Maria Gabriela Stevanato Furtado
Orientadora:
Profa. Dra. Franklina Maria Bragion de Toledo
Dissertação apresentada ao Instituto de Ciências Matemáticas e de Computação - ICMC-USP, como parte dos requisitos para obtenção do título de Mestre em Ciências - Ciências de Computação e Matemática Computacional. VERSÃO REVISADA
USP – São Carlos
Abril de 2012
1 Este trabalho foi financiando pela FAPESP
SERVIÇO DE PÓS-GRADUAÇÃO DO ICMC-USP
Data de Depósito: 26/04/2012
Ficha catalográfica elaborada pela Biblioteca Prof. Achille Bassi e Seção Técnica de Informática, ICMC/USP,
com os dados fornecidos pelo(a) autor(a)
F992p
Furtado, Maria Gabriela Stevanato
O planejamento da produção de pedidos em fundições de pequeno porte / Maria Gabriela Stevanato Furtado; orientadora Franklina Maria Bragion Toledo. -- São Carlos, 2012.
57 p.
Dissertação (Mestrado - Programa de Pós-Graduação em Ciências de Computação e Matemática Computacional) --Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, 2012.
1. Fundições. 2. Dimensionamento de lotes. 3. Relax-and-fix. 4. Planejamento de pedidos. I.
❆❣"❛❞❡❝✐♠❡♥*♦,
❆❣"❛❞❡&♦ ♣"✐♠❡✐"❛♠❡♥,❡ - ❉❡✉0 ❡ ,❛♠❜2♠ ,♦❞❛ - ♠✐♥❤❛ ❢❛♠5❧✐❛ 7✉❡ 0❡♠♣"❡ ❡0,✐✈❡"❛♠ ♣"❡0❡♥,❡ ❡♠ ♠✐♥❤❛ ✈✐❞❛✳
❆♦0 ♠❡✉0 ♣❛✐0 ❊❞✉❛"❞♦ ▼<"❝✐♦ ❡ ▼❛"✐❛ ❈"✐0,✐♥❛✱ - ♠✐♥❤❛ ✐"♠@ ▼❛"✐❛ ❋❡"♥❛♥❞❛ ❡ ❛♦0 ♠❡✉0 ❛✈B0 0❡✉ ❉❡♦♥✐❞✐♦ ✭◆✐③✐♦✮✱ ▼❛"✐❛ ❆♣❛"❡❝✐❞❛ ✭◆❡❣✉✐♥❤❛✮ ❡ ▼❛"✐❛ ❍❡❧❡♥❛ 7✉❡ 0❡♠♣"❡ ♠❡ ❛♣♦✐❛"❛♠ ♥♦0 ♠❡✉0 ❡0,✉❞♦0 ❡ ♠❡ ❛❥✉❞❛"❛♠ ♣❛"❛ 7✉❡ ❤♦✉✈❡00❡ ❛ "❡❛❧✐③❛&@♦ ❞❡0,❡ ,"❛❜❛❧❤♦✳
❆♦0 ♠❡✉0 ❛♠✐❣♦0 ❞♦ ❧❛❜♦"❛,B"✐♦ I❛✉❧❛✱ I❡❞"♦✱ ❱✐❝,♦"✱ ❚❛♠❛"❛✱ ❈❧❛✉❞✐♥❤❛ ❡ ❡♠ ❡0♣❡✲ ❝✐❛❧ ❛♦ ▼<"❝✐♦✱ I❛♠❡❧❛ ❡ ▼❛"❝@♦ 7✉❡ 0❡♠♣"❡ ♠❡ ❛❥✉❞❛"❛♠ ❡♠ ,✉❞♦ 7✉❡ ♣"❡❝✐0❡✐✳
❆❣"❛❞❡&♦ - ♠✐♥❤❛ ♦"✐❡♥,❛❞♦"❛ ❋"❛♥ ♣♦" ,♦❞♦ ❛♣♦✐♦✱ ❝♦♥0✐❞❡"❛&@♦ ❡ ♣❛❝✐M♥❝✐❛ 7✉❡ ,❡✈❡ ❞✉"❛♥,❡ ❛ "❡❛❧✐③❛&@♦ ❞❡0,❛ ♣❡07✉✐0❛✳
❆ ,♦❞♦0 ♦0 ♠❡✉0 ❛♠✐❣♦0 ❞❛ ❇❛""❛ ❡ ❡♠ ❡0♣❡❝✐❛❧ ❈❛"♦❧✱ ❈❛♠✐❧❛✱ ●✐0❡❧❡ ❡ ▼❛"✐❛♥❛ 7✉❡ 0❡♠♣"❡ ❡0,✐✈❡"❛♠ ❝♦♠✐❣♦✳
❆♦0 ♠❡✉0 ❛♠✐❣♦0 ❞❡ ❣"❛❞✉❛&@♦ 7✉❡ 0❡♠ ❡❧❡0 ❡✉ ♥@♦ ❡0,❛"✐❛ ♥♦ ♠❡0,"❛❞♦✿ ❇❡,✐♥❛✱ ❈❤✉❝❦ ✭❘♦❞"✐❣♦✮✱ ▲✉ ❡ ❏✉♥✐♦✳
❘❡"✉♠♦
❆ ✐♥❞$%&'✐❛ ❞❡ ❢✉♥❞✐,-♦ ♣'♦❞✉③ ✉♠❛ ✈❛%&❛ ❣❛♠❛ ❞❡ ✐&❡♥% ❝♦♠ ♣'❡%❡♥,❛ ♥❛ ❝❛❞❡✐❛ ♣'♦❞✉&✐✈❛ ❞❡ ✈5'✐♦% %❡&♦'❡% ❞❛ ❡❝♦♥♦♠✐❛✳ ❙-♦ ❣❡'❛❞♦% ♣❡❧♦ %❡&♦'✱ ❞❡%❞❡ ✐&❡♥% %✐♠♣❧❡% ❞❡ ✉%♦ ❞♦♠:%&✐❝♦ ❛&: ✐&❡♥% %♦✜%&✐❝❛❞♦%✱ ✉&✐❧✐③❛❞♦% ♣♦' ✐♥❞$%&'✐❛% ❞❡ ❜❛%❡ ❡ ♣❡❧♦ %❡&♦' ❞❡ ❛✉&♦♣❡,❛%✳ =♦' %❡' ✉♠ %❡❣♠❡♥&♦ ♠✉✐&♦ ✐♠♣♦'&❛♥&❡ ♣❛'❛ ❛ ❡❝♦♥♦♠✐❛ ❜'❛%✐❧❡✐'❛✱ ❡%&✉❞♦% ✈✐%❛♥❞♦ ♠❡❧❤♦'❛' %✉❛ ❡✜❝✐?♥❝✐❛ %-♦ ❢✉♥❞❛♠❡♥&❛✐% ♣❛'❛ ❛%%❡❣✉'❛' %✉❛ ❝♦♠♣❡&✐&✐✈✐❞❛❞❡ ❡♠ '❡❧❛,-♦ ❛♦ ❝❡♥5'✐♦ ♠✉♥❞✐❛❧✳ ❙❡❣✉♥❞♦ ❛ ❧✐&❡'❛&✉'❛✱ ✉♠ ❞♦% ♣'✐♥❝✐♣❛✐% ❢❛&♦'❡% @✉❡ ✐♥✢✉❡♥✲ ❝✐❛♠ %✉❛ ♣'♦❞✉&✐✈✐❞❛❞❡ : ♦ ♣❧❛♥❡❥❛♠❡♥&♦ ❞❛ ♣'♦❞✉,-♦✳ ◆♦% $❧&✐♠♦% ❛♥♦%✱ ♦% ✐♥✈❡%&✐♠❡♥&♦% ♥❡%&❛ 5'❡❛ ✈❡♠ ❛✉♠❡♥&❛♥❞♦ ❡ &❡♠ '❡❝❡❜✐❞♦ ♠❛✐% ❛&❡♥,-♦ ❞♦ ♣♦♥&♦ ❞❡ ✈✐%&❛ ❛❝❛❞?♠✐❝♦✳ ❊%&❛ ❞✐%%❡'&❛,-♦ ❛❜♦'❞❛ ♦ ♣❧❛♥❡❥❛♠❡♥&♦ ❞❛ ♣'♦❞✉,-♦ ❡♠ ❢✉♥❞✐,F❡% ❞❡ ♣❡@✉❡♥♦ ♣♦'&❡✱ ❝✉✲ ❥❛% ♣'✐♥❝✐♣❛✐% ❞❡❝✐%F❡% %-♦✿ ❞❡❝✐❞✐' @✉❛✐% ❧✐❣❛% ❢✉♥❞✐' ♥♦% ❢♦'♥♦% ❞✐%♣♦♥H✈❡✐% ❡ @✉❛✐% ✐&❡♥% ❞❡✈❡♠ %❡' ✈❛③❛❞♦% ❛ ♣❛'&✐' ❞❛% ❧✐❣❛% ❢✉♥❞✐❞❛%✳ ❯♠❛ @✉❡%&-♦ ❛✐♥❞❛ ♥-♦ ❝♦♥%✐❞❡'❛❞❛ ♥❛ ❧✐&❡'❛&✉'❛ : ❛ ♦❜'✐❣❛&♦'✐❡❞❛❞❡ ❞❡ ❝♦♠♣❧❡&❛' ❛ ♣'♦❞✉,-♦ ❞❡ &♦❞♦% ♦% ✐&❡♥% ❞❡ ✉♠ ♣❡❞✐❞♦ ♣❛'❛ @✉❡ ❡%&❡ %❡❥❛ ❝♦♥%✐❞❡'❛❞♦ ❛&❡♥❞✐❞♦ ❡ ❡♥&'❡❣✉❡ ❛♦ ❝❧✐❡♥&❡✳ ◆♦ ❡♥&❛♥&♦✱ ❡♠ ♠✉✐&♦% ❝❛✲ %♦% '❡❛✐%✱ ✉♠ ♣❡❞✐❞♦ ♥-♦ ♣♦❞❡ %❡' ❛&❡♥❞✐❞♦ ♣❛'❝✐❛❧♠❡♥&❡✱ ♦✉ %❡❥❛✱ ♦% ✐&❡♥% @✉❡ ❝♦♠♣F❡♠ ❡%%❡ ♣❡❞✐❞♦ ♣♦❞❡♠ ❢❛③❡' ♣❛'&❡ ❞❡ ✉♠ ♠❡%♠♦ ✐&❡♠ ✜♥❛❧✳ ❊♠ ♦✉&'♦% ❝❛%♦%✱ ♦ ♣❡❞✐❞♦ ♣♦❞❡ %❡' ❛&❡♥❞✐❞♦ ♣❛'❝✐❛❧♠❡♥&❡✱ ♠❛% ✐♥❝♦''❡✲%❡ ❡♠ ❝✉%&♦% ❛❞✐❝✐♦♥❛✐% ❞❡ ❡①♣❡❞✐,-♦✳ ❊%&❛ ❞✐%✲ %❡'&❛,-♦ ❜✉%❝❛ ♣'❡❡♥❝❤❡' ❡%&❛ ❧❛❝✉♥❛✱ ♣❛'❛ &❛♥&♦✱ ♣'♦♣♦♠♦%✿ ✭✶✮ ✉♠ ♠♦❞❡❧♦ ♠❛&❡♠5&✐❝♦ ♣❛'❛ &'❛&❛' ♦ ♣'♦❜❧❡♠❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥&♦ ❞❛ ♣'♦❞✉,-♦ ❞❡ ♣❡❞✐❞♦% ❡♠ ❢✉♥❞✐,F❡% ❞❡ ♣❡@✉❡♥♦ ♣♦'&❡❀ ✭✷✮ ✉♠ ♠♦❞❡❧♦ ♣❛'❛ &'❛&❛' ❛ ♣♦%%✐❜✐❧✐❞❛❞❡ ❞❡ ♠$❧&✐♣❧❛% ❡♥&'❡❣❛% ♣❛'❛ ♦ ♣'♦❜❧❡♠❛ ❡%&✉❞❛❞♦✳ ❆❧:♠ ❞✐%%♦✱ &❛♠❜:♠ : ♣'♦♣♦%&❛ ✉♠❛ ❤❡✉'H%&✐❝❛ ❘❡❧❛①✲❛♥❞✲❋✐① ✭'❡❧❛①❡✲❡✲✜①❡✮ ♣❛'❛ ❛ %♦❧✉,-♦ ❞♦ ♣'♦❜❧❡♠❛ ✐♥&❡❣'❛❞♦✳
❆❜"#$❛❝#
