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SOLUCIONES DE COMPROMISO EN LA SELECCIÓN DEL METODO EXTRACTIVO MINERO – CASO DE ESTUDIO EN MINERIA DE CARBON COLOMBIANA COMPROMISE COMPROMISE SOLUTIONS IN MINING METHOD SELECTION - CASE STUDY IN COLOMBIAN COAL MINING JORGE IVAN ROMERO GELVEZ Magister en Ingeniería, Ingeniería, Escuela Colombiana Colombiana de Carreras industriales, Colombia. jromer Colombia.
[email protected] [email protected] o
FELIX ANTONIO CORTES ALDANA Ph. D, Universidad Nacional de Colombia, ede !ogot", Colombia. #
[email protected] Colombia. #
[email protected]
GIOVANNI FRANCO SEPÚLVEDA Ph. D. $c%, Universidad Universidad Nacional de Colombia, Colombia, sede Medellín, Medellín, Colombia. g#
[email protected] Colombia. g#
[email protected]
Recibido p! !e"is!# D$M$A% cep&do# D$M$A% "e!si'( )i(*# D$M$A+
RESUME RESUMEN: N: E* p!op'si&o de es&e !&,c-*o es p!ese(&! -( e()o.-e c-(&i&&i"o p! * se*ecci'( de* /0&odo e1&!c&i"o /i(e!o /edi(&e e* des!!o**o /e&odo*'2ico de -( p!ob*e/ de &o/ de decisi'( /-*&ic!i&e!io disc!e& 3DMD4% 3DMD4% es&e e()o.-e se p!opo(e p!opo(e p! sopo!&! sopo!&! e* p!oceso de p*(eci p*(eci'( '( y dise5o dise5o /i(e!o+ /i(e!o+ Se*eccio(! Se*eccio(! e* /0&odo /0&odo e1&!c&i"o es -(o de *os p!ob*e/s de Decisi'( M-*&ic!i&e!io Disc!e& 3DMD4 do(de *os deciso!es 6( &e(ido p!ob*e/s e( * si2(ci'( de peso cd c!i&e!io+ P! !eso*"e! es&e p!ob*e/% es&e !&,c-*o p!opo(e e* /0&odo de * ENTROPIA+ E* p!ese(&e esc!i&o .-ie!e /(e7! * s-b7e&i"idd i(6e!e(&e es& p!ob*e/8&ic /edi(&e e* -so de* /0&odo VI9OR% e* c-* !!o7 co/o !es-*&do -( *&e!(&i" de co/p!o/iso+ L /e&odo*o2, p!op-es& e( es&e !&,c-*o se p*ic e( yci/ie(&o de c!b'( *oc*i:do e( e* cos&do occide(&* de* Ce!!o Ts7e!o e( No!&e de S(&(de!% Co*o/bi+ PALABRAS CLAVE# A(8*isis de decisi'( /-*&ic!i&e!io 3MCDA4% se*ecci'( de* /0&odo e1&!c&i"o% ENTROPIA% VI9OR+ ABSTRACT # T6e p-!pose o) &6is ppe! is &o p!ese(& .-(&i&&i"e pp!oc6 &o &6e se*ec&io( o) &6e /i(i(2 e1&!c&io( /e&6od by de"e*opi(2 /e&6odo*o2ic* p!ob*e/ o) disc!e&e /-*&ic!i&e!i /-*&ic!i&e!i decisio( /;i(2 3MCDM4% &6is pp!oc6 see;s &o s-ppo!& &6e p!ocess o) p*((i(2 (d /i(e desi2(+ Se*ec& &6e e1&!c&i"e /e&6od is o(e o) &6e p!ob*e/s o) Disc!e&e M-*&ic!i&e!i Decisio( 3MCDM4 <6e!e decisio($/;e!s decisio($/;e!s 6d p!ob*e/s i( ssi2(i(2
1. INTRODUCCIÓN E* p!ob*e/ de se*ecci'( de* /0&odo e1&!c&i"o se co(" co("ie ie!& !&ee e( e* spe spec& c&oo /8s /8s i/po i/po!& !&( (&e &e de * e1p*o&ci'( /i(e!% y .-e se debe se*eccio(! e* /0&odo .-e /e7o! e(c7e co( *os c!i&e!ios >(icos de cd yci/ie(&o &*es co/o so( *s c!c&e!,s&ics espci*es% co(dicio(es 2eo*'2ics% 6id!o2eo*'2ics% 6id!o2eo*'2ics% 2eo&ec(i 2eo&ec(i y o&!s co(side!cio co(side!cio(es (es &*es &*es co/o *s eco('/ics eco('/ics%% )c&o!es )c&o!es &ec(o*'2ic &ec(o*'2icos os y /bie(&* /bie(&*es+ es+
