o planejamento da produção de pedidos em fundições de pequeno … · 2012. 6. 15. · o...
TRANSCRIPT
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O planejamento da produção de pedidos em fundições de pequeno porte
Maria Gabriela Stevanato Furtado
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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:________________________
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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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*+,-!.! t >0 4/'! 4!2$,;,%!@B
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-
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= ."*-/. 45!(/. *./.) .) -*#() 45# 8.))5#1 ! 1#)1! /!*! /# #(*3#9! )>. ,.(*!"-$-F!/.)
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> 43 104 165% 43 104 165? 46 137 228@ 48 170 293A 47 136 225B 47 136 225C 47 135 224D 47 135 224E 47 135 224>F 47 135 224>> 52 217 383
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*!$"3!/* $ "#(-*! ( - !' "#-0' ,*-*"#4 5- !#+(*"' %#$" / -'$ '$ -#,&'(#$ (#$1," %'$
21 !"' ' !6-#(' %# 0#%*%'$ /'!/,17%'$4
8 9#, :; !$"3!/* $ ? ,'( % @',1AB' C 0 D#%*%'$ D#%*%'$ ='!/,17%'$
='!/,17%'$ 0'( = - (+' #" ,4 EFGHFI
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QR%* S 11, 84% 122 112
-
!"#$! %& '#()$*!+,( -,./)*!01,2!1( /!3! !( 12(*4201!( 0,. 25.#3, .671., +# /#+1+,(8
92(*4201!( :!$,3 +! ;,$)!/ ?#+1+,( ?#+1+,( -,20$)@+,(
-,20$)@+,( /,3 -!.!3A, #* !$8 BCDECF
E 194.972, 16 0, 55% 164 158C 195.077, 44 0, 58% 165 165G 234.945, 42 1, 17% 171 156HI 284.400, 24 1, 07% 207 193% 370.663, 33 1, 21% 195 178J 421.264, 47 2, 93% 215 218KI 328.353, 56 2, 11% 197 172L 376.208, 10 8, 51% 223 198MI 287.754, 92 2, 05% 195 167ED 340.266, 62 16, 22% 224 223EE 580.220, 70 2, 47% 231 235
NO+1! P 3, 53% 199 187
Q /3,/,(*! !*)!$ !*#2+# #. .O+1! ! 43 /#+1+,( +! 0!3*#13! 0,. 25.#3, .@21.,
+# /#+1+,(R #2S)!2*, ! /3,/,(*! +# -!.!3A, #* !$8 BCDECF !*#2+# #. .O+1! 40 /#+1+,(
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/#+1+,(R 3#(/#0*1U!.#2*# B*!"#$! %F8
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.,+#$, +# -!.!3A, #* !$8 BCDECF #. 28 /#+1+,(R 2! 92(*4201! 9 +! 0!3*#13! 0,. 25.#3,
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-
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!"#$ "!%&'( )*')'+'" ,+$ $-$)#$%&' -$ .,/%&' '01!#23' -' +'-!4' 4P )$*$ +2/25
+26$* $)!/$" ' $#*$"' !+ $#!/-!* $'" )!-2-'" -'" 742!/#!"8 9'+ 2"#'( $" *!"#*2%:!" ! '"
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-
!
LT∑
η=F1
Xj,η ≤NP∑
i=1
aji j ∈ N ; !"#$%
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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82(*4201!( 9!$,3 +! :,$);#+1+,( >#+1+,( -,20$)6+,(
-,20$)6+,( /#$, 4P2 /#$, 4P? 222.777, 41 0, 37% 42 42@ 223.055, 65 1, 70% 43 43A 259.639, 29 0, 47% 43 43BC 325.467, 71 5, 83% 45 44D 418.218, 59 4, 71% 40 40EC 961.742, 27 50, 75% 43 44F 375.564, 60 4, 72% 40 40% 469.304, 77 16, 06% 46 45G 342.727, 81 8, 50% 42 40?H 389.525, 40 16, 92% 47 47?? 789.887, 13 18, 59% 44 43
IJ+1! K 11, 69% 43 43
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82(*4201!( 9!$,3 +! :,$);#+1+,( >#+1+,( -,20$)6+,(
-,20$)6+,( /#$, 4P2 /#$, 4P?C 1201.782, 14 0, 36% 103 103@ 196.105, 95 0, 44% 104 104AC 236.448, 07 0, 80% 111 113B 328.253, 18 11, 72% 130 126D 385.117, 89 1, 00% 120 119E 456.061, 22 6, 56% 130 128F 341.789, 23 1, 94% 121 121%C 404.070, 15 11, 30% 135 134G 296.983, 99 1, 21% 117 119?HC 329.500, 10 8, 20% 135 135?? 626.999, 14 7, 12% 143 145
IJ+1! K 4, 60% 123 122
-
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,-):
;3)+5312!) ?- @!0 A#,2,-) A#,2,-) .-31$*B,-)
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4P :
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)!"1,!(2 1#*$,&'"!* 53' #$ ,+'*$ &'%!*&!$ *-# 6!7'% )!"+' &' 3% %'$%# ,+'% F*!(
' 53' #$ 13$+#$ &' 'C)'&,:-# $-# "'('/!*+'$8 !"! '$+' +,)# &' 1(,'*+' = %!,$ /!*+!4#$!
! '*0"'0! )!"1,!(8 #" ,$$# )"#)#%#$ 3% %#&'(# 53' !(=% &' /,$!" 1#%)('+!" # )'&,
+# 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
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