❚❤❡ ❢♦✉♥❞(② ✐♥❞✉+,(② ♣(♦❞✉❝❡+ ♣❧❡♥,② ♦❢ ❞✐✛❡(❡♥, ✐,❡♠+ ♣(❡+❡♥, ✐♥ ✈❛(✐♦✉+ +❡❝,♦(+ ♦❢ ,❤❡ ❡❝♦♥♦♠②✳ ❙✉❝❤ ✐,❡♠+ (❛♥❣❡ ❢(♦♠ +✐♠♣❧❡ ❤♦✉+❡❤♦❧❞ ❣❛❞❣❡,+ ,♦ +♦♣❤✐+,✐❝❛,❡❞ ❞❡✈✐❝❡+ ✉+❡❞ ❜② ❜❛+✐❝ ✐♥❞✉+,(✐❡+ ❛♥❞ ,❤❡ ❛✉,♦ ♣❛(,+ +❡❝,♦(✳ ❚❤✐+ ✐♥❞✉+,(② ✐+ ✐♠♣♦(,❛♥, ❢♦( ,❤❡ ❇(❛③✐❧✐❛♥ ❡❝♦♥♦♠② ❛♥❞ +,✉❞✐❡+ ❛✐♠✐♥❣ ❛, ,❤❡ ✐♠♣(♦✈❡♠❡♥, ♦❢ ✐,+ ❡✣❝✐❡♥❝② ❛(❡ ❢✉♥❞❛♠❡♥,❛❧ ,♦ ❡♥+✉(❡ ✐,+ ❝♦♠♣❡,✐,✐✈❡♥❡++ ✇♦(❧❞✇✐❞❡✳ ❆+ ❤✐❣❤❧✐❣❤,❡❞ ✐♥ ,❤❡ ❧✐,❡(❛,✉(❡✱ ❛♥ ✐♠♣♦(,❛♥, ❢❛❝,♦( ,❤❛, ✐♥✢✉❡♥❝❡+ ,❤❡ ♣(♦❞✉❝,✐♦♥ ✐♥ ,❤❡ +❡❝,♦( ✐+ ,❤❡ ♣(♦❞✉❝,✐♦♥ ♣❧❛♥♥✐♥❣✳ ■♥ (❡❝❡♥, ②❡❛(+✱ ,❤❡ ✐♥✈❡+,♠❡♥,+ ✐♥ ,❤✐+ ❛(❡❛ ❤❛✈❡ ❜❡❡♥ ✐♥❝(❡❛+✐♥❣ ❛♥❞ ♠♦(❡ ❛,,❡♥,✐♦♥ ❤❛+ ❜❡❡♥ ❞(❛✇♥ ❜② ❛❝❛❞❡♠✐❝ +,✉❞✐❡+✳ ❚❤✐+ ❞✐++❡(,❛,✐♦♥ ❞❡❛❧+ ✇✐,❤ ,❤❡ ♣(♦❞✉❝,✐♦♥ ♣❧❛♥♥✐♥❣ ✐♥ +♠❛❧❧ ❢♦✉♥❞(✐❡+✱ ✇❤♦+❡ ♠❛❥♦( ❞❡❝✐+✐♦♥+ ❛(❡ ,❤❡ ❞❡,❡(♠✐♥❛,✐♦♥ ♦❢ ,❤❡ ❛❧❧♦②+ ,♦ ❜❡ ♠❡(❣❡❞ ❛♥❞ ✐,❡♠+ ,♦ ❜❡ ♣(♦❞✉❝❡❞✳ ❆ A✉❡+,✐♦♥ ,❤❛, +,✐❧❧ ❤❛+ ♥♦, ❜❡❡♥ ❝♦♥+✐❞❡(❡❞ ✐♥ ,❤❡ ❧✐,❡(❛,✉(❡ ✐+ ,❤❡ ♦❜❧✐❣❛,✐♦♥ ,♦ ❝♦♠♣❧❡,❡ ,❤❡ ♣(♦❞✉❝,✐♦♥ ♦❢ ,❤❡ ♦(❞❡(+ ,♦ ❜❡ ❞❡❧✐✈❡(❡❞ ,♦ ,❤❡ ❝❧✐❡♥,✳ ❍♦✇❡✈❡(✱ ✐♥ ♠❛♥② (❡❛❧ ❝❛+❡+✱ ❛♥ ♦(❞❡( ❝❛♥♥♦, ❜❡ ♣❛(,✐❛❧❧② ❞❡❧✐✈❡(❡❞✱ ,❤❛, ✐+✱ ,❤❡ ♣✐❡❝❡+✱ ✇❤✐❝❤ ❛(❡ ♣❛(,+ ♦❢ ,❤❡ ♦(❞❡(✱ ♠❛② ❜❡ ♣❛(,+ ♦❢ ,❤❡ ✜♥❛❧ ♣(♦❞✉❝,✳ ■♥ ♦,❤❡( ❝❛+❡+✱ ,❤❡ ♦(❞❡( ♠❛② ❜❡ ♣❛(,✐❛❧❧② ❞❡❧✐✈❡(❡❞✱ ❜✉, ✇✐,❤ ❛❞❞✐,✐♦♥❛❧ ❡①♣❡❞✐,✐♦♥ ❝♦+,+✳ ■♥ ,❤✐+ ❞✐++❡(,❛,✐♦♥ ,❤❡ ♦❜❥❡❝,✐✈❡ ✐+ ❝❧♦+❡ ,❤❛, A✉❡+,✐♦♥✱ +♦ ✇❡ ♣(♦♣♦+❡✿ ✭✶✮ ❛ ♠❛,❤❡♠❛,✐❝❛❧ ♠♦❞❡❧ ❢♦( ♣(♦❞✉❝,✐♦♥✲♣❧❛♥♥✐♥❣ ♣(♦❜❧❡♠ ♦❢ ❝♦♠♣❧❡,❡ ♦(❞❡(+ ❢♦( +♠❛❧❧ ❢♦✉♥❞(② ✐♥❞✉+,(②❀ ✭✷✮ ❛ ♠❛,❤❡♠❛,✐❝❛❧ ♠♦❞❡❧ ,♦ ,(❡❛, ,❤❡ ♣♦++✐❜✐❧✐,② ♦❢ ♣❛(,✐❛❧ ❞❡❧✐✈❡(② ,♦ ,❤❡ +❛♠❡ ♣(♦❜❧❡♠✳ ❋✉(,❤❡(♠♦(❡✱ ✇❡ ♣(♦♣♦+❡ ❛ ❘❡❧❛①✲❛♥❞✲❋✐① ❤❡✉(✐+,✐❝ ❢♦( ,❤❡ ✐♥,❡❣(❛,❡❞ ♠♦❞❡❧✳
❙✉♠#$✐♦
✶ ■♥#$♦❞✉()♦ ♣✳ ✶
✷ ❯♠❛ ✈✐0)♦ ❣❡$❛❧ ❞❡ ❋✉♥❞✐(5❡0 ♣✳ ✸
✷✳✶ ❘❡✈✐)*♦ ❇✐❜❧✐♦❣01✜❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹
✷✳✶✳✶ ❋✉♥❞✐:;❡) ❞❡ ●0❛♥❞❡ ❡ ▼>❞✐♦ ?♦0@❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹
✷✳✶✳✷ ❋✉♥❞✐:;❡) ❞❡ ?❡A✉❡♥♦ ?♦0@❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻
✸ ❖ 8$♦❜❧❡♠❛ ❞❡ 8❧❛♥❡❥❛♠❡♥#♦ ❞❛ 8$♦❞✉()♦ ❞❡ 8❡❞✐❞♦0 ✭4P✮ ♣✳ ✾
✸✳✶ ▼♦❞❡❧♦ ?0♦♣♦)@♦ ♣❛0❛ ♦ 4P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶
✸✳✷ ❆♥1❧✐)❡ ❞♦ ▼♦❞❡❧♦ 4P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✽
✸✳✷✳✶ ❉❡✜♥✐:*♦ ❞❛) ✐♥)@G♥❝✐❛) ❞❡ @❡)@❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✽
✸✳✷✳✷ ❚❡)@❡) ❈♦♠♣✉@❛❝✐♦♥❛✐) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✵
✸✳✸ 4P )❡♠ ❝✉)@♦ ❞❡ ♣0❡♣❛0❛:*♦ ❡ ❡)@♦A✉❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✸
✸✳✸✳✶ ❚❡)@❡) ❈♦♠♣✉@❛❝✐♦♥❛✐) ♣❛0❛ ♦ 4P2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✹
✸✳✹ ❈♦♥❝❧✉);❡) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✻
✹ ▼♦❞❡❧♦ ■♥#❡❣$❛❞♦ ♣❛$❛ ♦ 4P ♣✳ ✷✼
✹✳✶ ▼♦❞❡❧♦ ▼❛@❡♠1@✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✼
✹✳✷ ❉❡✜♥✐:*♦ ❞♦) ❈✉)@♦) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✸
✹✳✸ ❚❡)@❡) ❈♦♠♣✉@❛❝✐♦♥❛✐) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✹
✹✳✹ ❈♦♥❝❧✉);❡) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✷
✺✳✶ #$✐♠❡✐$❛ ❆❜♦$❞❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✹
✺✳✷ ❙❡❣✉♥❞❛ ❆❜♦$❞❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✺
✺✳✸ ❚❡67❡6 ❈♦♠♣✉7❛❝✐♦♥❛✐6 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✻
✺✳✹ ❈♦♥❝❧✉6<❡6 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✷
✻ ❈♦♥❝❧✉'(❡' ❡ *+,①✐♠♦' *❛''♦' ♣✳ ✺✸
✶
✶ ■♥#$♦❞✉()♦
❊♠ ✷✵✵✺✱ ♦ '❡)♦* ❞❡ ❢✉♥❞✐01❡' ♥♦ ❇*❛'✐❧ ❡*❛ *❡'♣♦♥'6✈❡❧ ♣♦* 60♠✐❧ ❡♠♣*❡❣♦' ❞✐*❡)♦'✱
'❡♥❞♦ ❛ ♠❛✐♦*✐❛ ❡♠ ❢✉♥❞✐01❡' ❞❡ ♣❡9✉❡♥♦ ❡ ♠:❞✐♦ ♣♦*)❡ ❧♦❝❛❧✐③❛❞❛' ♣*✐♥❝✐♣❛❧♠❡♥)❡ ♥❛ *❡❣✐=♦ '✉❞❡')❡ ❞♦ ♣❛>' ✭❆❇■❋❆ ✲ ❆''♦❝✐❛0=♦ ❇*❛'✐❧❡✐*❛ ❞❡ ❋✉♥❞✐0=♦✱ ✷✵✵✺✮✳ ❖ ❢❛)✉*❛♠❡♥)♦ ❞♦ '❡)♦* ❡*❛ ❞❡5,6❜✐❧❤1❡' ❞❡ ❞I❧❛*❡' ❝♦♠ ❛ ♣*♦❞✉0=♦ ❞❡2,9♠✐❧❤1❡' ❞❡ )♦♥❡❧❛❞❛'✱ ❧❡✈❛♥❞♦
♦ ♣❛>' ❛ ♦❝✉♣❛* ♦ ':)✐♠♦ ❧✉❣❛* ❝♦♠♦ ♠❛✐♦* ♣*♦❞✉)♦* ♠✉♥❞✐❛❧ ✭❆❇■❋❆✱ ✷✵✵✺✮✳
❉❡✈✐❞♦ K ❝*✐'❡ ❡❝♦♥L♠✐❝❛ ♠✉♥❞✐❛❧ ❡ ❛ '✉❛ ❢♦*)❡ ❞❡♣❡♥❞M♥❝✐❛ ❞❡ ♦✉)*♦' '❡)♦*❡' ❞❛ ❡❝♦♥♦♠✐❛✱ ❞❡'❞❡ ♥♦✈❡♠❜*♦ ❞❡ ✷✵✵✽ ❛ ♣*♦❞✉0=♦ ❜*❛'✐❧❡✐*❛ ❞❡ ❢✉♥❞✐❞♦' ❡')6 ❝❛✐♥❞♦ ❜*✉'✲ ❝❛♠❡♥)❡ 9✉❛♥❞♦ ❝♦♠♣❛*❛❞❛ ❛♦' ❛♥♦' ❛♥)❡*✐♦*❡'✳ ❊♥)*❡)❛♥)♦✱ ❡')❡ '❡)♦* ❝♦♥)✐♥✉❛ '❡♥❞♦ ♠✉✐)♦ ✐♠♣♦*)❛♥)❡ ♣❛*❛ ❛ ❡❝♦♥♦♠✐❛✱ ♥=♦ 'I ♣❛*❛ ❛ ❜*❛'✐❧❡✐*❛✱ ❝♦♠♦ )❛♠❜:♠ ♣❛*❛ ❛ ♠✉♥❞✐❛❧✳ ❙❡❣✉♥❞♦ ❞❛❞♦' ❞❛ ❆❇■❋❆ ✭✷✵✵✾✮✱ ♦ )♦)❛❧ ❣❡*❛❧ ♣*♦❞✉③✐❞♦ *❡❧❛)✐✈♦ ❛♦ ♣*✐♠❡✐*♦ '❡♠❡')*❡ ❞❡ ✷✵✵✾✱ 9✉❛♥❞♦ ❝♦♠♣❛*❛❞♦ ❛♦ ♣*✐♠❡✐*♦ '❡♠❡')*❡ ❞❡ ✷✵✵✽✱ '♦❢*❡✉ ✉♠❛ 9✉❡❞❛ ❞❡ 42% ♥❛
♣*♦❞✉0=♦ ❡♠ )♦♥❡❧❛❞❛'✱ ♣*♦❞✉③✐♥❞♦ ❡♠ ♠:❞✐❛ 8258)♦♥❡❧❛❞❛'✴❞✐❛✳
❆)✉❛❧♠❡♥)❡✱ ❛ ♣*♦❞✉0=♦ ✈♦❧)♦✉ ❛ ❝*❡'❝❡*✳ ❈♦♠♣❛*❛♥❞♦ ❛ ♣*♦❞✉0=♦ ❡♥)*❡ ♦' ♠❡'❡' ❞❡ ❏❛♥❡✐*♦ ❛ ◆♦✈❡♠❜*♦ ❞❡ 2011 ❡♠ *❡❧❛0=♦ ❛♦ ♠❡'♠♦ ♣❡*>♦❞♦ ♥♦ ❛♥♦ ❛♥)❡*✐♦* )❡✈❡✲'❡ ✉♠
❛✉♠❡♥)♦ ❞❡4%❀ ❝♦♥'✐❞❡*❛♥❞♦ ♦' ❞♦✐' ♣❡*>♦❞♦' ❥6 ❝✐)❛❞♦' ❛ ❡①♣♦*)❛0=♦ )❛♠❜:♠ ❛✉♠❡♥)♦✉ 12,9%✳ ❏6 ♦ ♥X♠❡*♦ ❞❡ ❡♠♣*❡❣♦' ❞✐*❡)♦' ❡♠ ◆♦✈❡♠❜*♦ ❞❡ ✷✵✶✶ ❢♦✐ ❞❡ 66.090 ✭❆❇■❋❆✱
✷✵✶✶✮✳
