O planejamento da produção de pedidos em fundições de pequeno porte

Maria Gabriela Stevanato Furtado

O planejamento da produção de pedidos em fundições de pequeno porte1

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 Assinatura:________________________

Ficha catalográfica elaborada pela Biblioteca Prof. Achille Bassi e Seção Técnica de Informática, ICMC/USP,

com os dados fornecidos pelo(a) autor(a)

F992pFurtado, Maria Gabriela Stevanato O planejamento da produção de pedidos em fundiçõesde pequeno porte / Maria Gabriela Stevanato Furtado;orientadora Franklina Maria Bragion Toledo. -- SãoCarlos, 2012. 57 p.

Dissertação (Mestrado - Programa de Pós-Graduação emCiências 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.Toledo, Franklina Maria Bragion, orient. II. Título.

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!

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!

LT∑

η=F1

Xj,η ≤NP∑

i=1

aji j ∈ N ; !"#$%

K∑

k=1

Y kη ≥K∑

k=1

Y kη+1 η ∈ N (t) \Lt; !"##%

Y kη ∈ {0, 1} η ∈ L; k ∈ K; !"#!%

XPit ∈ {0, 1} i ∈ I; t ∈ T ; !"#&%

Xjη ≥ 0 '()*'+, j ∈ N ; i ∈ I; η ∈ L; !"#-%

I+jη ≥ 0 j ∈ N ; η ∈ L. !"#.%

IP−it ∈ {0, 1} i ∈ I; t ∈ T !"#/%

IP+it ∈ {0, 1} i ∈ I; t ∈ T !"#0%

123 425*623 . * / 37, 8,9:2+2;,3 ,3 ;*3:*+;

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IJ+1! K 4, 60% 123 122

!

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+# 1(,'*+'2 )'"%,+' ! '*+"'0! )!"1,!( )'&,

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!

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∑

j∈L(k)

(ρjXjη) ≤ 0(1Ykη !' η ∈ L; k ∈ K;

K∑

k=1

Y kη ≤ 1 !' η ∈ L;

LT∑

η=F1

Xjη ≤NP∑

i=1

aji !' j ∈ N ;

K∑

k=1

Y kη ≥K∑

k=1

Y kη+1 !' η ∈ N (t) \Lt.

2% $34(56$% +$ -(7()5! +$ $%#!34$ 1("( !% 1$+*+!% !)#*)4(' (% '$%'(%8 !4 %$9(8

IP+i,t−1 − IP−

i,t−1 +XPit = dit + IP+it − IP

−

it

!' i ∈ I; t ∈ T .

:! $)#()#!8 !'! !% *#$)% 1!+$' %$" $)#"$;4$% ()#$% 34$ ! 1$+*+! %$9( !) 74

#$"*A(+! 1$7( $)#"$;( +$ #!+!% !% %$4% *#$)%8 !4 %$9(/

t∑

l=1

wjil ≥ ajiXPit

1("( j ∈ S (i) ; i ∈ I; t ∈ T .

27>' +*%%!8 1"$ *%('!% (%%$;4"(" 34$ #!+( $)#"$;( $.#"( %$9( !)#(-*7*A(+(8 1!*% ( $7(

> (%%! *(+! 4' 4%#! +$ $.1$+*5&!? C'( $)#"$;( 1!" 7*$)#$ > 1"$,*%#(8 !4 %$9(8 34()+!

XPit = 1 %*;)*D ( 34$ 4'( $)#"$;( > "$(7*A(+( %$' 4%#! (+* *!)(7E (% +$'(*% $)#"$;(%8

!

!"#$%&'(%(# &)*'(#+ #,! !"*(-$.$/(%(# 0&.( 1('$21&. eeit 345& '&0'&"*( ( 45("*$%(%& %&

&"*'&6(# &)*'(# %! 0&%$%! i "! 0&'7!%! t8 ( 45(. 59 5#*! (%$ $"(. : (##! $(%! "( ;5" ?# #&65$"* '*'$ H! &"*("*!+ 0'& $#(9!# (##&65'('

45& "59 9! 0&'7!%! ! 9!%&.! ",! !"*(-$.$/& 45& ! 0&%$%! ;!$ !" .57%! & *(9-:9

% !"*& ( 0('*& %!# $*&"# &"*'&65 0(' $(.9&"*&> ?##$9+ 5#('&9!# ( 1('$21&. γtij "(

;5"

!

γjit ≤ aij (1−XPit) !" t ∈ T ; i ∈ I; j ∈ S (i) .