Dic6s co(side!cio(es o &/bi0( **/dos c!i& c!i&e! e!io ios% s% -s- -s-*/ */e( e(&e &e se e(ce(c-e( e(&! &!( ( e( co()*ic&o y &ie(e( />*&ip*es i(&e!esdos sob!e -(o o /8s de e**os? e( e* 8/bi&o de * se*ecci'( de* /0&odo e1&!c&i"o -s-*/e(&e e* deciso! es e* I(2e(ie!o de Mi(s y co/o p-ede "e!se e( * !e"isi'( de * *i&e!&-! e1is&e(&e e( 3Ge*"e: 3Ge*"e: e& *+ @BB4 @BB4 *os /0&odos des!! des!!o* o**d *dos os 6s& 6s& e* /o/e(& /o/e(&oo (o &o/( &o/( 2!( p!&e de* e1&e(so (>/e!o de c!i&e!ios
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.-e p-ede( co(side!!se+ Si( e/b!2o% * *i&e!&-! 6 ide(&i)icdo 2!(des 8!es e( *s c-*es p-ede( 2!-p!se * /yo!, de *os c!i&e!ios% se2>( 3H!&/( M-&/(s;y @@4 es&s so(# B+ C!c&e!,s&ics espci*es de* dep'si&o% @+ Co(dicio(es 2eo*'2ics e 6id!o2eo*'2ics+ + Co(side!cio(es eco('/ics% + Fc&o!es Tec(o*'2icos y + Co(side!cio(es /bie(&*es+ To/(do e* p!ob*e/ de se*ecci'( co/o -( p!ob*e/ de (8*isis de decisio(es /-*&ic!i&e!io 3MCDA4 se 6ce (eces!io -( de&**do p*(&e/ie(&o de * /(e! co/o se !eso*"e!8 es&e /is/o+ Se 6 disc-&ido /-c6o ce!c de* p*(&e/ie(&o y so*-ci'( ide* de *os p!ob*e/s /-*&ic!i&e!io% pe!o *o cie!&o es .-e cd /0&odo &ie(e s-s "e(&7s y s-s des"e(&7s% -( desc!ipci'( de&**d de *os p!i(cip*es /0&odos p-ede co(s-*&!se e( 3Ro/e!o B4 y e( 3Po/e!o* !b$Ro/e!o B4+ Adicio(*/e(&e p-ede co(s-*&!se sob!e des!!o**os /8s !ecie(&es e( 3Fi2-ei! e& *+ @4+ Es&e !&,c-*o p*ic e* /0&odo KC des!!o**do po! 3Mi**e!$Ti& e& *+ B4% p! !ed-ci! *s *&e!(&i"s y -&i*i:! so*o *&e!(&i"s "ib*es &0c(ic/e(&e e( e* des!!o**o de* (8*isis de decisi'( /-*&ic!i&e!io? pos&e!io!/e(&e p! si2(! *os pesos *os c!i&e!ios se p*ic e* /0&odo de * e(&!op, 3Ze*e(y Coc6!(e B@4+ L-e2o% se p*ic! e* /0&odo VI9OR p! ob&e(e! -( *&e!(&i" de co/p!o/iso% desc!i& co/o * /8s ce!c( * ide*+ A* )i(* se p!ese(&( *s co(c*-sio(es de* cso+
2. PLANTEAMIENTO DEL PROBLEMA Se .-ie!e esco2e! * *&e!(&i" de e1&!cci'( /8s dec-d p! -( yci/ie(&o de c!b'( -bicdo e( e* cos&do occide(&* de* ce!!o Ts7e!o% dep!&/e(&o de No!&e de S(&(de!% Co*o/bi+ Es&e yci/ie(&o es desc!i&o e( de&**e po! -( 2!-po i(&e!discip*i(! de Ge'*o2os e I(2e(ie!os% po! /edio de es&os se ob&ie(e( *os p!8/e&!os &0c(icos de * t!" 1+ A*2-(s de es&s c!c&e!,s&ics p-ede( co!!obo!!se e(# Re2io(es y :o(s co( c!b'( e( Co*o/bi de 3Me7i$-/( P-*ido$2o(:*e: B4 *o c-* 2e(e! "*ide: *os d&os y pe!/i&e s- co/p!obci'(+ P! e* (8*isis de &o/ de decisio(es /-*&ic!i&e!io% se &o/!( co/o *&e!(&i"s "8*ids *s .-e &e(2( -( po(de!ci'( posi&i" * p*ic! * &0c(ic KC 3Mi**e!$Ti& e& *+ B4 *o .-e pe!/i&e e*i/i(! *&e!(&i"s .-e (o so( "ib*es &0c(ic/e(&e y de7
>(ic/e(&e *&e!(&i"s p*icb*es+ Si bie( 6y -( b-e( c(&idd de /0&odos e1&!c&i"os% so*o se co(side!!( de *os B /0&odos desc!i&os e( 3Nic6o*s B4 y e( 3H!&/( M-&/(s;y @@4 A co(&i(-ci'( p!ese(&/os -( !es-/e( de *s *&e!(&i"s dp&do de 3A!&e2 Zp&e!o BB4 T!" 1. P!8/e&!os &0c(icos de* M(&o @ F-e(&e# Des!!o**o p!opio p!&i! de i()o!/ci'( de * e/p!es /i(e! T!"# 1. Tec6(ic* p!/e&e!s Se/ @ So-!ce# O<( de"e*op/e(& bsed o( i()o!/&io( )!o/ &6e /i(i(2 co/p(y P&0#t& Espeso! P!o)-(didd Tipo G!do de dis&!ib-ci'( I(c*i(ci'( RSS 3!oc; s-bs&(ce s&!e(2&64 RMR 3!oc; /ss !i&i(24
C"'++ E(&!e + / y @+B / / Tb-*! K(i)o!/e E(&!e B@ y @ Resis&e(ci M-y b7 E(&!e @B y