❆ ✐♥❞X')*✐❛ ❞❡ ❢✉♥❞✐0=♦ ♣*♦❞✉③ ✉♠❛ ✈❛')❛ ❣❛♠❛ ❞❡ ✐)❡♥'✱ ❝♦♠ ♣*❡'❡♥0❛ ♥❛ ❝❛❞❡✐❛ ♣*♦❞✉)✐✈❛ ❞❡ ✈6*✐♦' '❡)♦*❡' ❞❛ ❡❝♦♥♦♠✐❛✱ ❝♦♠♦ ♣♦* ❡①❡♠♣❧♦✱ ✐♥❞X')*✐❛ ❛✉)♦♠♦❜✐❧>')✐❝❛✱ '❛♥❡❛♠❡♥)♦ ❜6'✐❝♦ ❡ ❝♦♥')*✉0=♦ ❝✐✈✐❧✳
✷
♥❛ "#❡❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥*♦ ❞❛ ♣#♦❞✉-.♦ ✈❡♠ ❛✉♠❡♥*❛♥❞♦ ♥❛ ✐♥❞12*#✐❛ ❞❡ ❢✉♥❞✐-.♦✳
❖ ♣❧❛♥❡❥❛♠❡♥*♦ ❞❡ ♣#♦❞✉-.♦ *❡♠ ❝♦♠♦ ♦❜❥❡*✐✈♦ ♣#✐♥❝✐♣❛❧ ❛✉♠❡♥*❛# ❛ ♣#♦❞✉*✐✈✐❞❛❞❡ ❞❛2 ❢✉♥❞✐-8❡2❀ ♥♦ ❡♥*❛♥*♦ ✉♠❛ ♣#♦❞✉-.♦ ♠❛✐2 ❡✜❝✐❡♥*❡ *❛♠❜;♠ ❛❥✉❞❛✱ ❛✐♥❞❛ =✉❡ ✐♥❞✐#❡✲ *❛♠❡♥*❡✱ ❛ #❡❞✉③✐# ♦2 ✐♠♣❛❝*♦2 ❛♠❜✐❡♥*❛✐2 ❞❛2 ❢✉♥❞✐-8❡2✱ ♣♦✉♣❛♥❞♦ #❡❝✉#2♦2 ❝♦♠♦✱ ♣♦# ❡①❡♠♣❧♦✱ ❡♥❡#❣✐❛ ❡❧;*#✐❝❛✳
❆❧;♠ ❞❛ #❡❧❡✈C♥❝✐❛ ❡❝♦♥D♠✐❝❛ ❞❡2*❛❝❛❞❛ ❛♥*❡#✐♦#♠❡♥*❡✱ ❞♦ ♣♦♥*♦ ❞❡ ✈✐2*❛ ❛❝❛❞E♠✐❝♦ ♦ ♣#♦❜❧❡♠❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥*♦ *❛♠❜;♠ *❡♠ #❡❝❡❜✐❞♦ ♠❛✐2 ❛*❡♥-.♦ ✭❆#❛✉❥♦ ❡* ❛❧✳ ✭✷✵✵✽✮✱ ❚♦♥❛❦✐ ❡ ❚♦❧❡❞♦ ✭✷✵✶✵✮ ❡ ❈❛♠❛#❣♦ ❡* ❛❧✳ ✭✷✵✶✷✮✮✳ ❊♥*#❡*❛♥*♦✱ ✉♠❛ =✉❡2*.♦ ♣♦✉❝♦ ❡①❧♦#❛❞❛ ♥❛ ❧✐*❡#❛*✉#❛✱ ❝♦♠♦ ❞❡2*❛❝❛ ❈❛♠❛#❣♦ ✭✷✵✵✾✮✱ ; ❛ ♦❜#✐❣❛*♦#✐❡❞❛❞❡ ❞❡ ❝♦♠♣❧❡*❛# ❛ ♣#♦❞✉-.♦ ❞❡ *♦❞♦2 ♦2 ✐*❡♥2 ❞❡ ✉♠ ♣❡❞✐❞♦ ♣❛#❛ =✉❡ ❡2*❡ 2❡❥❛ ❝♦♥2✐❞❡#❛❞♦ ❛*❡♥❞✐❞♦ ❡ ❡♥*#❡❣✉❡ ❛♦ ❝❧✐❡♥*❡✳ ❊2*❡ ♣#♦❥❡*♦ ❞" ❝♦♥*✐♥✉✐❞❛❞❡ ❛♦ *#❛❜❛❧❤♦ ❞❡ ❱❡#❣✐♥❡ ✭✷✵✵✾✮✱ ❛ =✉❛❧ ❢♦✐ ❛ ♣#✐♠❡✐#❛ ❛✉*♦#❛ ❛ ❛❜♦#❞❛# ♦ ♣#♦❜❧❡♠❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥*♦ ❞❡ ♣❡❞✐❞♦2 ❡♠ ❢✉♥❞✐-8❡2✳
❊♠ ♠✉✐*♦2 ❝❛2♦2 #❡❛✐2✱ ✉♠ ♣❡❞✐❞♦ ♣♦❞❡ 2❡# ❛*❡♥❞✐❞♦ ♣❛#❝✐❛❧♠❡♥*❡ ❞❡2❞❡ =✉❡ 2❡❥❛ ❝♦♥2✐❞❡#❛❞♦ ✉♠ ❝✉2*♦ ❞❡ ❡①♣❡❞✐-.♦✱ ♣♦❞❡♥❞♦ ❡♥*.♦✱ ❤❛✈❡# ✈"#✐❛2 ❡♥*#❡❣❛2 ♣❛#❛ ✉♠ ♠❡2♠♦ ❝❧✐❡♥*❡✳ ❊♠ ♦✉*#♦2 ❝❛2♦2✱ ♦2 ✐*❡♥2 =✉❡ ❝♦♠♣8❡♠ ♦ ♣❡❞✐❞♦ ♣♦❞❡♠ 2❡# ♣❛#*❡2 ❞❡ ✉♠ ♠❡2♠♦ ♣#♦❞✉*♦ ✜♥❛❧✱ 2❡♥❞♦ ✐♥❝♦❡#❡♥*❡ ❛ ❡♥*#❡❣❛ ♣❛#❝✐❛❧ ❞❡2*❡ ♣❡❞✐❞♦✳ ❯♠ ❞♦2 ♣♦♥*♦2 ❝❤❛✈❡2 ❞❡2*❡ *#❛❜❛❧❤♦ ; ♣❡#♠✐*✐# ❛ ❡♥*#❡❣❛ ♣❛#❝✐❛❧ ❞♦ ♣❡❞✐❞♦ ❞❡2❞❡ =✉❡ ♦2 ❝✉2*♦2 ❛22♦❝✐❛❞♦2 ❛ ❡❧❡ 2❡❥❛♠ ❝♦♠♣✉*❛❞♦2 ❡ ❛♥❛❧✐2❛# ❛*; =✉❡ ♣♦♥*♦ ; ✈❛♥*❛❥♦2♦ ❛ ❡♥*#❡❣❛ ♣❛#❝✐❛❧ ❞❡ ✉♠ ♣❡❞✐❞♦✳
◆❡2*❡ *#❛❜❛❧❤♦ ✈❛♠♦2 ❛❜♦#❞❛# ♦ ♣#♦❜❧❡♠❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥*♦ ❞❛ ♣#♦❞✉-.♦ ❞❡ ♣❡❞✐❞♦2✱ ✈✐2❛♥❞♦ ♣❧❛♥❡❥❛# ♦2 ❧♦*❡2 ❞❡ ♣#♦❞✉-.♦ ♥✉♠ ❤♦#✐③♦♥*❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥*♦ ✜♥✐*♦ ✭♣#♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥2✐♦♥❛♠❡♥*♦ ❞❡ ❧♦*❡2 ✲ U❉▲✮ ❞❡ *❛❧ ❢♦#♠❛ =✉❡ ♦2 ♣❡❞✐❞♦2 2❡❥❛♠ ❛*❡♥❞✐❞♦2✳ ◆♦22♦ ♦❜❥❡*✐✈♦ ; ♣#♦♣♦# ✉♠ ♠♦❞❡❧♦ ❡♠ =✉❡ ❛ ♦♣-.♦ ❞❡ ❡♥*#❡❣❛ ♣❛#❝✐❛❧ ♥.♦ 2❡❥❛ ♣❡#♠✐*✐❞❛ ❡ ♦✉*#♦ ❡♠ =✉❡ ❛ ❡♥*#❡❣❛ ♣❛#❝✐❛❧ ; ♣❡#♠✐*✐❞❛✳ ❊2*❡ 1❧*✐♠♦ ❝♦♥2✐❞❡#❛ ♦ ♣#♦❜❧❡♠❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥*♦ ❞❛ ♣#♦❞✉-.♦ ❡ ❞❡ ❡①♣❡❞✐-.♦ ♣❛#❛ ♦2 ❝❧✐❡♥*❡2✳ ❈♦♠♦ ♦ ♣#♦❜❧❡♠❛ ; ❞❡ ❞✐❢X❝✐❧ 2♦❧✉-.♦✱ *❛♠❜;♠ ♣#♦♣♦♠♦2 ✉♠ ♠;*♦❞♦ ❤❡✉#X2*✐❝♦ ❞♦ *✐♣♦ ❡❧❛①✲❛♥❞✲✜① ♣❛#❛ 2✉❛ #❡2♦❧✉-.♦✳
❊2*❡ *❡①*♦ ❡2*" ♦#❣❛♥✐③❛❞♦ ❞❛ 2❡❣✉✐♥*❡ ♠❛♥❡✐#❛✿ ♥♦ ❈❛♣X*✉❧♦ 2✱ ❞❡2❝#❡✈❡♠♦2 ♦ ❛♠✲
❜✐❡♥*❡ ♣#♦❞✉*✐✈♦ ❞❡ ✉♠❛ ❢✉♥❞✐-.♦ ❡ ❛♣#❡2❡♥*❛♠♦2 ✉♠❛ #❡✈✐2.♦ ❜✐❜❧✐♦❣#"✜❝❛ 2♦❜#❡ ♦ ♣#♦✲ ❜❧❡♠❛ ❡2*✉❞❛❞♦✳ ◆♦ ❈❛♣X*✉❧♦ 3✱ ❞❡*❛❧❤❛♠♦2 ♦ ♣#✐♠❡✐#♦ ♠♦❞❡❧♦ ❡2*✉❞❛❞♦ ❡ ❛♣#❡2❡♥*❛♠♦2
#❡2✉❧*❛❞♦2 ❝♦♠♣✉*❛❝✐♦♥❛✐2✳ ❖ ♠♦❞❡❧♦ ✐♥*❡❣#❛❞♦ ; ❛♣#❡2❡♥*❛❞♦ ♥♦ ❈❛♣X*✉❧♦ 4 ❜❡♠ ❝♦♠♦
♦2 #❡2✉❧*❛❞♦2 ❝♦♠♣✉*❛❝✐♦♥❛✐2✳ ◆♦ ❈❛♣X*✉❧♦ 5✱ ❞❡2❝#❡✈❡♠♦2 ❛2 ❛❜♦#❞❛❣❡♥2 ❤❡✉#X2*✐❝❛2 ♣#♦✲
♣♦2*❛2 ❡ ♦2 #❡2✉❧*❛❞♦2 ♦❜*✐❞♦2 ❡ ✜♥❛❧♠❡♥*❡✱ ♥♦ ❈❛♣X*✉❧♦ 6 ❛♣#❡2❡♥*❛♠♦2 ❛2 ❝♦♥❝❧✉28❡2 ❡
✸
✷ ❯♠❛ ✈✐&'♦ ❣❡+❛❧ ❞❡ ❋✉♥❞✐12❡&
◆❛" ✐♥❞&"'(✐❛" ❞❡ ❢✉♥❞✐,-❡" ❤/ ❛❧❣✉♥" ♣(♦❝❡""♦" ❜/"✐❝♦"✱ '❛✐" ❝♦♠♦✿ ❢❛❜(✐❝❛( ♦" ♠♦❧❞❡" ❞♦" ✐'❡♥"✱ ♣(❡♣❛(❛( ❡ ❢✉♥❞✐( ❛" ❧✐❣❛"✱ ✈❛③❛( ♦ ♠❡'❛❧ ♥♦" ♠♦❧❞❡"✱ (❡'✐(❛( ♦" ✐'❡♥" ❞♦" ♠♦❧❞❡" ❡✱ ✜♥❛❧♠❡♥'❡✱ (❡♠♦✈❡( ❛" ♣♦""<✈❡✐" (❡❜❛(❜❛" (❡♠❛♥❡"❝❡♥'❡" ♥♦" ✐'❡♥"✳ ❊"'❡ ♣(♦❝❡""♦ ♣❡(♠✐'❡ ❢❛❜(✐❝❛( ✐'❡♥" ❞❡ '❛♠❛♥❤♦" ❡ ❢♦(♠❛" ✈❛(✐❛❞❛" ❝♦♠ ❜♦❛ ♣(❡❝✐"?♦ ❡ ❛♣❛(@♥❝✐❛✳
❇❛"✐❝❛♠❡♥'❡✱ ♦" ❡B✉✐♣❛♠❡♥'♦" ♣(❡"❡♥'❡" ❡♠ ✉♠❛ ❢✉♥❞✐,?♦ "?♦ ♦" ❢♦(♥♦" ❡ ❛" ♠/B✉✐♥❛" ❞❡ ♠♦❧❞❛❣❡♠✳ ❈♦♥❢♦(♠❡ ❛♣(❡"❡♥'❛❞♦ ❡♠ ❆(❛✉❥♦ ✭✷✵✵✸✮✱ ❛ ❋✐❣✉(❛ ✶ ✐❧✉"'(❛ ✉♠ ❡"B✉❡♠❛ ❜/"✐❝♦ ❞❛" ❛'✐✈✐❞❛❞❡" B✉❡ ♦❝♦((❡♠ ❞✉(❛♥'❡ ♦ ♣(♦❝❡""♦ ❞❡ ❢✉♥❞✐,?♦✳ M(✐♠❡✐(❛♠❡♥'❡✱ "?♦ (❡❝❡❜✐❞♦" ♦" ♣(♦❥❡'♦" ❞♦" ✐'❡♥" ❛ "❡(❡♠ ♣(♦❞✉③✐❞♦"✳ ❊♠ "❡❣✉✐❞❛✱ '❡♠ ✐♥<❝✐♦ ❞✉❛" ♥♦✈❛" ❡'❛♣❛"✿ ❛ (❡B✉✐"✐,?♦ ❞❡ ♠❛'N(✐❛✲♣(✐♠❛ ✭♣♦( ❡①❡♠♣❧♦✱ "✉❝❛'❛✮ ♣❛(❛ ♣♦"'❡(✐♦( ❢✉"?♦ ❞❡ ❧✐❣❛✱ ❡ ❛ ❢❛❜(✐❝❛,?♦ ❞♦" ♠♦❞❡❧♦" ❛ ♣❛('✐( ❞♦" B✉❛✐" "?♦ ♣(♦❞✉③✐❞♦" ♦" ♠♦❧❞❡" ✉'✐❧✐③❛❞♦" ♣❛(❛ ♣(♦❞✉,?♦ ❞♦" ✐'❡♥"✳ M♦( ✜♠✱ ♦❝♦((❡ ♦ ✈❛③❛♠❡♥'♦ ❡ ❛ "♦❧✐❞✐✜❝❛,?♦ ❞♦" ✐'❡♥"✱ ♦" B✉❛✐" "❡❣✉❡♠ ♣❛(❛ ♦ ❛❝❛❜❛♠❡♥'♦ ✜♥❛❧✳
❋✐❣✉(❛ ✶✿ M(✐♥❝✐♣❛✐" ❛'✐✈✐❞❛❞❡" ❡♠ ✉♠❛ ❢✉♥❞✐,?♦✱ ❢♦♥'❡✿ ❆(❛✉❥♦ ✭✷✵✵✸✮✳
✹
❡♠✱ ❝♦♠♦ ✉♠ ❞❡ (❡✉( ♠❛✐♦+❡( ❞❡(❛✜♦(✱ ♦ ❛ ❡♥❞✐♠❡♥ ♦ ❛♦( ❝❧✐❡♥ ❡( (❡♠ ❛ +❛(♦✳ ❊((❛( ❢✉♥❞✐23❡( (4♦ ❡♠ (✉❛ ♠❛✐♦+✐❛ ❞❡ ♣❡6✉❡♥♦ ♣♦+ ❡✳