#"$ %&'()*! $ ('+ $,$-.($/$ 0 %&$,)! /'( !,)$+ ,$ 1&,2*! !34').5! 6!+ &,./$/' /'

$/$ .)'" %&' 1!+ ',)+'7&' ' ! %&$,)! $ +'( ',)$+ 6!+ ',)+'7$ '8)+$ %&' ! !++'9 :6)$"!(

6!+ ,*! !,)$3.-.;$+ &"$ ',)+'7$< !& ('4$< $((." %&' ! 6'/./! 1!+ !, -&=/! >%&' )!/$(

!( ('&( .)',( 1!+'" ',)+'7&'(< XP = 1? '(($ ',)+'7$ ,*! 0 !,)$3.-.;$/$9

@ 1&,2*! !34').5! !"3.,$ %&$)+! 6$+ '-$(A >1? &()!( /' $)+$(! /!( 6'/./!(B >2?

+'/&2*! /' &()!( /' $)+$(! 6$+$ ',)+'7$ /' .)',( /!( 6'/./!( >C $?B >3? ., ',).5! 6$+$

6+!/&2*! /' .)',( /!( 6'/./!( ,*! !"6-')$/!( >5.($ +'/&;.+ ! /'(6'+/= .! ,$( 1!+,$/$(?B

>4? &()!( /' ',)+'7$( '8)+$(>DEE?9 @ 1&,2*! !34').5! !"6-')$ 0 /$/$ 6!+A

F.,

T∑

t=1

NP∑

i=1

HP−it IP−

it −T∑

t=1

NP∑

i=1

N∑

j=1j∈S(i)

RcaHPp−jitγjit −N∑

j=1

H+jT I+jT +

NP∑

i=1

T∑

t=1

CEE eeit

'" %&' HPp−tij 0 ! &()! 6$+ .$- 6'-! $)+$(! /$ ',)+'7$ /! .)'" j /! 6'/./! i ,! 6'+=!/!

t.

: "!/'-! .,)'7+$/! >4PI? 0 /$/! 6!+A

F.,

T∑

t=1

NP∑

i=1

HP−it IP−

it −T∑

t=1

NP∑

i=1

N∑

j=1j∈S(i)

RcaHPp−jitγjit −N∑

j=1

H+jT I+jT +

NP∑

i=1

T∑

t=1

CEE eeit

>G9H?

(9$9A

I+j,t−1 +Lt∑

η=Ft

Xjη = I+jt +

NP∑

i=1i∈A(j)

wjit j ∈ N ; t ∈ T >G9I?

IP+i,t−1 − IP−

i,t−1 +XPit = dit + IP+it − IP

−

it i ∈ I; t ∈ T ; >G9J?∑

j∈L(k)

(ρjXjη) ≤ D$6Ykη η ∈ L; k ∈ K; >G9G?

K∑

k=1

Y kη ≤ 1 η ∈ L; >G9K?

!

LT∑

η=F1

Xjη ≤NP∑

i=1

aji j ∈ N ; !"#$

t∑

l=1

wjil ≥ ajiXPit j ∈ S (i) ; i ∈ I; t ∈ T ; !"%$

wjit ≤ aji (XPit + eeit) i ∈ I; j ∈ S (i) ; t ∈ T ; !"&$

T∑

t=1

wjit ≤ aji i ∈ A (j) ; j ∈ N ; !"'$

T∑

t=1

eeit ≤Max eei i ∈ I !"()$

XPit + eeit ≤ 1 i ∈ I; t ∈ T !"(($

γjit ≤ wjit t ∈ T ; i ∈ I; j ∈ S (i) ; !"(*$

γjit ≤ aij (1−XPit) t ∈ T ; i ∈ I; j ∈ S (i) ; !"(+$

K∑

k=1

Y kη ≥K∑

k=1

Y kη+1 η ∈ N (t) \Lt; !"(!$

wjit ≥ 0 j ∈ N ; t ∈ T ; i ∈ A (j) ; !"(,$

Y kη ∈ {0, 1} η ∈ L; k ∈ K; !"(#$

XPit ∈ {0, 1} i ∈ I; t ∈ T ; !"(%$

Xjη ≥ 0 -./0-12 j ∈ N ; η ∈ L; !"(&$

I+jη ≥ 0 j ∈ N ; η ∈ L. !"('$

IP−it ∈ {0, 1} i ∈ I; t ∈ T !"*)$

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