2.1. D#$%&'(%')* +# "t#&*t',$ %&'t#&'$ (& $"/%'*& #" (&!"#0 A"t#&*t', 1 Cie*o Abie!&o 3Ope( pi&4# L &0c(ic de e1p*o&ci'( cie*o bie!&o% es * /8s co/>( de(&!o de *os /0&odos de e1p*o&ci'( s-pe!)ici*+ Los p!8/e&!os de !e*ci'( de des/o(&e y 8(2-*o de * pe(die(&e so( c!,&icos e( * de&e!/i(ci'( de si es p*icb*e es&e /0&odo e( p!&ic-*!+ A"t#&*t', 2 H-(di/ie(&o de b*o.-es 3*oc; c"i(24# Co(sis&e e( di"idi! e* yci/ie(&o e( 2!(des b*o.-es de secci'( c-d!(2-*! de "!ios /i*es de /e&!os c-d!dos+ Cd b*o.-e se soc" p!c&ic(do -( e1c"ci'( 6o!i:o(&* co( e1p*osi"os e( s- bse+ Los yci/ie(&os do(de se p*ic debe( se! de 2!( po&e(ci y e1&e(si'(% co( pocs i(&e!c*cio(es de es&0!i* y !/i)iccio(es+ A"t#&*t', C8/!s po! S-b(i"e*es 3S-b*e"e* S&opi(24# Se p*ic yci/ie(&os "e!&ic*es o co( )-e!&e pe(die(&e y .-e
Dy( B% @@ 2e(0!ic/e(&e se c*si)ic( e( c!8&e!es i("e!&idos% b!!e(os *!2os y b!!e(os de b(ico+ A"t#&*t', 3 H-(di/ie(&o po! s-b(i"e*es 3s-b*e"e* c"i(24# Co(sis&e e( * di"isi'( de* yci/ie(&o e( (i"e*es y es&os s- "e:% e( s-b(i"e*es .-e se "( e1&!ye(do e( se(&ido desce(de(&e A"t#&*t', 4 T7os L!2os 3*o(2<**4# Es&e /0&odo p-ede -&i*i:!se e( * e1p*o&ci'( de yci/ie(&os es&!&i)icdos de*2dos% de espeso!es -(i)o!/es e i(c*i(cio(es p!e)e!e(&e/e(&e de pe.-e5s /ode!ds A"t#&*t', 5 C8/!s y pi*!es 3!oo/ (d pi**!4# E( es&e /0&odo se c!e -( co(7-(&o de c8/!s de7(do pi*!es p! sos&e(e! e* &ec6o+ Ls di/e(sio(es de *s c8/!s y * secci'( de *os pi*!es depe(de( de *s c!c&e!,s&ics de* /i(e!*% de * es&bi*idd de *os 6s&,*es% de* espeso! de !ec-b!i/ie(&o y de *s &e(sio(es sob!e * !oc+ A"t#&*t', 6 C8/!s */c0( 3S6!i(;2e S&opi(24# E( e* /0&odo de e1p*o&ci'( po! */ce(/ie(&o p!o"isio(* o c8/!s */c0(% e* /i(e!* es co!&do e( &7os 6o!i:o(&*es% co/e(:(do de * p!&e b7 y "(:(do 6ci !!ib+ E* /i(do po! */ce(/ie(&o p!o"isio(* es -( /0&odo bs&(&e -&i*i:do e( "e&s co( b-:/ie(&os p!o(-(cidos do(de e* /i(e!* es *o s-)icie(&e/e(&e !esis&e(&e co/o p! /(&e(e! si( sopo!&e &(&o *s !ocs e(c7o(ds co/o e* &ec6o de* &7eo+ P! -( /i(do e)icie(&e e* 2!do de* dep'si&o debe &e(e! -( 8(2-*o de i(c*i(ci'( /yo! de 2!dos+ A"t#&*t', 7 Co!&e y Re**e(o 3C-& (d )i**4# E* /i(e!* se !!(c po! !eb(ds 6o!i:o(&*es% e( se(&ido sce(de(&e% desde * 2*e!, de )o(do+ K( "e: "o*do se e1&!e co/p*e&/e(&e de * c8/!% &!"0s de -(os co*de!os% e)ec&-8(dose co(&i(-ci'( e* !e**e(o de* 6-eco c!edo co( es&0!i*es% co( *o .-e se co(si2-e c!e! -( p*&)o!/ de &!b7o es&b*e y e* sos&e(i/ie(&o de *os 6s&,*es+ A"t#&*t', 8 M0&odo de E(&ibci'( co( C-d!os+ 3S.-!e se&4# Co(sis&e e( e* sos&e(i/ie(&o co( /de!% dispo(ie(do es& e( )o!/ de p!*e*ep,pedo !ec&os do(de *os e*e/e(&os "e!&ic*es o es&e/p*es sopo!&( *s p!esio(es "e!&ic*es% *os 6o!i:o(&*es o cod*es *s p!esio(es de *os 6s&,*es y *os c-&!o e*e/e(&os de -(i'( !es&(&es !i2idi:( e* co(7-(&o Los c!i&e!ios -&i*i:dos e( es&e p!ob*e/ de se*ecci'( so( ci(co% c!c&e!,s&ics espci*es de*
B