❆ ❋✐❣✉+❛ ✷✱ ❛❞❛♣ ❛❞❛ ❞❡ ❈❛♠❛+❣♦ ❡ ❛❧✳ ✭✷✵✶✷✮✱ ✐❧✉( +❛ ✉♠ ❢♦+♥♦ ❞❡ ✉♠❛ ❢✉♥❞✐24♦ ❡ ❛❧❣✉♥(✐ ❡♥( ❛ (❡+❡♠ ♣+♦❞✉③✐❞♦(✳
❋✐❣✉+❛ ✷✿ ❋♦+♥♦ ❞❡ ✉♠❛ ❢✉♥❞✐24♦ ❡ ♦( ✐ ❡♥( ❢✉♥❞✐❞♦(✱ ❢♦♥ ❡✿ ❈❛♠❛+❣♦ ❡ ❛❧✳ ✭✷✵✶✷✮✳
❖✉ +❛ ❝❧❛((✐✜❝❛24♦ ❡♥❝♦♥ +❛❞❛ ♣❛+❛ ❛( ❢✉♥❞✐23❡( C 6✉❛♥ ♦ D (✉❛ ♣+♦❞✉24♦✿ ♣♦❞❡♠ (❡+ ❢❡++♦(❛( ✭❢✉♥❞✐23❡( 6✉❡ ♣+♦❞✉③❡♠ ❧✐❣❛( D ❜❛(❡ ❞❡ ❢❡++♦ ❡ ❛2♦✮ ❡ ♥4♦✲❢❡++♦(❛( ✭❢✉♥❞✐23❡( 6✉❡ ♣+♦❞✉③❡♠ ❧✐❣❛( D ❜❛(❡ ❞❡ ❝♦❜+❡✱ ③✐♥❝♦✱ ❛❧✉♠G♥✐♦✱ ❡ ❝✮✳
❖( ❢♦+♥♦( ♣+❡(❡♥ ❡( ♥❛( ❢✉♥❞✐23❡( ❛♠❜C♠ (4♦ ❜❛( ❛♥ ❡ ✈❛+✐❛❞♦(✿ ♣♦((✉❡♠ ❝❛♣❛❝✐✲ ❞❛❞❡( ❞✐❢❡+❡♥ ❡(✱ ❛❧❣✉♥( (I ♣♦❞❡♠ (❡+ ✉ ✐❧✐③❛❞♦( ♣❛+❛ ❛ ❢✉(4♦ ❞❡ ❧✐❣❛( ❡(♣❡❝G✜❝❛( ❡ ✉ ✐❧✐③❛♠ ❞✐✈❡+(♦( ✐♣♦( ❞❡ ❡♥❡+❣✐❛✳
✷✳✶ ❘❡✈✐'(♦ ❇✐❜❧✐♦❣./✜❝❛
❆( ❢✉♥❞✐23❡( ❞❡ ♠❡+❝❛❞♦ J♠ ✉♠ ♣❛♣❡❧ ✐♠♣♦+ ❛♥ ❡ ♥❛ ❡❝♦♥♦♠✐❛ ❜+❛(✐❧❡✐+❛✳ ▼✉✐ ♦( ❡( ✉❞♦( ♠♦( +❛♠ 6✉❡ ❛ ♣+♦❞✉24♦ ❞❛( ❢✉♥❞✐23❡( ♣♦❞❡ (❡+ ♠❡❧❤♦+❛❞❛ ❛ ✜♠ ❞❡ ♣+♦♣♦+❝✐♦♥❛+ ✉♠ ❛✉♠❡♥ ♦ ❡♠ (✉❛ ❡✜❝✐J♥❝✐❛✱ ♦+♥❛♥❞♦✲❛( ♠❛✐( ❝♦♠♣❡ ✐ ✐✈❛(✳
M+✐♠❡✐+❛♠❡♥ ❡ ✈❛♠♦( ❛❜♦+❞❛+ ♦( ❡( ✉❞♦( ✈♦❧ ❛❞♦( ♣❛+❛ ❢✉♥❞✐23❡( ❞❡ ❣+❛♥❞❡ ❡ ♠C❞✐♦ ♣♦+ ❡✳ ❊♠ (❡❣✉✐❞❛✱ ❞❡(❝+❡✈❡♠♦( ♦( +❛❜❛❧❤♦( 6✉❡ ❡♥❢♦❝❛♠ ❢✉♥❞✐23❡( ❞❡ ♣❡6✉❡♥♦ ♣♦+ ❡✳
✷✳✶✳✶ ❋✉♥❞✐()❡+ ❞❡ ●-❛♥❞❡ ❡ ▼0❞✐♦ 2♦-3❡
✺
♣❡"#♦❞♦ ❡ &✉❛♥*♦+ ✐*❡♥+ ♣"♦❞✉③✐" ❡♠ ❝❛❞❛ ♠0&✉✐♥❛ ❞❡ ♠♦❧❞❛❣❡♠✳ ❉♦✐+ ❝❛+♦+ +5♦ ❡+*✉✲ ❞❛❞♦+✳ ❖ ♣"✐♠❡✐"♦ ❡♠ &✉❡ ✉♠❛ 8♥✐❝❛ ❧✐❣❛ ♣"♦❞✉③ *♦❞♦+ ♦+ ✐*❡♥+ ❡ ♦ +❡❣✉♥❞♦ ❡♠ &✉❡ ✈0"✐♦+ *✐♣♦+ ❞❡ ❧✐❣❛+ +5♦ ❢✉♥❞✐❞❛+✳ ;❛"❛ ♦ +❡❣✉♥❞♦ ❝❛+♦✱ = ♣"♦♣♦+*♦ ✉♠ ♠=*♦❞♦ ❤❡✉"#+*✐❝♦ ❜❛+❡❛❞♦ ♥❛ "❡❧❛①❛A5♦ ❞♦ ♣"♦❜❧❡♠❛✱ "❡❞✉③✐♥❞♦ ❛♦ ❝❛+♦ ❡♠ &✉❡ +B *❡♠ ✉♠❛ ❧✐❣❛ ❛ +❡" ❢✉♥✲ ❞✐❞❛✳ ❆ ❤❡✉"#+*✐❝❛ ❛♣"❡+❡♥*❛❞❛ ❢♦✐ ✐♠♣❧❡♠❡♥*❛❞❛ ♥❛ ❧✐♥❣✉❛❣❡♠ ❈ ❡ ♦+ "❡+✉❧*❛❞♦+ ❢♦"❛♠ ❝♦♠♣❛"❛❞♦+ ❛♦+ ❞♦ ♣❛❝♦*❡ ❞❡ ♦*✐♠✐③❛A5♦ ❈;▲❊❳ ❱❡"+5♦ 4.0✳ ❋♦"❛♠ ❝♦♠♣❛"❛❞♦+ ♦+ ❣❛♣✬+
❡ ♦ *❡♠♣♦ ❝♦♠♣✉*❛❝✐♦♥❛❧ ❣❛+*♦✱ ❡ ♦+ "❡+✉❧*❛❞♦+ ♠❡❧❤♦"❡+ ❢♦"❛♠ ❞♦ ♣❛❝♦*❡ ❞❡ ♦*✐♠✐③❛A5♦ ❈;▲❊❳✳
❊♠ ❆"❛✉❥♦ ❡ ❆"❡♥❛❧❡+ ✭✷✵✵✸✮✱ ❢♦✐ ♣"♦♣♦+*♦ ✉♠ ♠♦❞❡❧♦ ♣❛"❛ ♦ ♣"♦❜❧❡♠❛ ❞❡ ♣❧❛♥❡❥❛✲ ♠❡♥*♦ ❞❛ ♣"♦❞✉A5♦ ❡♠ ❢✉♥❞✐AQ❡+ ❞❡ ♠=❞✐♦ ♣♦"*❡ ❜❛+❡❛❞♦ ♥♦ ♠♦❞❡❧♦ ❞❡+❡♥✈♦❧✈✐❞♦ ♣♦" ❙❛♥*♦+✲▼❡③❛ ❡* ❛❧✳ ✭✷✵✵✷✮✳ ❖+ ❛✉*♦"❡+ ♣"♦♣✉+❡"❛♠ ✉♠ ♠♦❞❡❧♦ ❡①*❡♥❞✐❞♦ &✉❡ ❝♦♥+✐❞❡"❛ ❝✉+*♦+ ❞❡ ♣"❡♣❛"❛A5♦ ❡ ❛*"❛+♦ ♥♦ ❛*❡♥❞✐♠❡♥*♦ ❞❛ ❞❡♠❛♥❞❛✳ ❖ ♦❜❥❡*✐✈♦ ❞❡+*❡ *"❛❜❛❧❤♦ ❢♦✐ ♣"♦♣♦" ✉♠ ♠♦❞❡❧♦ ❞❡ ♣"♦❣"❛♠❛A5♦ ✐♥*❡✐"❛ ♠✐+*❛ ❡ ✉♠ ♠=*♦❞♦ ❞❡ +♦❧✉A5♦ ♣❛"❛ ❛✉①✐❧✐❛" ♥❛ "❡+♦❧✉A5♦ ❞♦+ ♣"♦❜❧❡♠❛+✳ ❖ ♠=*♦❞♦ ❞❡ +♦❧✉A5♦ ❤❡✉"#+*✐❝❛ = ❞✐✈✐❞✐❞♦ ❡♠ ✸ ❡*❛♣❛+✿ ♥❛ ♣"✐♠❡✐"❛✱ *❡♠✲+❡ ✉♠❛ "❡❧❛①❛A5♦ ❞♦ ♣"♦❜❧❡♠❛❀ ♥❛ +❡❣✉♥❞❛✱ ✉♠❛ ❤❡✉"#+*✐❝❛ ❞❡*❡"♠✐♥❛ ❛ ❧✐❣❛ &✉❡ ❞❡✈❡ +❡" ♣"♦❞✉③✐❞❛❀ ❡ ♥❛ *❡"❝❡✐"❛ ❢❛+❡✱ *❡♠✲+❡ ❛ ♣"♦❣"❛♠❛A5♦ ❞❛+ ♠0&✉✐♥❛+ ❞❡ ♠♦❧❞❛❣❡♠✳ ❚❡+*❡+ ❝♦♠♣✉*❛❝✐♦♥❛✐+ "❡❛❧✐③❛❞♦+ ♠♦+*"❛♠ &✉❡ &✉❛♥*♦ W &✉❛❧✐❞❛❞❡ ❞❛ +♦❧✉A5♦ ♦+ ♠=*♦❞♦+ ❤❡✉"#+*✐❝♦+ +✉♣❡"❛"❛♠ ♦+ "❡+✉❧*❛❞♦+ ♦❜*✐❞♦+ ♣❡❧♦ ♣❛❝♦*❡ ❞❡ ♦*✐♠✐③❛A5♦ ❈;▲❊❳
7.1✳ ❊♠ ♠=❞✐❛✱ ♦ ♣"♦❝❡❞✐♠❡♥*♦ ❤❡✉"#+*✐❝♦ ♣"♦❞✉③✐✉ +♦❧✉AQ❡+ ♠❡❧❤♦"❡+ &✉❡ ♦ ❈;▲❊❳✳
◆♦ *"❛❜❛❧❤♦ ❞❡ ❆"❛✉❥♦ ❡ ❆"❡♥❛❧❡+ ✭✷✵✵✹✮ ❢♦✐ ❛♣"❡+❡♥*❛❞♦ ✉♠ ❡+*✉❞♦ +♦❜"❡ ♦ ♣❧❛♥❡✲ ❥❛♠❡♥*♦ ❞❛ ♣"♦❞✉A5♦ ❡♠ ✉♠❛ ❢✉♥❞✐A5♦ ❝❛*✐✈❛ ❞❡ ❣"❛♥❞❡ ♣♦"*❡✳ ❊+*❛ ❢✉♥❞✐A5♦ ❝♦♥+✐+*❡ ❡♠ *"Z+ ❧✐♥❤❛+ ❞❡ ♠♦❧❞❛❣❡♠✱ ❝❛❞❛ ✉♠❛ ❝♦♠ ✉♠ ❝♦♥❥✉♥*♦ ❞❡ ❢♦"♥♦+ ❞✐+♣♦♥#✈❡✐+✳ ❆ ♣"♦✲ ❣"❛♠❛A5♦ ❞♦ ♣❧❛♥❡❥❛♠❡♥*♦ ❞❛ ♣"♦❞✉A5♦ ❞❡✈❡ ❞❡❝✐❞✐" &✉❛❧ ❧✐❣❛ ❢✉♥❞✐" ❡♠ ❝❛❞❛ ❢♦"♥♦ ❡ ❛ &✉❛♥*✐❞❛❞❡ ❞❡ ❝❛❞❛ ✐*❡♠ &✉❡ ❞❡✈❡ +❡" ♣"♦❞✉③✐❞❛✳ ❖+ ❛✉*♦"❡+ ♣"♦♣✉+❡"❛♠ ✉♠ ♠♦✲ ❞❡❧♦ ❞❡ ♦*✐♠✐③❛A5♦ ✐♥*❡✐"❛ ♠✐+*❛ ♣❛"❛ ♦ ♣"♦❜❧❡♠❛✱ "❡+♣❡✐*❛♥❞♦ ❛+ ❝❛♣❛❝✐❞❛❞❡+ ❞♦+ ❢♦"♥♦+✱ ❞❡ ❢♦"♠❛ ❛ ❛*❡♥❞❡" ❛ ❞❡♠❛♥❞❛ ❡ ♠✐♥✐♠✐③❛♥❞♦ ❝✉+*♦+ ❞❡ ❛*"❛+♦+ ❡ ❞❡ ❡+*♦&✉❡+✳ ❚❡+*❡+ ❝♦♠♣✉*❛❝✐♦♥❛✐+ ❢♦"❛♠ "❡❛❧✐③❛❞♦+ ♣❛"❛ ✈❛❧✐❞❛" ♦ ♠♦❞❡❧♦✳ ❋♦"❛♠ +✐♠✉❧❛❞♦+ 5❞✐❛+ ❞♦ ❤♦"✐✲
③♦♥*❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥*♦ ❡ ♦ ♠♦❞❡❧♦ ❢♦✐ "❡+♦❧✈✐❞♦ 5✈❡③❡+ ✉*✐❧✐③❛♥❞♦ ♦ ♣❛❝♦*❡ ❞❡ ♦*✐♠✐③❛A5♦
❆♠♣❧✴❈;▲❊❳ ♥❛ ✈❡"+5♦7.1✳ ❖+ "❡+✉❧*❛❞♦+ ❢♦"❛♠ ❝♦♠♣❛"❛❞♦+ ❛♦+ ❞❛❞♦+ "❡❛✐+ ❞❛ ❢✉♥❞✐A5♦
❡ ♠♦+*"❛"❛♠ &✉❡ ♦ ♠♦❞❡❧♦ ♠❛*❡♠0*✐❝♦ ♣❡"♠✐*✐✉ ✉♠ ❛✉♠❡♥*♦ ♥♦ "❡♥❞✐♠❡♥*♦ ❞❛+ ❧✐♥❤❛+ ❡ ❞❛ ♣"♦❞✉A5♦✱ ✉♠❛ ✈❡③ &✉❡ ❡✈✐*♦✉ ❛*"❛+♦+ ❡ ♠❛♥*❡✈❡ ♦ ♥#✈❡❧ ❞❡ ❡+*♦&✉❡✳
✻
❛❞♦ ♠❛①✐♠✐③❛ ❛ ✉ ✐❧✐③❛*+♦ ❞❛, ♠-.✉✐♥❛, ❡ ❞♦, ❢♦2♥♦, ❡ ♠✐♥✐♠✐③❛ ♦ ❛ 2❛,♦ ♥❛ ♣2♦❞✉*+♦✳ ❖, ❡, ❡, ,❡ ❜❛,❡❛2❛♠ ❡♠ ❞❛❞♦, 2❡❛✐, ❞❡ ♣2♦❞✉*+♦ ❡ 27, ✈❛2✐❛*9❡, ❞❡ ❛❧❣♦2✐ ♠♦, ❣❡♥; ✐✲ ❝♦, ❢♦2❛♠ ❛✈❛❧✐❛❞❛, ❝♦♠ ❡, ❡, ❞❛❞♦,✳ ❖, 2❡,✉❧ ❛❞♦, ❢♦2❛♠ ❝♦♠♣❛2❛❞♦, ❛♦, ♦❜ ✐❞♦, ♣❡❧❛ ,♦❧✉*+♦ ❞♦ ♣2♦❜❧❡♠❛ ♥♦ ♦❢#✇❛&❡ ❈?▲❊❳ ✾✳✵ ❡ ♠♦, 2❛2❛♠ .✉❡ ❛, ✈❛2✐❛*9❡, ❞♦ ❛❧❣♦2✐ ♠♦ ❣❡♥; ✐❝♦ ♣2♦❞✉③❡♠ ,♦❧✉*9❡, ❞❡ ♠❡❧❤♦2 .✉❛❧✐❞❛❞❡ .✉❡ ♦, 2❡,✉❧ ❛❞♦, ❞♦ ❈?▲❊❳✳
