@IFED<EK8C @DG8:KJ# I<JLCK@E> =IFD ;@JK@E:K GFC@:@<J =FI ;<:@J@FE JLGGFIK @E GFC@:P D8B@E>% 5?@J KPG< F= DF;<CJ D8P :FD9@E< 9FKKFD$LG K<:?EFCF>P 8GGIF8:?<J N@K? KFG$;FNE D8:IF$<:FEFD@: DF;<CJ# @E N?@:? @E;LJKI@<J# :FDDF;@K@<J# :FEJLD<IJ 8E; >FM<IED<EK <OG<E;@KLI<J# 8J N<CC 8J =FI<@>E KI8;< 8E; @EM<JKD<EK# 8I< ;@J8>>I<>8K<;% 5?<J< DF;<CJ 8CCFN K8B@E> @EKF 8::FLEK K?< <E<I>P :8II@<IJ 8JJF:@8K<; N@K? GI@D8IP JLGGC@<J !<%>% D@E@E># G<KIFC<LD <OKI8:K@FE"# :FEM<IJ@FE 8E; GIF:<JJ@E> GIF:<JJ<J !<%>% GFN<I GC8EKJ# I<=@E<I@<J" 8E; <E;$LJ< ;<D8E; =FI <E<I>P J<IM@:<J !<%>% 8LKFDF9@C<J"% 0FI<FM<I# K?< ;<D8E; =FI <E<I>P J<IM@:<J D8P 9< ;@J8>>I<>8K<; 9P J<:KFI !@%<% I<J@;<EK@8C# @E;LJKI@8C# KI8EJGFIK8K@FE 8E; :FDD<I:@8C" 8E; 9P JG<:@=@: =LE:K@FEJ N@K?@E 8 J<:KFI !<%>% I<J@;<EK@8C 8@I :FE;@K@FE@E># ?<8K@E># C@>?K@E># ?FK N8K<I"% -E K?< =I8D<NFIB F= 0+( DF;<CJ# FGK@D@Q8K@FE DF;<CJ 8I< D8@ECP ;<;@:8K<; KF ;<:@J@FE$D8B@E> FE K?< :?F@:< F= K<:?EFCF>P# >@M<E 8E F9A<:K@M< =LE:K@FE !><E<I8CCP K?< D@E@D@Q8K@FE F= FG<I8K@FE8C 8E; =@O<; :FJKJ" 8E; JFD< :FEJKI8@EKJ FE K<:?EFCF>@:8C 8M8@C89@C@KP% 5?<J< DF;<CJ @;<EK@=P K?< K<:?EFCF>@<J K?8K J?FLC; 9< :?FJ<E KF FGK@D@Q< K?< F9A<:K@M< =LE:K@FE# JL9A<:K KF K?< J8K@J=8:K@FE F= K?< :FEJKI8@EKJ% * I<GI<J<EK8K@M< <O8DGC< @J 0*3.*/ $ 08IB<K 8CCF:8K@FE DF;<C $ =FI <E<I>P GFC@:P 6)7 8E; +,10 $ +E<I>P ,CFN 1GK@D@Q8K@FE DF;<C 6')7% 4@E:< K?< JLJK8@E89C< ;<M<CFGD<EK :FE:<GK @J @E?<I<EKCP 8 DLCK@;@D<EJ@FE8C FE<# DLCK@:I@K<I@8 D<K?F;J GIFM@;< 8 JL@K89C< =I8D<NFIB =FI ;<8C@E> N@K? K?< :FE=C@:K@E> 8O<J F= <M8CL8K@FE LE;<ICP@E> JLJK8@E89@C@KP GIF9C<DJ Lausanne, 14th – 17th June 2010 Proceedings of Ecos 2010 www.ecos2010.ch Page 1-329