dep'si&o% co(dicio(es 2eo*'2ics 6id!o2eo*'2ics y 2eo&ec(i% co(side!cio(es eco('/ics% )c&o!es &ec(o*'2icos y po! -*&i/o )c&o!es /bie(&*es+ K( cso de se*ecci'( de* /0&odo e1&!c&i"o p! -( yci/ie(&o di),ci*/e(&e es i2-* o&!o% y .-e *s co(dicio(es de* dep'si&o y e* &ipo de /i(e!* (ecesi& de -( (8*isis p!&ic-*!% po! es&o /is/o p-ede( /p*i!se o !ed-ci!se *os c!i&e!ios y *s *&e!(&i"s e( -( cso espec,)ico+ Se p-ede "e! -( (8*isis e( de&**e de cd *&e!(&i" y c!i&e!io e( 3H!&/( M-&/(s;y @@4 do(de se e1po(e( *s di)e!e(&es *&e!(&i"s de e1&!cci'( y *os c!i&e!ios .-e i()*-ye( )"o! y e( co(&! de cd -( de e**s+
C&'t#&'1. C!c&e!,s&ics espci*es de* dep'si&o+ So( p!obb*e/e(&e *os /8s de&e!/i((&es% debido .-e e**os decide( /p*i/e(&e si se esco2e /i(e!, cie*o bie!&o o /i(e!, s-b&e!!8(e% * &s de p!od-cci'(% e* /(e7o de* /&e!i* y e* dise5o de * /i( e( e* dep'si&o+ ScB+ T/5o 3especi*/e(&e *&-! o espeso!4 M1i/i:! Sc@+ Fo!/ 3&b-*!% *e(&ic-*!% /si"o% i!!e2-*!4 M1i/i:! Sc+ Posici'( 3I(c*i(ci'( o c,d4 M1i/i:! Sc+ P!o)-(didd+ M1i/i:! C&'t#&'2. Co(dicio(es 2eo*'2ics e 6id!o2eo*'2ics y p!opieddes Geo&0c(ics 3Mec8(ic de !ocs y s-e*os4+ Ls c!c&e!,s&ics 2eo*'2ics de* dep'si&o /i(e!* y de *os /&e!i*es dyce(&es * dep'si&o% i()*-e(ci( * se*ecci'( de* /0&odo e1&!c&i"o+ Especi*/e(&e e( *os /0&odos s-b&e!!8(eos do(de se (ecesi&( p!8/e&!os de co(&!o* de * e1c"ci'( e( e* s-bs-e*o+ L 6id!o2eo*o2, )ec& e* d!e(7e y *os !e.-e!i/ie(&os de bo/beo e( s-pe!)icie y s-b&e!!8(eos+ L /i(e!*o2, !e2-* *os !e.-isi&os de p!oces/ie(&o de* /i(e!*+ Ls p!opieddes /ec8(ics de *os /&e!i*es .-e co/p!i/e( e* dep'si&o y * !oc i( si&- 3y s-e*o si es co(side!b*e s- espeso!4 so( )c&o!es c*"e e( * se*ecci'( de* e.-ipo -&i*i:! e( /i(e!, s-pe!)ici* y s- "e: *
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Hoyos
c(&idd de c*ses de /0&odos si es& es s-b&e!!8(e 3(o sopo!&d% sopo!&d y e1c"d4+ Sc+ Dis&!ib-ci'(+ M1i/i:! Sc+ Roc; /ss !&i(2s 3RMR4 M1i/i:! Sc+ Roc; s-bs&(ce s&!e(2&6 3RSS4 M1i/i:! C&'t#&' Co(side!cio(es eco('/ics+ A* )i(*% es&s co(side!cio(es de&e!/i(( e* 01i&o de -( e/p!es /i(e!+ Es&os )c&o!es 2obie!(( * e*ecci'( de* /0&odo /i(e!o po!.-e )ec&( * s*id de /&e!i*% * i("e!si'(% e* )*-7o de c7% e* pe!iodo de !e&o!(o de * i("e!si'( y de be(e)icio+ Sc+Ts de dese/pe5o+ M1i/i:! Sc+P!od-cci'( 3P!od-cci'( po! -(idd de &ie/po4 M1i/i:! ScB+ I("e!si'( de Cpi&*+ Mi(i/i:! ScBB+ P!od-c&i"idd 3&o(e*ds po! &-!(o de e/p*edo4 M1i/i:! ScB@+ Cos&os co/p!&i"os de *os /0&odos de /i(e!, posib*es+ Mi(i/i:! C&'t#&'3 Fc&o!es Tec(o*'2icos L /e7o! co/bi(ci'( e(&!e e* &e!!e(o y e* /0&odo .-e se i(&e(& esco2e!+ E* /0&odo esco2ido p-ede &e(e! i/pc&os (e2&i"os e( e* /i(e!* e1&!,do e( c-(&o s- -so pos&e!io! 3p!oces/ie(&o% )-(dici'(4 ScB+ Rec-pe!ci'( de * /i( 3po!ci'( de* dep'si&o e1&!,do c&-*/e(&e4 M1i/i:! ScB+ Di*-ci'( 3c(&idd de despe!dicios p!od-cidos co( e* /i(e!*4 Mi(i/i:! ScB+ L )*e1ibi*idd de* /0&odo co( e* c/bio de co(dicio(es+ M1i/i:! ScB+ Se*ec&i"idd de* /0&odo p! dis&i(2-i! e* /i(e!* y *os !esid-os+ M1i/i:! C&'t#&'4 Co(side!cio(es /bie(&*es (o s'*o e* /bie(&e ),sico% si(o e* c*i/ soci*% po*,&ico% eco('/ico+ ScB+ Es&bi*idd de *s be!&-!s+ M1i/i:! ScB+ S-bside(ci% o e)ec&os e( * s-pe!)icie de e1c"ci'(+ M1i/i:! ScB+ Co(dicio(es de s*-d y se2-!idd+ M1i/i:!