❱■▲❊▲❆ ❏❯◆■❖❘ ✭✷✵✵✼✮ ♣2♦♣Q, ✉♠ ♠♦❞❡❧♦ ♣❛2❛ ♦ ♣2♦❜❧❡♠❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥ ♦ ❡ ♣2♦✲ ❣2❛♠❛*+♦ ❞❛ ♣2♦❞✉*+♦ ❡♠ ✉♠❛ ❢✉♥❞✐*+♦ ❝❛ ✐✈❛ .✉❡ ❢♦✐ ❜❛,❡❛❞♦ ❡♠ ❆2❛✉❥♦ ❡ ❆2❡♥❛❧❡, ✭✷✵✵✹✮✳ ❊, ❡ 2❛❜❛❧❤♦ ❡, ✉❞❛ ♦ ♣❧❛♥❡❥❛♠❡♥ ♦ - ✐❝♦✲♦♣❡2❛❝✐♦♥❛❧ ❡♥❢♦❝❛♥❞♦ ♦ ♣2♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥,✐♦♥❛♠❡♥ ♦ ❞❡ ❧♦ ❡,✱ .✉❡ ❝♦♥,✐, ❡ ❡♠ ♣2♦❣2❛♠❛2 ♦, ❢♦2♥♦, ❡ ❛, ❧✐♥❤❛, ❞❡ ♠♦❧❞❛❣❡♠✱ 2❡,♣❡✐ ❛♥❞♦ ❛, ❝❛♣❛❝✐❞❛❞❡, ♣❛2❛ ❛ ❡♥❞❡2 ❛ ❞❡♠❛♥❞❛ ❝♦♠ ♦ ♠❡♥♦2 ❛ 2❛,♦ ♣♦,,U✈❡❧✳ ❋♦✐ ♣2♦♣♦, ❛ ✉♠❛ ❤❡✉2U, ✐❝❛ ❧❛❣2❛♥❣✐❛♥❛ ♣❛2❛ ❛ 2❡,♦❧✉*+♦ ❞♦ ♣2♦❜❧❡♠❛✳ ❖, 2❡,✉❧ ❛❞♦, ❝♦♠✲ ♣✉ ❛❝✐♦♥❛✐, ❢♦2❛♠ ❝♦♠♣❛2❛❞♦, ❛♦, ❞❡ ❆2❛✉❥♦ ❡ ❆2❡♥❛❧❡, ✭✷✵✵✹✮✱ W ,♦❧✉*+♦ ♦❜ ✐❞❛ ♥❛ ♣2- ✐❝❛ ❡ ❛ ,♦❧✉*+♦ ✉ ✐❧✐③❛♥❞♦ ♦ ♣❛❝♦ ❡ ❞❡ ♦ ✐♠✐③❛*+♦ ❆♠♣❧✴❈♣❧❡① ♥❛ ✈❡2,+♦ ✶✵✳✵✳ ❖, 2❡,✉❧ ❛❞♦, ❞❡, ❛ ❤❡✉2U, ✐❝❛ ,✉♣❡2❛2❛♠ ♦, 2❡,✉❧ ❛❞♦, ✉ ✐❧✐③❛❞♦, ♥❛ ♣2- ✐❝❛ ❡♠ 2❡❧❛*+♦ ❛♦, ❛ 2❛,♦, ❡ ♣2❡♣❛2❛*9❡,✳ ❊♠ 2❡❧❛*+♦ ❛♦ ♣❛❝♦ ❡ ❞❡ ♦ ✐♠✐③❛*+♦ ❆♠♣❧✴❈♣❧❡①✱ ♦, 2❡,✉❧ ❛❞♦, ❢♦2❛♠ ,✉♣❡2❛❞♦, ♥♦ .✉❡ ❞✐③ 2❡,♣❡✐ ♦ ❛♦ ❛ 2❛,♦✳ ◗✉❛♥❞♦ ❝♦♠♣❛2❛❞❛ W ,♦❧✉*+♦ ♦❜ ✐❞❛ ❡♠ ❆2❛✉❥♦ ❡ ❆2❡♥❛❧❡, ✭✷✵✵✹✮ ♦ ♣2♦❣2❛♠❛ ❛♣2❡,❡♥ ♦✉ ✉♠ ♥[♠❡2♦ ♠❡♥♦2 ❞❡ ♣2❡♣❛2❛*9❡,✱ ♠❛, 2❡,✉❧ ♦✉ ❡♠ ♠❛✐♦2 ❛ 2❛,♦ .✉❡ ♦ ♠; ♦❞♦ ❞❡ ❆2❛✉❥♦ ❡ ❆2❡♥❛❧❡, ✭✷✵✵✹✮✳
✷✳✶✳✷ ❋✉♥❞✐()❡+ ❞❡ ,❡-✉❡♥♦ ,♦/0❡
❊♠ ❙✐❧✈❛ ❡ ▼♦2❛❜✐ ♦ ✭✷✵✵✹✮✱ ; ♣2♦♣♦, ♦ ✉♠ ♠; ♦❞♦ ♣❛2❛ 2❡,♦❧✈❡2 ♦ ♣2♦❜❧❡♠❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥ ♦ ❞❛ ♣2♦❞✉*+♦ ❞❡ ✉♠❛ ❢✉♥❞✐*+♦ ❞❡ ♠❡2❝❛❞♦✱ ,✐ ✉❛❞❛ ♥❛ ❝✐❞❛❞❡ ❞❡ ❙+♦ ❈❛2❧♦,✱ ✐♥ ❡2✐♦2 ❞♦ ❡, ❛❞♦ ❞❡ ❙+♦ ?❛✉❧♦✳ ❖ ♣2♦❜❧❡♠❛ ❡♥✈♦❧✈❡ ♦ ♣❧❛♥❡❥❛♠❡♥ ♦ ❞❛ ♣2♦❞✉*+♦ ♣❛2❛ ✉♠❛ ,❡♠❛♥❛ ❡♠ ✉♠❛ ❢✉♥❞✐*+♦ ❝♦♠ 27, ❢♦2♥♦,✳ ❆ ❝❛2 ❡✐2❛ ❞❡ ♣❡❞✐❞♦, ❞❛ ,❡♠❛♥❛ ; ❝♦♥❤❡❝✐❞❛ ❡ ♦ ♦❜❥❡ ✐✈♦ ; ♠❛①✐♠✐③❛2 ❛ ♣2♦❞✉ ✐✈✐❞❛❞❡ ,❡♠❛♥❛❧ ❞❛ ❢✉♥❞✐*+♦✳ ❖, ❛✉ ♦2❡, ♠♦❞❡❧❛♠ ♦ ♣2♦❜❧❡♠❛ ❝♦♠♦ ✉♠ ♣2♦❜❧❡♠❛ ❞❡ ❝♦2 ❡ ❞❡ ❡, ♦.✉❡ ✭?❈❊✮ ❡♠ .✉❡ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞♦, ❢♦2♥♦, ; 2❡♣2❡,❡♥ ❛❞❛ ♣♦2 ♦❜❥❡ ♦, ♠❛✐♦2❡, .✉❡ ,+♦ ❝♦2 ❛❞♦, ❡♠ ♦❜❥❡ ♦, ♠❡♥♦2❡, ✭♦, ✐ ❡♥,✮✱ ❡ ♦ ♠; ♦❞♦ ❞❡ ,♦❧✉*+♦ ✉ ✐❧✐③❛❞♦ ; ✉♠❛ ❤❡✉2U, ✐❝❛ ❣✉❧♦,❛ ♣❛2❛ ♦ ♣2♦❜❧❡♠❛ ❞❛ ♠♦❝❤✐❧❛✳ ❖ ♠; ♦❞♦ ❢♦✐ ❛✈❛❧✐❛❞♦ ✉ ✐❧✐③❛♥❞♦ ❞❛❞♦, 2❡❛✐, ❞❡ ❞✉❛, ,❡♠❛♥❛, ❞❡ ♣❡❞✐❞♦,✱ ❡ ♦, 2❡,✉❧ ❛❞♦, ♠♦, 2❛2❛♠ .✉❡ ❛ ❛❜♦2❞❛❣❡♠ ♣2♦❞✉③ ♠❡❧❤♦2❡, ,♦❧✉*9❡, .✉❡ ❛, ✉ ✐❧✐③❛❞❛, ♣❡❧❛ ❡♠♣2❡,❛✱ ♣♦✐, ♥♦ ♠❡,♠♦ ♣❡2U♦❞♦ ♣2♦❞✉③✐✉ ♦, ♠❡,♠♦, ✐ ❡♥, ❝♦♠ ✉♠ ❞✐❛ ❛ ♠❡♥♦, ❞❡ ♣2♦❞✉*+♦✳
✼
❞♦ ❛#$❛%♦ ♥❛ ♣$♦❞✉)*♦ ❞♦% ✐#❡♥%✳ ❖ ♣❧❛♥❡❥❛♠❡♥#♦ ❞❡ ♣$♦❞✉)*♦ ❝♦♥%✐❞❡$❛ ✉♠ ❤♦$✐③♦♥#❡ $♦❧❛♥#❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥#♦✱ ♥♦ 6✉❛❧ %*♦ ♣$♦♣♦%#♦% ❞♦✐% ♠7#♦❞♦% ♣❛$❛ %✉❛ $❡%♦❧✉)*♦✳ ❖ ♣$✐♠❡✐$♦ ✉#✐❧✐③❛ ❜✉%❝❛ ❧♦❝❛❧ ❡ ♦ %❡❣✉♥❞♦ ✉#✐❧✐③❛ ♦ ♠7#♦❞♦ ❡❧❛①✲❛♥❞✲✜①✳ ❖% $❡%✉❧#❛❞♦% ❝♦♠♣✉#❛❝✐♦♥❛✐% ♠♦%#$❛$❛♠ 6✉❡ ♣❛$❛ ✉♠ ❝❛%♦ $❡❛❧ ❛ ❛❜♦$❞❛❣❡♠ ♣♦$ ❤♦$✐③♦♥#❡ $♦❧❛♥#❡ ✉#✐❧✐③❛♥❞♦ ❜✉%❝❛ ❧♦❝❛❧ ❢♦✐ ♠❛✐% ❡✜❝✐❡♥#❡✳
❈♦♠ ❜❛%❡ ♥♦ #$❛❜❛❧❤♦ ❞❡ ❆$❛✉❥♦ ❡# ❛❧✳ ✭✷✵✵✹✮✱ ❡♠ ❆$❛✉❥♦ ❡# ❛❧✳ ✭✷✵✵✽✮✱ ♦% ❛✉#♦$❡% ♣$♦♣✉%❡$❛♠ ✉♠❛ ♠❡❧❤♦$✐❛ ♣❛$❛ ♦ ♠7#♦❞♦ ❛♥#❡$✐♦$♠❡♥#❡ ♣$♦♣♦%#♦✳ ❋♦$❛♠ ❛♣$❡%❡♥#❛❞♦% 6✉❛#$♦ ♥♦✈♦% ♠7#♦❞♦% ♣❛$❛ ❛ $❡%♦❧✉)*♦ ❞♦ ♣$♦❜❧❡♠❛ ❡%#✉❞❛❞♦✿ ❘❡❧❛①✲❛♥❞✲✜① ❀ ❜✉%❝❛ ❧♦❝❛❧❀ ❉✐♠✐♥✐-❤✐♥❣ ♥❡✐❣❤❜♦✉ ❤♦♦❞ ❡ ❙✐♠✉❧❛4❡❞ ❛♥♥❡❛❧✐♥❣✳ ❖% #❡%#❡% ❝♦♠♣✉#❛❝✐♦♥❛✐% ♠♦%#$❛$❛♠ 6✉❡ ♣❛$❛ ❡①❡♠♣❧♦% ❣❡$❛❞♦% ❞❡ ❢♦$♠❛ $❛♥❞I♠✐❝❛✱ ♦ ♠7#♦❞♦ ❡❧❛①✲❛♥❞✲✜① ♦❜#❡✈❡ ♦% ♠❡❧❤♦$❡% $❡%✉❧#❛❞♦% ❡♠ $❡❧❛)*♦ J 6✉❛❧✐❞❛❞❡ ❞❛ %♦❧✉)*♦✱ ❡♥#$❡#❛♥#♦ ♦% ♦✉#$♦% #$K% ♠7#♦❞♦% ❢♦$❛♠ ♠❛✐% $L♣✐❞♦%✳ ❚❡%#❡% #❛♠❜7♠ ❢♦$❛♠ $❡❛❧✐③❛❞♦% ♣❛$❛ ✉♠❛ ❝❛$#❡✐$❛ $❡❛❧ ❞❡ ♣❡❞✐❞♦% ❡♠ 6✉❡ ♦% $❡%✉❧#❛❞♦% ❢♦$❛♠ %❡♠❡❧❤❛♥#❡%✳ ❆ %♦❧✉)*♦ ♦❜#✐❞❛ ♣❛$❛ ♦ ♣$♦❜❧❡♠❛ $❡❛❧ ❢♦✐ ❝♦♠♣❛$❛❞❛ ❝♦♠ ♦% $❡%✉❧#❛❞♦% $❡❛✐% ❡ ♦❜%❡$✈♦✉✲%❡ 6✉❡ ♦% ♠7#♦❞♦% ❝♦♠♣✉#❛❝✐♦♥❛✐% ❡$❛♠ ❝❛♣❛③❡% ❞❡ ❣❡$❛$ ♠❡❧❤♦$❡% %♦❧✉)O❡% ❡♠ ♠❡♥♦$ #❡♠♣♦ ❞❡ ♣$♦❝❡%%❛♠❡♥#♦✳
❊♠ ❚❡✐①❡✐$❛✳❏$✳ ❡# ❛❧✳ ✭✷✵✵✺✮✱ ❚❡✐①❡✐$❛✳❏$✳ ❡# ❛❧✳ ✭✷✵✵✻❛✮ ❡ ❚❡✐①❡✐$❛✳❏$✳ ❡# ❛❧✳ ✭✷✵✵✻❜✮ ❢♦$❛♠ ❡%#✉❞❛❞♦% ♠♦❞❡❧♦% ♣❛$❛ ❛ ♣$♦❣$❛♠❛)*♦ ❞❛ ♣$♦❞✉)*♦ ❡♠ ❢✉♥❞✐)O❡% ❞❡ ♠❡$❝❛❞♦✳ ❆ ♠♦#✐✈❛)*♦ ❞♦% #$❛❜❛❧❤♦% ❢♦✐ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦ ❛♠❜✐❡♥#❡ ♣$♦❞✉#✐✈♦ ❞❡%%❛% ❢✉♥❞✐)O❡%✱ ❛ 6✉❛❧ 7 ❞❡❝♦$$❡♥#❡ ❞♦% ♣$♦❝❡❞✐♠❡♥#♦% 6✉❡ %*♦ ❡♠♣$❡❣❛❞♦% ♣❛$❛ ❡❧❛❜♦$❛$ ❛ ♣$♦❣$❛♠❛)*♦ ❞❡ %✉❛ ♣$♦❞✉)*♦✳ ❖ ♠♦❞❡❧♦ ✈✐%❛ ♠❛①✐♠✐③❛$ ♦ ❧✉❝$♦ #❡♥❞♦ ❝♦♠♦ $❡%#$✐)O❡% ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❡♥❡$❣✐❛ ❞✐%♣♦♥T✈❡❧ ♣❛$❛ ♦♣❡$❛$ ♦% ❢♦$♥♦% ❡ %✉❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❢✉%*♦✳ ❖% ♠7#♦❞♦% #❡%#❛❞♦% ❢♦$❛♠ ♦% %❡❣✉✐♥#❡%✿ ❛♣❧✐❝❛)O❡% ❞❡ ❛❧❣♦$✐#♠♦% ❣❡♥7#✐❝♦% ♣❛$❛ ❛ ❡❧❛❜♦$❛)*♦ ❞❛ ♣$♦❣$❛♠❛)*♦ ❞❛ ♣$♦❞✉)*♦❀ ✉♠❛ ❤❡✉$T%#✐❝❛ ❜❛%❡❛❞❛ ❡♠ ❜✉%❝❛ ❡♠ L$✈♦$❡❀ ❡ ✉♠ ♠♦❞❡❧♦ ❞❡ ♣$♦❣$❛♠❛)*♦ ✐♥#❡✐$❛ ❜✐♥L$✐❛✳ ❖% ❛✉#♦$❡% ✉#✐❧✐③❛$❛♠ ♣❛$❛ ❛ ❛♥L❧✐%❡32❝❛%♦% ❡①♣❡$✐♠❡♥#❛✐%✳ ❖% $❡%✉❧#❛❞♦%
❛♣$❡%❡♥#❛$❛♠ %♦❧✉)O❡% ✈✐L✈❡✐% ♣❛$❛ 84% ❞♦% ❝❛%♦% ❝♦♠ #❡♠♣♦ ♠❡♥♦$ 6✉❡ ✉♠ ♠✐♥✉#♦✱ ❡
♣❛$❛ ♦% ♦✉#$♦% 16% ❞♦% ❝❛%♦% %♦❧✉)O❡% ✈✐L✈❡✐% ❢♦$❛♠ ♦❜#✐❞❛% ❛♥#❡% ❞♦% #$K% ♠✐♥✉#♦%✳ ❖%
$❡%✉❧#❛❞♦% ❡%#❛✈❛♠ ❡♠ ♠7❞✐❛ ❛ 10%❞❛ ❡%#✐♠❛#✐✈❛ ❞❛ %♦❧✉)*♦ U#✐♠❛✳
✽
♦❧✈❡% ♦ ❞♦✐ ♣%♦❜❧❡♠❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥.♦✳ ❊♠ ❋✐♥❦ ✭✷✵✵✼✮✱ ❢♦✐ ♣%♦♣♦ .♦ ✉♠ ♠;.♦❞♦ ❞❡ ♦❧✉<=♦ ❜❛ ❡❛❞♦ ❡♠ ♠;.♦❞♦ ❡❧❛①✲❛♥❞✲✜① ❡ ❜✉ ❝❛ ❧♦❝❛❧✳ ❖ %❡ ✉❧.❛❞♦ ❝♦♠♣✉.❛❝✐♦♥❛✐ ♠♦ .%❛%❛♠ @✉❡ ♦ ♠;.♦❞♦ ♦❜.❡✈❡ %❡ ✉❧.❛❞♦ ♣✐♦%❡ @✉❡ ♦ ♦❜.✐❞♦ ✉.✐❧✐③❛♥❞♦ ❞✐%❡.❛♠❡♥.❡ ♦ ♦❢.✇❛%❡ ❞❡ ♦.✐♠✐③❛<=♦ ❈D▲❊❳ ✈❡% =♦ 10.0✳ ❊♠ ❈❛♠❛%❣♦ ✭✷✵✵✾✮ ❝♦♠ ❜❛ ❡ ♥❛ ♣%♦♣♦ .❛
❞❡ ❞❡❝♦♠♣♦ ✐<=♦ ❞❡ ❚♦♥❛❦✐ ✭✷✵✵✻✮✱ ♦ ❛✉.♦% ♣%♦♣K ❞♦✐ ♠;.♦❞♦ ❡✈♦❧✉.✐✈♦ ♣❛%❛ %❡ ♦❧✈❡% ♦ ♣%♦❜❧❡♠❛✳ ◆♦ ♣%✐♠❡✐%♦✱ ❛ ❢✉♥<=♦ ❞❡ ❛✈❛❧✐❛<=♦ ❞♦ ❛❧❣♦%✐.♠♦ ❣❡♥;.✐❝♦ ✉.✐❧✐③❛ ❛ ❤❡✉%N .✐❝❛ ❧❛❣%❛♥❣✐❛♥❛ ❞❡ ❚♦♥❛❦✐ ✭✷✵✵✻✮ ♣❛%❛ ❞❡✜♥✐% ❛ ♣%♦❞✉<=♦ ❞♦ ✐.❡♥ ✳ ◆❛ ❡❣✉♥❞❛ ♣%♦♣♦ .❛✱ ♦ ❛✉.♦% ✉.✐❧✐③❛ ♦ ♠;.♦❞♦ ❞❛ ♠♦❝❤✐❧❛ ❝♦♠♦ ❢✉♥<=♦ ❛✈❛❧✐❛<=♦✳ ❖ %❡ ✉❧.❛❞♦ ♠♦ .%❛%❛♠ @✉❡ ❛ ❡❣✉♥❞❛ ♣%♦♣♦ .❛ ; ❛ ♠❛✐ ❡✜❝✐❡♥.❡ ✭❈❆▼❆❘●❖ ❡' ❛❧✳✱ ✷✵✶✷✮✳
✾
✸ ❖ "#♦❜❧❡♠❛ ❞❡ "❧❛♥❡❥❛♠❡♥-♦ ❞❛
"#♦❞✉/0♦ ❞❡ "❡❞✐❞♦2 ✭
4
P
✮
❖ ♣"♦❜❧❡♠❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥,♦ ❞❛ ♣"♦❞✉./♦ ❞❡ ♣❡❞✐❞♦1 ✭43✮ ❡1,✉❞❛❞♦ ❢♦✐ ✐♥1♣✐"❛❞♦
♥✉♠❛ ❢✉♥❞✐./♦ ❞❡ ♣❡6✉❡♥♦ ♣♦",❡ ✭❢✉♥❞✐./♦ ❞❡ ♠❡"❝❛❞♦✮ ❞♦ ✐♥,❡"✐♦" ❞♦ ❡1,❛❞♦ ❞❡ ❙/♦ 3❛✉❧♦✳ ❆,✉❛❧♠❡♥,❡✱ ❡1,❛ ❢✉♥❞✐./♦ ♣♦11✉✐ ❛♣❡♥❛1 ✉♠ ❢♦"♥♦ ❝♦♠ ❝❛♣❛❝✐❞❛❞❡ ❧✐♠✐,❛❞❛ ❛
360 6✉✐❧♦1✱ ♦✉ 1❡❥❛✱ ❛ 6✉❛♥,✐❞❛❞❡ ♠<①✐♠❛ ❞❡ ❧✐❣❛ 6✉❡ ♣♦❞❡ 1❡" ♣"♦❞✉③✐❞❛ ♣♦" ✈❡③ A 360
6✉✐❧♦1✳ ❉✉"❛♥,❡ ✉♠ ❞✐❛ ♦ ❢♦"♥♦ ♣♦❞❡ 1❡" ✉,✐❧✐③❛❞♦ ❛,A ❞❡③ ✈❡③❡1✱ ❞❡✈❡♥❞♦ 1❡" ❧✐❣❛❞♦ 1❡♠♣"❡ ❛♥,❡1 ❞♦ ✐♥C❝✐♦ ❞♦ ❞✐❛ ❞❡ ,"❛❜❛❧❤♦✱ ♣♦✐1 1✉❛ ♣"✐♠❡✐"❛ ❝❛"❣❛ ,❡♠ ,❡♠♣♦ ❞❡ ♣"❡♣❛"♦ ♠❛✐1 ❞❡♠♦"❛❞♦✱ ❞❡✈✐❞♦ E ♥❡❝❡11✐❞❛❞❡ ❞❡ ❛6✉❡❝✐♠❡♥,♦ ♣❛"❛ ❛,✐♥❣✐" ❛ ,❡♠♣❡"❛,✉"❛ ✐❞❡❛❧ ♣❛"❛ ❢✉1/♦✳
❆♣F1 ❛ ❧✐❣❛ 1❡" ❢✉♥❞✐❞❛✱ ♦1 ♠♦❧❞❡1 1/♦ ✈❛③❛❞♦1 ❡ ❛1 1♦❜"❛1 1/♦ ❞❡1❝❛",❛❞❛1 ❛,"❛✈A1 ❞❛ ❢✉1/♦ ❞❡ ❧✐♥❣♦,❡1✱ ♦1 6✉❛✐1 1/♦ "❡✉,✐❧✐③❛❞♦1 ❝♦♠♦ ♠❛,A"✐❛1✲♣"✐♠❛1 ♣❛"❛ ❛ ♣"♦❞✉./♦ ❞❡ ♥♦✈❛1 ❧✐❣❛1✳ ❊♠❜♦"❛ ♣♦11❛♠ 1❡" "❡❛♣"♦✈❡✐,❛❞♦1✱ ❛ ♣"♦❞✉./♦ ❞❡ ❧✐♥❣♦,❡1 ❛❝❛""❡,❛ ❞❡1♣❡"❞C❝✐♦ ❞❛ ❡♥❡"❣✐❛ ❡❧A,"✐❝❛ ❝♦♥1✉♠✐❞❛ ♥❛ ❢✉1/♦ ❞❛ ❧✐❣❛✳ ▼✉✐,❛1 ✈❡③❡1 ❡1,❛ ♣"♦❞✉./♦ A ♥❡❝❡11<"✐❛✱ ✉♠❛ ✈❡③ 6✉❡ ♦ ❢♦"♥♦ ♣"❡❝✐1❛ 1❡" ♣"❡❡♥❝❤✐❞♦ ♣♦" ✉♠❛ 6✉❛♥,✐❞❛❞❡ ♠C♥✐♠❛ ❞❡ ❧✐❣❛ ♣❛"❛ ❡✈✐,❛" 1❡✉ ❞❡1❣❛1,❡✳ ▲♦❣♦✱ ✉♠ ❜♦♠ ♣❧❛♥❡❥❛♠❡♥,♦ ❞❡ ♣"♦❞✉./♦ ❞❡✈❡ ,❡" ♦ ❝♦♠♣"♦♠✐11♦ ❞❡ ❡✈✐,❛" ♦ ❞❡1♣❡"❞C❝✐♦ ❞❡ ❧✐❣❛ ❡ ♥/♦ ♣❡"♠✐,✐" 6✉❡ ♦❝♦""❛ ❝♦♠ ♠✉✐,❛ ❢"❡6✉K♥❝✐❛ ❛ 1✉❜✉,✐❧✐③❛./♦ ❞♦ ❢♦"♥♦✳
❊1,❛ ❢✉♥❞✐./♦ ♦♣❡"❛ ♥♦ 1✐1,❡♠❛ ✏♠❛❦❡ %♦ ♦'❞❡'✑✱ ♦✉ 1❡❥❛✱ ❢❛❜"✐❝❛ ♦1 ♣"♦❞✉,♦1 1♦❜ ❡♥❝♦♠❡♥❞❛✳ ❖ ❝♦♥❥✉♥,♦ ❞❡ ❝❧✐❡♥,❡1 A ❡①,❡♥1♦ ❡ ❛ ❝❛",❡✐"❛ ❞❡ ♣❡❞✐❞♦1 ,❡♠ ❛❧❣✉♠❛1 ❝❛"❛❝✲ ,❡"C1,✐❝❛1 ♣❛",✐❝✉❧❛"❡1✱ ,❛✐1 ❝♦♠♦ ❣"❛♥❞❡ ✈❛"✐❡❞❛❞❡ ❞❡ ✐,❡♥1 ✭,❛♠❛♥❤♦1✱ ♣❡1♦1✱ 6✉❛♥,✐❞❛❞❡1✮ ❡ ❣"❛♥❞❡ ❞✐✈❡"1✐❞❛❞❡ ❞❡ ❧✐❣❛1 ❛ 1❡"❡♠ ❢✉♥❞✐❞❛1✳
✶✵
✐!❡♥$ %✉❡ ❝♦♠♣+❡♠ ✉♠ ♠❡$♠♦ ♣❡❞✐❞♦✱ ♦$ %✉❛✐$ $/♦ ❞❡ !❛♠❛♥❤♦$ ❞✐❢❡2❡♥!❡$ ❡ ♣♦❞❡♠ $❡2 !❛♠❜4♠ ❞❡ ❧✐❣❛$ ❞✐❢❡2❡♥!❡$✳
❋✐❣✉2❛ ✸✿ ■!❡♥$ %✉❡ ❝♦♠♣+❡♠ ✉♠ ♠❡$♠♦ ♣❡❞✐❞♦✳
❊♥!2❡❣❛2 ✉♠ ♣❡❞✐❞♦ ♣❛2❝✐❛❧♠❡♥!❡ ♣♦❞❡ !❛♠❜4♠ $❡2 ✐♥❝♦❡2❡♥!❡ $❡ ♦$ ✐!❡♥$ %✉❡ ♦ ❝♦♠✲ ♣+❡ ❢♦2❡♠ ♣❛2!❡$ ❞❡ ✉♠ ♠❡$♠♦ ♣2♦❞✉!♦✱ ❝♦♠♦ ♣♦2 ❡①❡♠♣❧♦✱ ❛ ❜♦♠❜❛ ❞❡ ?❣✉❛ ✐❧✉$!2❛❞❛ ♥❛ ❋✐❣✉2❛ ✹✱ ❡♥!/♦ ♣❛2❛ ❡$!❡ ❝❧✐❡♥!❡ ❡$♣❡❝A✜❝♦ ♥/♦ 4 ✐♥!❡2❡$$❛♥!❡ %✉❡ ❛♣❡♥❛$ ❛❧❣✉♥$ ✐!❡♥$ $❡❥❛♠ ❡♥!2❡❣✉❡$ ❡ ♦✉!2♦$ ♥/♦✱ ♣♦✐$ ♣❛2❛ ♣2♦❞✉③✐2 ❛ ❜♦♠❜❛ ❞❡ ?❣✉❛ 4 ♥❡❝❡$$?2✐❛ ❛ ❡♥!2❡❣❛ ❞❡ !♦❞♦$ ♦$ $❡✉$ ✐!❡♥$✳
❋✐❣✉2❛ ✹✿ ■!❡♥$ %✉❡ ❝♦♠♣+❡♠ ✉♠ ♠❡$♠♦ ♣2♦❞✉!♦✳
E♦2!❛♥!♦✱ ♠❡$♠♦ $❡ ♦$ ✐!❡♥$ %✉❡ ❝♦♠♣+❡♠ ✉♠ ♠❡$♠♦ ♣❡❞✐❞♦ ♥/♦ ❢♦2❡♠ ♣❛2!❡$ ❞❡ ✉♠ ♠❡$♠♦ ♣2♦❞✉!♦ ✭❝♦♠♦ ❛ ❜♦♠❜❛ ❞❛ ?❣✉❛ ✐❧✉$!2❛❞❛ ❛❝✐♠❛✮✱ ❝✉$!♦$ ❛❞✐❝✐♦♥❛✐$ ♣♦❞❡♠ $❡2 ❛❝❛22❡!❛❞♦$ $❡ ♦ ♣❡❞✐❞♦ ❢♦2 ❡♥!2❡❣✉❡ ♣❛2❝✐❛❧♠❡♥!❡✱ ❝♦♠♦ ♣♦2 ❡①❡♠♣❧♦✱ ❝✉$!♦$ ❝♦♠ ❡①♣❡❞✐H/♦✳ ❊$!❛$ %✉❡$!+❡$ ♥♦$ ♠♦!✐✈❛2❛♠ ❛ !2❛❜❛❧❤❛2 ❝♦♠ ♦ ♣❧❛♥❡❥❛♠❡♥!♦ ❞❛ ♣2♦❞✉H/♦ ❞❡ ♣❡❞✐❞♦$✱ %✉❡ ✈✐$❛ 2❡❞✉③✐2 ♦$ ❝✉$!♦$ ❡ ❛!❡♥❞❡2 ❝♦♠♣❧❡!❛♠❡♥!❡ ♦$ ❝❧✐❡♥!❡$✳
✶✶
❊♠ "❡$✉♠♦✱ ♦ ♦❜❥❡*✐✈♦ ❞❛ ❡♠♣"❡$❛ 0 ❡♥❝♦♥*"❛" ✉♠ ♣❧❛♥♦ ❞❡ ♣"♦❞✉45♦ 6✉❡ ♠✐♥✐♠✐③❡ ♦$ ❝✉$*♦$ ❛$$♦❝✐❛❞♦$ 8 ♣"♦❞✉45♦✱ ❛♦ ❡$*♦6✉❡ ❡ ❛♦ ❛*"❛$♦ ♣❛"❛ ❛*❡♥❞❡" ❛♦$ ♣❡❞✐❞♦$✱ "❡$♣❡✐*❛♥❞♦ ❛$ "❡$*"✐49❡$ ❞♦ ❛♠❜✐❡♥*❡ ❞❡ ♣"♦❞✉45♦✳
❉✐❛♥*❡ ❞❡$$❛$ ❝❛"❛❝*❡"<$*✐❝❛$✱ ♥♦$$♦ ♣"♦❜❧❡♠❛ ♣♦❞❡ $❡" ♠♦❞❡❧❛❞♦ ❝♦♠♦ ✉♠ ♣"♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥$✐♦♥❛♠❡♥*♦ ❞❡ ❧♦*❡$ 6✉❡ ❝♦♥$✐$*❡ ❡♠ ❞❡*❡"♠✐♥❛" 6✉❛♥*♦ ♣"♦❞✉③✐" ❞❡ ❝❛❞❛ ♣"♦❞✉*♦✱ ❡♠ ❝❛❞❛ ♣❡"<♦❞♦ ❞❡ ✉♠ ❤♦"✐③♦♥*❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥*♦ ✜♥✐*♦✳ ◆♦$$♦ ♦❜❥❡*✐✈♦ 0 ♠✐♥✐♠✐③❛" ♦$ ❛*"❛$♦$ ❡♠ ❛*❡♥❞❡" ♦$ ♣❡❞✐❞♦$ ❞♦$ ❝❧✐❡♥*❡$✳