. PROPUESTA METODOLOGICA L /e&odo*o2, p!op-es& co/o y-d p! &o/ de decisio(es e( * se*ecci'( de* /0&odo e1&!c&i"o se des!!o** co( bse * p!op-es& /e&odo*'2ic p*(&ed e( 3Co!&0s$A*d( e& *+ @4 y dp&d e( 3Ge*"e: e& *+ @BB4+ Se p!opo(e i(ici*/e(&e * p*icci'( de* /0&odo KC des!!o**do po! 3Mi**e!$Ti& e& *+ B4 p! !ed-ci! e* co(7-(&o de *&e!(&i"s y -&i*i:! >(ic/e(&e A*&e!(&i"s "ib*es &0c(ic/e(&e+ L co(s&!-cci'( de * /&!i: de decisi'( se !e*i: e( bse * i()o!/ci'( de
3H!&/( M-&/(s;y @@4% .-ie(es co/p!( *s "e(&7s y des"e(&7s de *os s-b c!i&e!ios * B co( cd -( de *s *&e!(&i"s p*(&eds p! !eso*"e! es&e p!ob*e/ de se*ecci'(% po! *o c-* *os "*o!es si2(dos cd -(o de es&os se!8( co(s&(&es e( c-*.-ie! p!ob*e/ de se*ecci'( de* /0&odo e1&!c&i"o+ Po! o&! p!&e *os s-b c!i&e!ios B * "!i!( de c-e!do *os p!8/e&!os &0c(icos de cd si&-ci'( espec,)ic y se!8( de&e!/i(dos -( /odi)icci'( de * esc* KC% co(se!"(do * c!di(*idd y p!opo!cio(*idd de *os d&os y e*i/i((do *os "*o!es (e2&i"os p!opios de * esc* de* /0&odo KC+ 9'/& 1. P!op-es& /e&odo*'2ic F-e(&e# Des!!o**o p!opio 9'/&# 1. P!oposed /e&6odo*o2y So-!ce# O<( de"e*op/e(&
L /&!i: de decisi'( 2e(0!ic "is& e( * T!" 2% se co(s&!-ye p!&i! de * co("e!si'( de *s "*o!cio(es /os&!ds e( 3H!&/( M-&/(s;y @@4 Tods *s "*o!cio(es dds e( * Tb* @ *os c!i&e!ios so( c-*i&&i"s e1cep&-(do e* ScB@ * c-* es po!ce(&-*% po! *o .-e se !e/p*: cd "*o!ci'( co( -( ,(dice (-/0!ico de ;# Esc* B# Hi2-es& % Hi26 % Mode!&e % Lo< @% Lo
Dy( B% @@ Mode!&e @% Poo! B? Esc* # L!2e sc*e % L!2e % Mode!&e @% S/** B? Esc* # L!2e % Hi26 % Mode!&e @ y S/** B+ D(do co/o !es-*&do * /&!i: 2e(0!ic c-(&i&&i" p!ese(&e e( * T!" + P! &e!/i(! * /&!i: de decisi'( e i(c*-i! * i()o!/ci'( co!!espo(die(&e *os S-b c!i&e!ios B%@%%%% y se -&i*i:! * esc* .-e p!opo(e e* /0&odo KC * c-* p*(&e -( i(&e!"*o e(&!e $ y e* c-* co(side! "*o!es (e2&i"os >(ic/e(&e
@
p! /os&!! .-e /0&odos (o so( "ib*es &0c(ic/e(&e? p! &!b7! >(ic/e(&e co( "*o!es posi&i"os se /odi)ic! dic6 esc* "*o!es posi&i"os co/e(:(do e( B y &e!/i((do e( po! *o c-* $ se !e/p*: co( B y e* "*o! de co( p! /(&e(e! * p!opo!cio(*idd y c!di(*idd de *os d&os+
T!" 2. M&!i: de decisi'( Ge(0!ic+ F-e(&e# Des!!o**o p!opio p!&i! de 3H!&/( M-&/(s;y @@? Mi**e!$ Ti& e& *+ B4 T!"# 2. Ge(e!ic decisio( /&!i1+ So-!ce# O<( de"e*op/e(& bsed o( 3H!&/( M-&/(s;y @@? Mi**e!$Ti& e& *+ B4
T!" . M&!i: de decisi'( Ge(0!ic (-/0!ic+ F-e(&e# Des!!o**o p!opio p!&i! de 3H!&/( M-&/(s;y @@? Mi**e!$Ti& e& *+ B4 T!"# . N-/e!ic 2e(e!ic decisio( /&!i1+ So-!ce# O<( de"e*op/e(& bsed o( 3H!&/( M-&/(s;y @@? Mi**e!$Ti& e& *+ B4
Hoyos
@B
Fi(*/e(&e% debido e* &/5o de * /&!i: de decisi'( y * /(e7o de * s-b7e&i"idd% se p*ic e* /0&odo de si2(ci'( de pesos /edi(&e * e(&!op,% p*(&edo po! 3Ze*e(y Coc6!(e B@4 e* c-* de&e!/i( psi"/e(&e *os pesos de *os c!i&e!ios si( -( i(&e(ci'( co(scie(&e de &o/! decisio(es% e*i/i((do * p!e)e!e(ci y e1pec&&i"s 2e(e!ds po! e* -so de deciso!es% co/o p-ede "e!se e( 3A267(i :::i e& *+ @BB4+ E* /0&odo de VI9OR p*(&edo po! 3Op!ico"ic T:e(2 @4 es -&i*i:do p! de&e!/i(! * *&e!(&i" de co/p!o/iso+ Se2>( 3-i7(o H-!&do @B@4% ci&(do 3ei Li( @4% e* /0&odo VI9OR es -( 6e!!/ie(& e)ec&i" e( e* A(8*isis de Decisi'( M-*&ic!i&e!io% p!&ic-*!/e(&e e( si&-cio(es do(de e* deciso! (o es&8 cpci&do% o (o sbe c'/o e1p!es! s p!e)e!e(ci+ A co(&i(-ci'( se desc!ibe( e( de&**e cd -( de *s 6e!!/ie(&s p*icds p! so*-cio(! es&e p!ob*e/+
3. METODO UBC E* /0&odo de se*ecci'( KC es **/do s, po! 6be!se des!!o**do e( * K(i"e!si&y o) !i&is6 Co*-/bi po! 3Mi**e!$Ti& e& *+ B4+ Es&e /0&odo s-!2e (&e * (ecesidd de /e7o!! * &0c(ic des!!o**d po! 3Nic6o*s B4+ Co/o (-e"o po!&e se i(&!od-ce e* "*o! $B p! si2(! -( peso (e2&i"o si( e*i/i(! -( /0&odo co/p*e&/e(&e% &* co/o *o 6c, * &0c(ic de Nic6o*s co( e* "*o! de