❈♦♠♦ ♣"♦♣♦$*♦ ❡♠ ❱❡"❣✐♥❡ ✭✷✵✵✾✮✱ ♦ ♣"♦❜❧❡♠❛ 0 ♠♦❞❡❧❛❞♦ ❝♦♠♦ ✉♠ ♣"♦❜❧❡♠❛ ❞❡ ❞✐♠❡♥$✐♦♥❛♠❡♥*♦ ❞❡ ❧♦*❡$ ♠✉❧*✐❡$*H❣✐♦ ❡♠ 6✉❡ ❝❛❞❛ ♣❡❞✐❞♦ 0 ❝♦♥$✐❞❡"❛❞♦ ❝♦♠♦ ✉♠ ✐*❡♠ ✜♥❛❧✱ ❡♥6✉❛♥*♦ ♦$ ✐*❡♥$ 6✉❡ ♦ ❝♦♠♣9❡ $5♦ "❡♣"❡$❡♥*❛❞♦$ ♣♦" ✐*❡♥$ ❝♦♠♣♦♥❡♥*❡$✳ ❈❛❞❛ ♣❡❞✐❞♦ ♣♦❞❡ $❡" ❝♦♠♣♦$*♦ ♣♦" ✈H"✐♦$ ✐*❡♥$ 6✉❡ ♣♦❞❡♠ ♦✉ ♥5♦ *❡" ❞❡♣❡♥❞I♥❝✐❛ ❡♥*"❡ $✐ ❡ 6✉❡ *❛♠❜0♠ ♣♦❞❡♠ ♦✉ ♥5♦ ❢❛③❡" ♣❛"*❡ ❞❡ ✉♠ ♠❡$♠♦ ♣"♦❞✉*♦ ✜♥❛❧✱ ❧♦❣♦ ♥✉♠ ♠❡$♠♦ ♣❡❞✐❞♦✱ ♣♦❞❡♠♦$ *❡" ✈H"✐♦$ ♣"♦❞✉*♦$ ✜♥❛✐$ ❝♦♠♣♦$*♦$ ♣♦" ✐*❡♥$ ❝♦♠♣♦♥❡♥*❡$✳ K♦" ❡①❡♠♣❧♦✱ ✈❛♠♦$ $✉♣♦" 6✉❡ ✉♠❛ ❝❛"*❡✐"❛ ❞❡ ♣❡❞✐❞♦$ 0 ❝♦♠♣♦$*❛ ♣❡❧♦$ ♣❡❞✐❞♦$ ❞❛ ❋✐❣✉"❛ ✺✳ ❊$*❛ ❝❛"*❡✐"❛ ♣♦❞❡ $❡" "❡♣"❡$❡♥*❛❞❛ ♣❡❧❛ ❡$*"✉*✉"❛ ❞❡ ♣"♦❞✉*♦ ❞❛ ❋✐❣✉"❛ ✻✱ ❡♠ 6✉❡ ♦$ ♣❡❞✐❞♦$ $5♦ ✐♥❞❡①❛❞♦$ ♣♦" ❧❡*"❛$ ❡ ♦$ ✐*❡♥$ ❝♦♠♣♦♥❡♥*❡$ ♣♦" ♥P♠❡"♦$ ✐♥*❡✐"♦$✳ K❛"❛ "❡♣"❡$❡♥*❛" ❛ 6✉❛♥*✐❞❛❞❡ ❞♦ ✐*❡♠ ❝♦♠♣♦♥❡♥*❡ j♥♦ ♣❡❞✐❞♦ i✉*✐❧✐③❛♠♦$ ♦ ♣❛"Q♠❡*"♦ aji✱ ❝♦♠♦ ✐❧✉$*"❛❞♦ ♥♦$ ❛"❝♦$ ❞❛ ❋✐❣✉"❛ ✻✳ K❛"❛ ♦ ❡①❡♠♣❧♦✱ *❡♠♦$ 6✉❡ a1A = 2✱ a2A = 4✱ a41 = 1✱ a51 = 2✱ a2B = 3✱ ❡ ♣♦" ✜♠✱ a3B = 1✳
❋✐❣✉"❛ ✺✿ ❈❛"*❡✐"❛ ❞❡ K❡❞✐❞♦$✳
✸✳✶ ▼♦❞❡❧♦ ()♦♣♦+,♦ ♣❛)❛ ♦
4
P
✶✷
❋✐❣✉$❛ ✻✿ ❉❡♣❡♥❞-♥❝✐❛ ❡♥/$❡ ♦1 ✐/❡♥1 ❞❡ ✉♠ ♣❡❞✐❞♦✳
❧✐❣❛1✳ ◆❡1/❡ /$❛❜❛❧❤♦✱ ❝❛❞❛ ❢✉1:♦ ❞♦ ❢♦$♥♦ ; ❝❤❛♠❛❞❛ ❞❡ ❢♦$♥❛❞❛✳
<❛$❛ $❡♣$❡1❡♥/❛$ ❛1 ❢♦$♥❛❞❛1 ❆$❛✉❥♦ ✭✷✵✵✸✮ ♣$♦♣D1 1✉❜❞✐✈✐❞✐$ ✉♠ ♣❡$F♦❞♦ ❡♠ 1✉❜♣❡$F♦✲ ❞♦1✱ ✉♠ ♣❛$❛ ❝❛❞❛ ❢♦$♥❛❞❛✳ <♦$ ❡①❡♠♣❧♦✱ ❝♦♥1✐❞❡$❡♠♦1 ✉♠ ❤♦$✐③♦♥/❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥/♦ ❝♦♠ ❞♦✐1 ❞✐❛1 ❡ J✉❡ ❡♠ ❝❛❞❛ ❞✐❛ ♣♦❞❡♠♦1 ❢✉♥❞✐$ ❞❡③ ❢♦$♥❛❞❛1✱ ❞❡1/❛ ❢♦$♠❛ /❡$F❛♠♦1 ❞♦✐1 ♣❡$F♦❞♦1 ❝♦♠ ❞❡③ 1✉❜♣❡$F♦❞♦1 ❝❛❞❛ ✉♠✱ ❝♦♠♦ ✐❧✉1/$❛ ❛ ❋✐❣✉$❛ ✼✳
❋✐❣✉$❛ ✼✿ ◗✉❛♥/✐❞❛❞❡ ❞❡ ♣❡$F♦❞♦1 ❡ 1✉❜♣❡$F♦❞♦1✳
❈♦♠♦ ♣$♦♣♦1/♦ ❡♠ ❆$❛✉❥♦ ✭✷✵✵✸✮✱ ♣❛$❛ $❡♣$❡1❡♥/❛$ ♦1 ♣❡$F♦❞♦1 ❡ ♦1 1✉❜♣❡$F♦❞♦1 ♥♦ ♠♦❞❡❧♦✱ ❢♦$❛♠ ✉/✐❧✐③❛❞♦1 ♦1 F♥❞✐❝❡1 t ❡ η✱ $❡1♣❡❝/✐✈❛♠❡♥/❡✳ ❖ F♥❞✐❝❡ t ✈❛$✐❛ ❞❡ 1 ❛/;
♦ ♥O♠❡$♦ ❞❡ ♣❡$F♦❞♦1 ❞♦ ❤♦$✐③♦♥/❡✱ ❝❤❛♠❛❞♦ ❞❡ T✳ ❊♥J✉❛♥/♦ η ✈❛$✐❛ ❞❡ 1 ❛ LT✱ ❡♠ J✉❡ ♦ ♣❛$Q♠❡/$♦ LT $❡♣$❡1❡♥/❛ ❛ O❧/✐♠❛ ❢♦$♥❛❞❛ ♥♦ O❧/✐♠♦ ♣❡$F♦❞♦✳ <❛$❛ ❢❛❝✐❧✐/❛$ ❛ ♠♦❞❡❧❛❣❡♠✱ 1:♦ ❞❡✜♥✐❞♦1 ♣❛$❛ ♦1 1✉❜♣❡$F♦❞♦1 ❞♦✐1 F♥❞✐❝❡1 ❛✉①✐❧✐❛$❡1 Ft ❡Lt J✉❡ ✐♥❞✐❝❛♠✱ $❡1♣❡❝/✐✈❛♠❡♥/❡✱ ♦ ♣$✐♠❡✐$♦ ❡ ♦ O❧/✐♠♦ 1✉❜♣❡$F♦❞♦ ❞♦ ♣❡$F♦❞♦ t✳ ❆ ❋✐❣✉$❛ ✽ ✐❧✉1/$❛ ♦
♠♦❞♦ ❝♦♠♦ ♦1 F♥❞✐❝❡1 ❡1/:♦ ❞✐1♣♦1/♦1 ♥♦ ❝♦♠❡T♦ ❡ ✜♥❛❧ ❞❡ ❝❛❞❛ ♣❡$F♦❞♦✳ <❛$❛ ♦ ❡①❡♠♣❧♦ ❛♥/❡$✐♦$✱ L1= 10 ❡ L2= 20✳
✶✸
❋✐❣✉$❛ ✽✿ ❮♥❞✐❝❡- ♣❛$❛ ♦ ✐♥0❝✐♦ ❡ ♦ ✜♥❛❧ ❞❡ ❝❛❞❛ ♣❡$0♦❞♦✳
❛♦ ✜♥❛❧ ❞♦ ♣❡$0♦❞♦ t ❡ 0❝❛-♦ ❝♦♥4$5$✐♦✳
❋✐❣✉$❛ ✾✿ ❉❡♠❛♥❞❛- ❛4❡♥❞✐❞❛- ❛♦ ✜♥❛❧ ❞❡ ❝❛❞❛ ♣❡$0♦❞♦✳
❆- ✈❛$✐5✈❡✐- ✉4✐❧✐③❛❞❛- ♣❛$❛ $❡♣$❡-❡♥4❛$ ❛ ♣$♦❞✉<=♦✱ ♦ ❡-4♦?✉❡ ❡ ♦ ❛4$❛-♦ ❞♦- ♣❡❞✐❞♦-✭✐4❡♥- ✜♥❛✐-✮ -=♦✿
XPit=
(
1,-❡ ♦ ♣❡❞✐❞♦ i B ❝♦♥❝❧✉0❞♦ ♥♦ ♣❡$0♦❞♦ t; 0,❝❛-♦ ❝♦♥4$5$✐♦✳
IPit+=
(
1,-❡ ♦ ♣❡❞✐❞♦ i B ❡-4♦❝❛❞♦ ♥♦ ✜♥❛❧ ❞♦ ♣❡$0♦❞♦ t ♣❛$❛ ♦ ♣❡$0♦❞♦ t+ 1; 0,❝❛-♦ ❝♦♥4$5$✐♦✳
IP−
it =
(
1,-❡ ♦ ♣❡❞✐❞♦ i B ❛4$❛-❛❞♦ ♥♦ ♣❡$0♦❞♦ t; 0,❝❛-♦ ❝♦♥4$5$✐♦✳
❆ ❡?✉❛<=♦ ?✉❡ ❞❡-❝$❡✈❡ ♦ ❜❛❧❛♥<♦ ❞❡ ❡-4♦?✉❡ ❞♦- ♣❡❞✐❞♦- B ❞❛❞❛ ♣♦$✿
IPi,t+−1−IP
−
i,t−1+XPit =dit+IPit+−IP
−
it
❝♦♠ i= 1, ..., N P ✭❡♠ ?✉❡ N P $❡♣$❡-❡♥4❛ ♦ ♥D♠❡$♦ 4♦4❛❧ ❞❡ ♣❡❞✐❞♦-✮ ❡ t= 1, ..., T✱ ?✉❡
♣♦❞❡ -❡$ ✐❧✉-4$❛❞❛ ❝♦♠♦ ♠♦-4$❛♠♦- ♥❛ ❋✐❣✉$❛ ✶✵✳
✶✹
❋✐❣✉$❛ ✶✵✿ ❘❡♣$❡,❡♥.❛/0♦ ❞♦ ❜❛❧❛♥/♦ ❞❡ ❡,.♦5✉❡ ♣❛$❛ ♦ ♣❡❞✐❞♦ i♥♦ ♣❡$6♦❞♦ t✳
❞♦, ,✉❜♣❡$6♦❞♦,η✳ ◆♦ ❡♥.❛♥.♦✱ ,✉❛ ❞❡♠❛♥❞❛ ♦❝♦$$❡ ❛♣❡♥❛, ♥♦ <❧.✐♠♦ ,✉❜♣❡$6♦❞♦ ❞❡ ❝❛❞❛
♣❡$6♦❞♦✱ ♦✉ ,❡❥❛✱ 5✉❛♥❞♦ η=Lt✱ ❝♦♠♦ ✐❧✉,.$❛ ❛ ❋✐❣✉$❛ ✶✶✳ ❖ ♣❛$?♠❡.$♦ aji$❡♣$❡,❡♥.❛ ❛ 5✉❛♥.✐❞❛❞❡ ❞❡♠❛♥❞❛❞❛ ❞♦ ✐.❡♠ j ♥♦ ♣❡❞✐❞♦ i❡ ♦ ❝♦♥❥✉♥.♦ S(i) $❡♣$❡,❡♥.❛ ♦, ✐.❡♥, 5✉❡
♣❡$.❡♥❝❡♠ ❛♦ ♣❡❞✐❞♦ i✳
❋✐❣✉$❛ ✶✶✿ ❘❡♣$❡,❡♥.❛/0♦ ❞❛ ❞❡♠❛♥❞❛ ♣❛$❛ ♦, ✐.❡♥, ❝♦♠♣♦♥❡♥.❡,✳
▲♦❣♦✱ ♣❛$❛ ♦, ✐.❡♥, ❝♦♠♣♦♥❡♥.❡,✱ ❛ ❡5✉❛/0♦ ❞❡ ❜❛❧❛♥/♦ ❞❡ ❡,.♦5✉❡ A ❞❛❞❛ ♣♦$✿
Ij,t+−1+
Lt
X
η=Ft
Xjη =Ijt++ N P
X
i=1
j∈S(i)
ajiXPit
❡♠ 5✉❡Xjη ❡Ijt+,0♦✱ $❡,♣❡❝.✐✈❛♠❡♥.❡✱ ❛ 5✉❛♥.✐❞❛❞❡ ♣$♦❞✉③✐❞❛ ❞♦ ✐.❡♠ j♥♦ ,✉❜♣❡$6♦❞♦η ❡ ❛ 5✉❛♥.✐❞❛❞❡ ❡,.♦❝❛❞❛ ❞♦ ✐.❡♠j ♥♦ ♣❡$6♦❞♦t✳ ◆♦.❡ 5✉❡ ♦ ❛.$❛,♦ ❞♦, ✐.❡♥, ❝♦♠♣♦♥❡♥.❡,
♥0♦ A ♣❡$♠✐.✐❞♦ ❡①♣❧✐❝✐.❛♠❡♥.❡✱ ✉♠❛ ✈❡③ 5✉❡ A ❝♦♥,✐❞❡$❛❞♦ ♥♦ ❛.❡♥❞✐♠❡♥.♦ ❞♦ ♣❡❞✐❞♦✱ ✈✐,.♦ 5✉❡ ❛.$❛,❛$ ❛ ♣$♦❞✉/0♦ ❞❡ ✉♠ ✐.❡♠ ❝♦♠♣♦♥❡♥.❡ ✐♠♣❧✐❝❛ ❡♠ ❛.$❛,❛$ ♦ ♣❡❞✐❞♦ .♦❞♦✳
✶✺
◆♦""♦ ♦❜❥❡&✐✈♦ ) ♠✐♥✐♠✐③❛. ♦" ❝✉"&♦" ❞❡ ♣.♦❞✉34♦ ❞♦" ♣❡❞✐❞♦" 5✉❡ ❡♥✈♦❧✈❡♠ ❝✉"&♦" ❞❡ ♣.❡♣❛.❛34♦ ❞❡ ❧✐❣❛" ♣❛.❛ ♣.♦❞✉34♦✱ ❞❡ ❡"&♦5✉❡ ❡ ❞❡ ❛&.❛"♦ ♣❛.❛ ❛&❡♥❞❡. ♦" ♣❡❞✐❞♦"✳ ❖" ❝✉"&♦" ❞❡ ♣.❡♣❛.❛34♦ ♣❛.❛ ♣.♦❞✉34♦ ❞❡ ❧✐❣❛" "4♦ ❝♦♠♣✉&❛❞♦" ❛♣❡♥❛" 5✉❛♥❞♦ ❤< ❛ &.♦❝❛ ❞❡ ♣.♦❞✉34♦ ❡♥&.❡ ❛" ❧✐❣❛"✱ ♦✉ "❡❥❛✱ "❡ ❡"&<✈❛♠♦" ♣.♦❞✉③✐♥❞♦ ❛ ❧✐❣❛ k ❡ ♣❛""❛♠♦" ❛ ♣.♦❞✉③✐.