$+ Po! o&! p!&e% *s c*i)iccio(es de /ec8(ic de !ocs )-e!o( 7-s&ds co( (-e"os "*o!es+ P-ede co(s-*&!se e* /0&odo p!o)-(didd e( 3Mi**e!$Ti& e& *+ B4 T!" 3. C!i&e!ios de* /0&odo KC+ F-e(&e# 3Mi**e!$Ti& e& *+ B4 T!"# 3. KC /e&6od C!i&e!i+ So-!ce# 3Mi**e!$ Ti& e& *+ B4 1. 9&0 #*#&" E.-i$ Tods *s di/e(sio(es es&8( e( di/e(sio(* e* /is/o o!de( de /2(i&-d Tb-*! Dos di/e(sio(es &ie(e( /-c6s "eces e* /is/o espeso!% .-e (o s-e*e s-pe!! *os / I!!e2-*! Ls di/e(sio(es "!,( e( co!&s dis&(cis+ 2. E$(#$& +#" 0*t M-y / es&!ec6o Es&!ec6o $B/ I(&e!/edio B$B/ G!-eso $B/ M-y G!-eso QB/ . I*%"'*%')* P*(o @ 2!dos I(&e!/edio @$ 2!dos E/pi(do Q 2!dos 3. P&;/*+'++ S-pe!)ici* $B / I(&e!/edio B$/ P!o)-(do Q/ 4. D'$t&'!/%')* K(i)o!/e E* 2!do e( c-*.-ie! p-(&o de*
Dy( B% @@ dep'si&o (o "!, si2(i)ic&i"/e(&e de * c*i)icci'( /edi+ G!dcio(es E* 2!do &ie(e c!c&e!,s&ics :o(*es% y c/bi 2!d-*/e(&e de -( *-2! o&!o+ E!!8&ico E* 2!do c/bi !dic*/e(&e e( co!&s dis&(cis+ 5. R%< 0$$ &t'*$ M-y d0bi* $@ D0bi* @$ Mode!do $ F-e!&e $ M-y F-e!&e $B 6. R%< $/!$t*%# $t&#*t= >9/#&? /*'@'" E$t&#$ (&'*%'(" M-y d0bi* D0bi* $B Mode!do B$B F-e!&e QB
4. METODO DE LA ENTROPIA E* /0&odo de * E(&!op, )-e des!!o**do po! 3Ze*e(y B@4 co/o -( /0&odo ob7e&i"o de si2(ci'( de *os pesos% e( )-(ci'( de * /&!i: de decisi'(% si( .-e )ec&e * p!e)e!e(ci de* deciso!% se2>( 3Po/e!o* !b$Ro/e!o B4 * i/po!&(ci !e*&i" de* c!i&e!io 7 e( -( si&-ci'( de decisi'(% /edid po! s- peso <7% es&8 di!ec&/e(&e !e*cio(d co( * c(&idd de i()o!/ci'( i(&!,(sec/e(&e po!&d po! e* co(7-(&o de *s *&e!(&i"s !espec&o dic6o c!i&e!io+ C-(& /yo! di"e!sidd 6y e( *s e"*-cio(es de *s *&e!(&i"s /yo! i/po!&(ci debe!8 &e(e! dic6o c!i&e!io+ L /edid de es& di"e!sidd es&8 bsd e( e* co(cep&o de * e(&!op, e( -( c(* de i()o!/ci'( p*(&edo po! 3S6((o( e"e! @@4+ E* p!ocedi/ie(&o es e* si2-ie(&e# Se &o/( *s e"*-cio(es aij 3iB%/437B%(4 (o!/*i:ds co/o )!cci'( de * s-/ a de *s e"*-cio(es o!i2i(*es de cd i ij c!i&e!io 7+ Se c*c-* * e(&!op, 3E74+
∑
E j − BS *o2 m T ∑ i aij T*o2 aij
3B4
Do(de / N-/e!o de *&e!(&i"s e( * /&!i: de e"*-cio(es (o!/*i:ds y aij
@@
C!i&e!ios o &!ib-&os (o!/*i:dos+ Se c*c-* * di"e!sidd de* c!i&e!io 3D74+ D j = B − E j
3@4
Se c*c-* e* peso (o!/*i:do de cd c!i&e!io 374+ 34 & j = D j S ∑ j D j = B+A
4. METODO VIKOR E* /0&odo V*se9!i&e!i7-/s; Op&i/i:ci7 I 9o/p!o/is(o Rese(7e% .-e &!d-ce de* bos(io% Op&i/i:cio( M-*&ic!i&e!io y so*-ci'( de co/p!o/iso% VI9OR de .-, e( de*(&e% )-e des!!o**do e( B po! Se!)i/ Op!ico"ic% co/o -( /0&odo de A(8*isis M-*&ic!i&e!io p! * op&i/i:ci'( de sis&e/s disc!e&os co/p*e7os co( c!i&e!ios co()*ic&i"os e i(co(/e(s-!b*es 3Op!ico"ic T:e(2 @4+ Se2>( 3-i7(o H-!&do @B@4% ci&(do 3Op!ico"ic B4% e* /0&odo Vi;o! de&e!/i( e* !(;i(2 de *&e!(&i"s% * so*-ci'( de co/p!o/iso y *os i(&e!"*os de es&bi*idd p! * so*-ci'( de co/p!o/iso ob&e(id co( *os pesos i(ici*es ddos+ Es&e /0&odo c*si)ic -( co(7-(&o de *&e!(&i"s% co( c!i&e!ios e( co()*ic&o% y se*eccio( * *&e!(&i" de co/p!o/iso% e(&e(did co/o * A*&e!(&i" .-e se e(c-e(&! /8s ce!c( * ide* y /8s *e7( de * peo! de e**s+ Es&e /0&odo d co/o !es-*&do -( !(;i(2 /-*&ic!i&e!io bsdo e( * p!&ic-*! /edid de Uce!c(, * so*-ci'( Uide*+ L /edid /-*&ic!i&e!io p! * c*si)icci'( de co/p!o/iso se des!!o** p!&i! de * Lp$ /0&!ic% -&i*i:d co/o -( )-(ci'( de 2!e2ci'( e( -( /0&odo de p!o2!/ci'( de co/p!o/iso 3=- B? Ze*e(y B@4 E* p!i/e! pso es co(s&!-i! * /&!i: de decisio(es y (o!/*i:!* po! e* /0&odo de * iesi/ co/po(e(&e de* "ec&o! -(i&!io+ 'i =
ai
3
∑a 4
@ BS @
34
B
Do(de Vi B Ls *&e!(&i"s de* co(7-(&o UJ so( de(o&ds co/o AB% A@% A7WW++A/+ P! * *&e!(&i" A7% * c*i)icci'( de* iesi/o spec&o es (o&do po! # ij % po! e7e/p*o # ij es
Hoyos
@ e* iesi/o "*o! de* c!i&e!io p! * *&e!(&i" A7? m es e* (>/e!o de *&e!(&i"s% n es e* (>/e!o de c!i&e!ios+ L so*-ci'( de* /0&odo VI9OR co/ie(: co( * si2-ie(&e )o!/ de * Lp$ /e&ic#
!ep!ese(& * dis&(ci e(&!e *s *&e!(&i"s y * peo! opci'(% *i so( *os pesos de c!i&e!io e1p!esdos e( * p!e)e!e(ci de *os deciso!es co/o * i/po!&(ci !e*&i" de* c!i&e!io
BS (
( n T T − 34 ) ( % j = ∑ *i ( # i − # ij ) S ( # i − # i ) i =B B ≤ ( ≤ ∞? 7 = B% @%++++% J+ Es&e co(cep&o 2e(e!* de dis&(ci Lp !ep!ese(&% e( e* /0&odo VI9OR% *s dis&(cis de M(6&&( y de C6e"is6e" p! e* c8*c-*o de y + E( e* p!i/e! cso% p!