❛ ❧✐❣❛ k′
✳ ❆ &.♦❝❛ ❞❡ ♣.♦❞✉34♦ ) .❡♣.❡"❡♥&❛❞❛ ♥♦ ♠♦❞❡❧♦ ♣❡❧❛ ✈❛.✐<✈❡❧ Zk
η 5✉❡ ❛""✉♠❡ ♦ ✈❛❧♦. 1 "❡ ❛ ♣.♦❞✉34♦ ❞❛ ❧✐❣❛ k ♥4♦ ♦❝♦..❡✉ ♥♦ "✉❜♣❡.>♦❞♦ η−1 ❡ ♦❝♦..❡ ♥♦ "✉❜♣❡.>♦❞♦
η✳ ❊"&❛ "✐&✉❛34♦ ) ✐♠♣♦"&❛ ♣❡❧❛ .❡"&.✐34♦✿
Zk η ≥Y
k η −Y
k η−1
❡♠ 5✉❡ ❛ ✈❛.✐<✈❡❧Yk
η ) ✐❣✉❛❧ ❛1"❡ ❛ ❧✐❣❛k) ♣.♦❞✉③✐❞❛ ♥♦ "✉❜♣❡.>♦❞♦η❡0✱ ❝❛"♦ ❝♦♥&.<.✐♦✳ ❖" ❝✉"&♦" ❞❡ ❡"&♦5✉❡ ❡"&4♦ ❛""♦❝✐❛❞♦" ❛♦" ✐&❡♥" ❝♦♠♣♦♥❡♥&❡" ❡ ❛♦" ♣❡❞✐❞♦" ❝♦♠♣❧❡&♦"✳ ❈♦♠♦ ✉♠ ♣❡❞✐❞♦ ) ❝♦♠♣♦"&♦ ❞❡ ✐&❡♥" ❝♦♠♣♦♥❡♥&❡"✱ "❡♠ ♣❡.❞❛ ❞❡ ❣❡♥❡.❛❧✐❞❛❞❡✱ ♦♣&❛♠♦" ♣♦. ❝♦♥&❛❜✐❧✐③❛. ♦" ❝✉"&♦" ❞♦" ♣❡❞✐❞♦" ✐♠♣❧✐❝✐&❛♠❡♥&❡✱ ❝♦♠♣✉&❛♥❞♦ ❛♣❡♥❛" ♦" ❝✉"&♦" ❞❡ &♦❞♦" ♦" ✐&❡♥" ❝♦♠♣♦♥❡♥&❡" ✭"❡♠❡❧❤❛♥&❡ ❛ ♣♦❧>&✐❝❛ ❞❡ ❡"&♦5✉❡ ❞❡ ❡"❝❛❧4♦✮✳ ◆♦ ❡♥&❛♥&♦✱ ♦" ❛&.❛"♦" "D &❡♠ "✐❣♥✐✜❝❛❞♦ ♣❛.❛ ♦" ♣❡❞✐❞♦" ❝♦♠♣❧❡&♦"✱ ❧♦❣♦✱ ❛ ❢✉♥34♦ ♦❜❥❡&✐✈♦ ❞♦ ♣.♦❜❧❡♠❛ ) ❞❡"❝.✐&❛ ♣♦.✿
▼✐♥ K X k=1 LT X η=1
skηZkη+ T X t=1 N P X i=1 HP− itIP − it + T−1
X
t=1
N
X
j=1 Hjt+I
+
jt− N
X
j=1 HjT+I
+
jT
❡♠ 5✉❡✿ skt ) ♦ ❝✉"&♦ ❞❡ &.♦❝❛ ♣❛.❛ ❛ ♣.♦❞✉34♦ ❞❛ ❧✐❣❛ k ♥♦ ♣❡.>♦❞♦t❀HP
−
it ) ♦ ❝✉"&♦ ❞❡ ❛&.❛"♦ ♣♦. ♥4♦ ❛&❡♥❞❡. ♦ ♣❡❞✐❞♦ i♥♦ ✜♥❛❧ ❞♦ ♣❡.>♦❞♦ t❀Hjt+ ) ♦ ❝✉"&♦ ❞❡ ❡"&♦5✉❡ ❞♦ ✐&❡♠
j ♥♦ ✜♥❛❧ ❞♦ ♣❡.>♦❞♦ t.
❆ ✜♠ ❞❡ ✐♥❝❡♥&✐✈❛. ❛ ♣.♦❞✉34♦ ❞❡ ✐&❡♥" ❝♦♠♣♦♥❡♥&❡" ♣❛.❛ ♣.♦❞✉③✐. ♣❛.❝✐❛❧♠❡♥&❡ ♣❡❞✐❞♦" ♥4♦ ❝♦♠♣❧❡&❛❞♦" ❛&) ♦ ✜♥❛❧ ❞♦ ❤♦.✐③♦♥&❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥&♦✱ ♦ ❝✉"&♦ ❞❡ ❡"&♦5✉❡ ❞❡"&❡" ✐&❡♥" ) ❛❜❛&✐❞♦ ❞♦ ❝✉"&♦ &♦&❛❧ ♥♦ I❧&✐♠♦ ♣❡.>♦❞♦✱ ❝♦♠♦ ❞❡"❝.✐&♦ ♥❛ I❧&✐♠❛ ♣❛.❝❡❧❛ ❞❛ ❢✉♥34♦ ♦❜❥❡&✐✈♦✳
❖ ♠♦❞❡❧♦ ❝♦♠♣❧❡&♦ ♣.♦♣♦"&♦ ♣❛.❛ .❡♣.❡"❡♥&❛. ♦ ♣.♦❜❧❡♠❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥&♦ ❞❡ ♣.♦✲ ❞✉34♦ ❞❡ ♣❡❞✐❞♦" ✭4K✮ ) ❞❛❞♦ ♣♦.✿
▼✐♥ K X k=1 LT X η=1
skηZkη+ T X t=1 N P X i=1 HP− itIP − it + T−1
X t=1 N X j=1 H+
✶✻
✳❛✳✿
Ij,t+−1+
Lt
X
η=Ft
Xjη =Ijt++ N P
X
i=1
j∈S(i)
ajiXPit j ∈ N;t∈ T; ✭✸✳✷✮
IPi,t+−1−IP
−
i,t−1+XPit=dit+IPit+−IP
−
it i∈ I;t∈ T; ✭✸✳✸✮
X
j∈L(k)
(ρjXjη) ≤❈❛♣Yηk η∈ L;k∈ K; ✭✸✳✹✮
K
X
k=1
Yηk ≤1 η∈ L; ✭✸✳✺✮
LT
X
η=F1
Xj,η ≤ N P
X
i=1
aji j ∈ N; ✭✸✳✻✮
Zk η ≥Y
k η −Y
k
η−1 η∈ L;k∈ K; ✭✸✳✼✮
K
X
k=1 Yηk ≥
K
X
k=1
Yηk+1 η∈N(t)\Lt; ✭✸✳✽✮
Yk
η ∈ {0,1} η∈ L;k∈ K; ✭✸✳✾✮
Zηk∈ {0,1} η∈ L;k∈ K; ✭✸✳✶✵✮
XPit∈ {0,1} i∈ I;t∈ T; ✭✸✳✶✶✮
Xjη ≥0 ✐♥4❡✐6♦ j ∈ N;i∈ I;η ∈ L; ✭✸✳✶✷✮
Ijη+ ≥0 j ∈ N;η ∈ L. ✭✸✳✶✸✮
IP−
it ∈ {0,1} i∈ I;t∈ T ✭✸✳✶✹✮
IP+
it ∈ {0,1} i∈ I;t∈ T ✭✸✳✶✺✮
❊♠ :✉❡✿
❮♥❞✐❝❡&✿
• k∈ {1, ..., K}=K <♦ ♦ 4✐♣♦ ❞❡ ❧✐❣❛ ❀
• i∈ {1, ..., N P}=I <♦ ♦ ♣❡❞✐❞♦ ❀
• j ∈ {1, ..., N}=N <♦ ♦ ✐4❡♥ :✉❡ ❝♦♠♣B❡♠ ♦ ♣❡❞✐❞♦ ❀
• N S C ♦ ♥D♠❡6♦ ❞❡ ✉❜♣❡6F♦❞♦ ♣♦6 ♣❡6F♦❞♦❀
• η ∈ {1, ..., LT}=L <♦ ♦ ✉❜♣❡6F♦❞♦ ❞❡ 4❡♠♣♦❀
• t∈ {1, ..., T}=T <♦ ♦ ♣❡6F♦❞♦ ❞❡ 4❡♠♣♦❀
✶✼
• Lt=t∗N S ♦ "❧$✐♠♦ '✉❜♣❡,-♦❞♦ ❞♦ ❞✐❛ t❀
❈♦♥❥✉♥%♦&✿
• S(i) '1♦ ♦' ✐$❡♥' 3✉❡ ♣❡,$❡♥❝❡♠ ❛♦ ♣❡❞✐❞♦ i❀
• L(k) '1♦ ♦' ✐$❡♥' 3✉❡ ♣♦❞❡♠ '❡, ♣,♦❞✉③✐❞♦' ❛ ♣❛,$✐, ❞❛ ❧✐❣❛ k❀
• ηf = {L1, L2, ..., LT} ♦ ❝♦♥❥✉♥$♦ ❢♦,♠❛❞♦ ♣❡❧♦' "❧$✐♠♦' '✉❜♣❡,-♦❞♦' ❞❡ ❝❛❞❛ ♣❡,-♦❞♦ t❞♦ ❤♦,✐③♦♥$❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥$♦❀
• N(t) =F1, ..., Lt ♦ ❝♦♥❥✉♥$♦ ❢♦,♠❛❞♦ ♣♦, $♦❞♦' ♦' '✉❜♣❡,-♦❞♦' ❞♦ ♣❡,-♦❞♦ t.
(❛*+♠❡%*♦&✿
• Cap ❛ ❝❛♣❛❝✐❞❛❞❡ ❞♦ ❢♦,♥♦❀
• ρj ♦ ♣❡'♦ ❜,✉$♦ ❞♦ ✐$❡♠ ❝♦♠♣♦♥❡♥$❡ j❀
• dit = 1'❡ ♦ ♣❡❞✐❞♦ i❞❡✈❡ '❡, ❡♥$,❡❣✉❡ ♥♦ ♣❡,-♦❞♦ t❡ 0 ❝❛'♦ ❝♦♥$,;,✐♦❀
• HP−
it ♦ ❝✉'$♦ ♣❡❧♦ ❛$,❛'♦ ❞❛ ❡♥$,❡❣❛ ❞♦ ♣❡❞✐❞♦ i ♥♦ ♣❡,-♦❞♦t;
• H+
jt ♦ ❝✉'$♦ ♣♦, ❛♥$❡❝✐♣❛<1♦ ❞❡ ♣,♦❞✉<1♦ ❞❡ ✉♠❛ ✉♥✐❞❛❞❡ ❞♦ ✐$❡♠ j ♥♦ ♣❡,-♦❞♦t;
• skη ♦ ❝✉'$♦ ❛''♦❝✐❛❞♦ = $,♦❝❛ ♣❛,❛ ❛ ♣,♦❞✉<1♦ ❞❛ ❧✐❣❛ k ♥♦ '✉❜♣❡,-♦❞♦η❀
❱❛*✐0✈❡✐&✿
• Xjη ❛ 3✉❛♥$✐❞❛❞❡ ♣,♦❞✉③✐❞❛ ❞♦ ✐$❡♠ j ♥♦ '✉❜♣❡,-♦❞♦η❀
• Ijη+ ❛ 3✉❛♥$✐❞❛❞❡ ❡'$♦❝❛❞❛ ❞♦ ✐$❡♠ j ♥♦ '✉❜♣❡,-♦❞♦ η❀
• Yk
η ✉♠❛ ✈❛,✐;✈❡❧ ❜✐♥;,✐❛ ✭Yηk= 1 ✐♥❞✐❝❛ 3✉❡ ♦ ❢♦,♥♦ ♣,❡♣❛,❛❞♦ ♣❛,❛ ♣,♦❞✉③✐, ❛ ❧✐❣❛k ♥♦ '✉❜♣❡,-♦❞♦η✱Yk
η = 0 ❝❛'♦ ❝♦♥$,;,✐♦✮❀
• Zk
η ❛ ✈❛,✐;✈❡❧ 3✉❡ ✐♥❞✐❝❛ '❡ ❝♦♥$❛❜✐❧✐③❛❞♦ ♦ ❝✉'$♦ ❞❡ ♣,❡♣❛,❛<1♦ ❞❛ ❧✐❣❛ k ♥♦ '✉❜♣❡,-♦❞♦η✿ Zk
η = 0'❡Yηk−1≥Yηk ❡ Zηk = 1'❡ Yηk−1< Yηk;
• XPit ✉♠❛ ✈❛,✐;✈❡❧ ❜✐♥;,✐❛ 3✉❡ ❛''✉♠❡ ♦ ✈❛❧♦, 1 '❡ ♦ ♣❡❞✐❞♦ i ❢♦✐ ❝♦♥❝❧✉-❞♦ ♥♦ ♣❡,-♦❞♦ t✭0❝❛'♦ ❝♦♥$,;,✐♦✮❀
• IPit+ ✉♠❛ ✈❛,✐;✈❡❧ ❜✐♥;,✐❛ 3✉❡ ❛''✉♠❡ ♦ ✈❛❧♦,1'❡ ♦ ♣❡❞✐❞♦i ❡'$♦❝❛❞♦ ❞♦ ♣❡,-♦❞♦
t♣❛,❛ ♦ ♣❡,-♦❞♦ t+ 1 ✭0 ❝❛'♦ ❝♦♥$,;,✐♦✮❀
• IP−
it ✉♠❛ ✈❛,✐;✈❡❧ ❜✐♥;,✐❛ 3✉❡ ❛''✉♠❡ ♦ ✈❛❧♦, 1 '❡ ♦ ♣❡❞✐❞♦ i ❡'$; ❛$,❛'❛❞♦ ♥♦ ♣❡,-♦❞♦ t✭0❝❛'♦ ❝♦♥$,;,✐♦✮✳