e* c8*c-*o de % se -&i*i: * (o!/ LB% do(de pB co!!espo(die(&e * /edid de /yo! dis&(ci e(&!e dos p-(&os+ E( e* se2-(do cso% p! c*c-*! se -&i*i: * dis&(ci de C6e"yse" o (o!/ .-e se !e)ie!e * /e(o! dis&(ci e(&!e dos p-(&os do(de + 3Op!ico"ic T:e(2 @? e**"e! M!&i(e: @B4 Se2>( 3-i7(o H-!&do @B@4 ci&(do 3Op!ico"ic T:e(2 @4 * c*si)icci'( de co/p!o/iso de VI9OR se !e*i: /edi(&e *os si2-ie(&es psos# a)
As-/ie(do .-e cd *&e!(&i" es e"*-d de c-e!do cd )-(ci'( de c!i&e!io% * 7e!!.-, de co/p!o/iso pod!, se! des!!o**d /edi(&e * co/p!ci'( de * /edid de ce!c(, * so*-ci'( ide* + T + Se de&e!/i(( *os /e7o!es # i T y *os peo!es # i − "*o!es p! cd -( de *s )-(cio(es de c!i&e!io iB%@%W+%(+ Si * iesi/ )-(ci'( de* c!i&e!io !ep!ese(& -( be(e)icio e(&o(ces # i T = /1 # ij y # i − = /i( # ij +
b4 Te(ie(do * ide(&i)icci'( de *os /e7o!es y peo!es "*o!es p! cd )-(ci'( de c!i&e!io% se de&e!/i(( *os "*o!es S7 y R7% 7 B%@%W% J /edi(&e *s !e*cio(es n j = ∑ A *i ( # i T − # ij ) S ( # i T − # i − ) 34 34 , j = /1 i *i ( # i T − #ij ) S ( #i T − # i − ) Do(de !ep!ese(& *s dis&(cis de *s *&e!(&i"s * /e7o! so*-ci'(? j
c)
C*c-*! *os "*o!es - j /edi(&e * !e*ci'( ( j − T ) ( , j − , T ) + (B− v) − - j = v − (8 ( − T ) ( , − ,T ) ) Do(de T = /i( j j ? − = /1 j j ? , T = /i( j , j ? , − = /1 j j y se i(&!od-ce co/o e* "*o! .-e !ep!ese(& * posici'( de* deciso! )!e(&e * !ies2o+ No!/*/e(&e e* V*o! de " se &o/ co/o + p! !ep!ese(&! -( posici'( (e-&! )!e(&e * !ies2o -(.-e se p-ede &o/! c-*.-ie! "*o! de B+
d4 Je!!.-i:! *s *&e!(&i"s% o!2(i:(do se2>( *os "*o!es de S% R y e( o!de( dec!ecie(&e+ Los !es-*&dos ob&e(idos so( &!es *is&s o!de(ds+ P!opo(2 co/o so*-ci'( de co/p!o/iso * *&e!(&i" A3B4% * c-* es * /e7o! de &ods se2>( * /edid 3/,(i/o4% si se c-/p*e( *s si2-ie(&es co(dicio(es# I+
Ve(&7 cep&b*e+ -3 .3@4 4 − - 3 .3B4 4 ≥ D-% Do(de D- = BS 3 / − B4 y .3@ 4
es * *&e!(&i" .-e oc-p * se2-(d posici'( e( * *is& o!de(d po! "*o! de + II+
Es&bi*idd cep&b*e e( * decisi'(+ L *&e!(&i" debe!8 se! &/bi0( * /e7o! e( *s *is&s S yo R+
5. DESARROLLO METODOLOGICO Se p*ic * &0c(ic KC p! !ed-ci! *s *&e!(&i"s so*o ci(co% *s c-*es p!ese(&( -( "*ide: &0c(ic se2>( *s co(dicio(es p!opis de es&e yci/ie(&o /i(e!*+ Se p-ede obse!"! * p*icci'( de* /is/o e( * 9'/& 2. do(de .-ed( co/o *&e!(&i"s
Dy( B% @@ "8*ids %, A"t#&*t', 4 T7os L!2os 3*o(2<**4% A"t#&*t', 7 Co!&e y Re**e(o 3Cut and +ill 4+ A"t#&*t', 5 C8/!s y pi*!es 3room and (illar%, A"t#&*t', C8/!s po! S-b(i"e*es 3 ublevel to(ing A"t#&*t', 8 M0&odo de E(&ibci'( co( C-d!os 30uare set 4+ E( c-(&o se &ie(e( *s *&e!(&i"s "ib*es &0c(ic/e(&e% se *o2! !ed-ci! * c(&idd de *&e!(&i"s co(side!! e( e* des!!o**o de* /0&odo VI9OR+ Es&s *&e!(&i"s cep&ds% p! e* p!ob*e/% p-ede( "e!se e( * T!"4. Do(de se p!ese(& * /&!i: de decisi'( )i(* p! es&e p!ob*e/+ Co( bse * /&!i:
)i(*% p!ese(&d e( * Tb* % se !*i: * si2(ci'( de pesos /edi(&e * e(&!op,% * c-* se p-ede obse!"! e( * Fi2-! + P! es&e p!ob*e/ se p-ede "e! co/o e* c!i&e!io )i((cie!o cB@ es e* /8s i/po!&(&e p! * decisi'( )i(*+ Co/o se p-ede obse!"! e( * (&e!io! /&!i: de do/i((ci y do/i((ci po!ce(&-*% (i(2-( *&e!(&i" do/i( *s de/8s e( &odos *os c!i&e!ios? 6o! se c*c-* e* ,(dice 0 p! p!ese(&! e* !(.-i( de *&e!(&i"s y * *&e!(&i" de co/p!o/iso% se esco2e co/o *&e!(&i" de co/p!o/iso * .-e &e(2 e* /e(o! "*o! e( e* ,(dice 0+
9'/& 2. Res-*&dos de T0c(ic KC F-e(&e# Des!!o**o p!opio p!&i! de 3Mi**e!$Ti& e& *+ B4 9'/&# 2. KC Tec6(ic* Res-*&s So-!ce# O<( de"e*op/e(& bsed o( 3Mi**e!$Ti& e& *+ B4
T!" 4. M&!i: de decisi'( )i(*+ F-e(&e# Des!!o**o p!opio T!"# 4. Decisio( M&!i1+ So-!ce# O<( de"e*op/e(&
9'/& . Asi2(ci'( de pesos co( e* /0&odo de * e(&!op,+ F-e(&e# Des!!o**o p!opio 9'/&# . Assi2(i(2
@
Hoyos
@
T!" 4. M&!i: de do/i((ci po!ce(&-*+ F-e(&e# Des!!o**o p!opio T!"# 4. Pe!ce(& do/i((ce /&!i1+ So-!ce# O<( de"e*op/e(& A A A A A A
B B B B
A B B@ BB B
A B B B BB
A BB B B@ B
A B B B B
A A A A A
A
A
A
T!" 5. C*c-*o de ,(dice .+ F-e(&e# Des!!o**o p!opio T!"# 5. Pe!ce(& do/i((ce /&!i1+ So-!ce# O<( de"e*op/e(&
T!" 5. C*c-*o de ,(dice .+ F-e(&e# Des!!o**o p!opio T!"# 5. Pe!ce(& do/i((ce /&!i1+ So-!ce# O<( de"e*op/e(&
A
A
Dy( B% @@
6. CONCLUSIONES Los !es-*&dos de* /0&odo VI9OR 3T7o *!2o% c8/!s y pi*!es% c8/!s po! s-b(i"e*es4 )o!/( -( co(7-(&o de *&e!(&i"s de co/p!o/iso% *s c-*es so( cep&ds po! e1pe!&os .-e p!&icip!o( e( e* p!oceso de decisi'(+ Fi(*/e(&e% p! es&e dep'si&o )-e -&i*i:do e* /0&odo de &7o *!2o+ E* (8*isis de do/i((ci es /-y >&i*% po!.-e pe!/i&e ide(&i)ic! *&e!(&i"s do/i(ds+ Ade/8s% y-d de&e!/i(! si -( *&e!(&i" do/i( *s de/8s+ E* (8*isis po!ce(&-* de do/i((ci% pe!/i&e "is-*i:! e* (i"e* de s-pe!io!idd e(&!e *&e!(&i"s de -( /(e! )8ci* y de -&i*idd p! i! ide(&i)ic(do *&e!(&i"s p!opids p! * so*-ci'( de* p!ob*e/+ Los !es-*&dos ob&e(idos e( es&e &!b7o% pe!/i&e( e"ide(ci! co/o e* /0&odo VI9OR% co*bo! p! /e7o!! e* p!oceso de &o/ de decisio(es% y .-e pe!/i&e es&!-c&-!! de -( )o!/ *'2ic -( 2!( c(&idd de i()o!/ci'(% &(&o de* p!ob*e/ co/o de *s posib*es so*-cio(es .-e se p-ede( p*(&e!+ P! es&-dios pos&e!io!es se pod!, 2!e2! -( "*o!ci'( s-b7e&i" 7-(&o co( e* /0&odo de * e(&!op, y 2!e2!*s e( -( "ec&o! de pesos >(ico &* co/o *o /-es&! 3A267(i :::i e& *+ @BBb4 RE9ERENCIAS A267(i :::i% A+% Os(*oo% M+ 9!i/i% +% @BB+ De!i"i(2 p!e)e!e(ce o!de! o) ope( pi& /i(es e.-ip/e(& &6!o-26 MADM /e&6ods# App*ic&io( o) /odi)ied VI9OR /e&6od+ E1(ert 2stems *ith ((lications% 34% pp+@Y@+ A"i*b*e &# 6&&p#*i(;i(26-b+e*se"ie!+co/!e&!ie"epiiSB B Accessed M!c6 @% @B[+ A267(i :::i% A+% Os(*oo% M+ 9!i/i% +% @BBb+ De!i"i(2 p!e)e!e(ce o!de! o) ope( pi& /i(es e.-ip/e(& &6!o-26 MADM /e&6ods# App*ic&io( o) /odi)ied VI9OR /e&6od+ E1(ert 2stems *ith
@
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