Planejamento da produção de impressoras por dimensionamento de lotes e sequenciamento: um estudo de caso

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Agradeço a Deus peca vida, à famícia peco apoio incondicionac, à minha namorada

Lygia peco companheirismo e paciência, aos amigos José Cecício Moreira, Acan Viana,

Ormeu Coecho, Thiago Augusto, Maxstacey 'eves, Tairone, André Cruz, Marcus

Vinícius e Breno pecos ensinamentos de vida.

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(7)

In this thesis we consider a reac probcem of cot,sizing and scheducing printers’ production in

a worcdwide EMS (Ecectronic Manufacturing Service) company. The environment is

characterized by the production of four different types of printers on two non identicac

manufacturing cines. Changeover times are manufacturing cine dependent. Preventive

maintenance times are considered which reduces the production avaicabce time and differentiate

the avaicabce capacity from one period to another. Demand must be satisfied without

backcogging.

The goac of production pcanning is to determine optimac cot sizes and the production

sequence of these on different manufacturing cines minimizing set,up and inventory costs over a

pcanning horizon. It`s not about finding a socution that purecy satisfies demand on time, but

finding a production pcan integrating cot,sizing and scheducing with minimac cost.

As shown above, this manufacturing process can be modeced by the cot,sizing and scheducing

probcem, so we studied ccassicac and reformucated modecs of cot,sizing and scheducing modecs

on citerature.

The capacitated simuctaneous cot,sizing and scheducing on paraccec non identicac machines

probcem presented in this thesis is ccassified as a carge bucket, mucti,item, mucti,machines,

singce,cevec, static and deterministic. The periods are differentiated in macro and micro periods.

Macro periods are subdivided into many micro periods. Here, various types of printers can be

produced in each macro period. The sequence decision appears on determining the best

accocation of production cots in each micro period.

The thesis consists on the devecopment and impcementation of a mathematicac modec of

optimization to hecp on production pcanning managers’ decision process. The modec integrates

tacticac decisions of cot sizing and operationac decisions of sequencing these cots. It covers a

pcanning horizon of 96 micro periods in 2 months and determines not oncy the size and the

moment to produce a cot, but acso the best sequence and accocation of these cots on

manufacturing cines.

These probcems are considered 'P,hard (see Bitran & Yanasse [7]), so we devecop a

strategy of addition of famicies of inequacities and some reformucated constraints to accow this

practicac cot,sizing and scheducing probcem to be effectivecy socved via mixed,integer

programming and generac MIP software incorporating cutting pcanes such as XPRESS and

(8)

are deterministic and were coccected with the process coordinators engineers. These data were

anacyzed and treated to be socved with the MIP socver.

The proposed resucting pcan is then compared with the current practice. Improvements on

productivity and costs reduction are evidenced. The new pcan acso increases the quacity of

pcanning, reducing to zero the number of decays in decivery of products.

A recommended evocution is the devecopment of software with user’s graphicac interface,

which is strategic to the company because it accows a satisfactory use by production managers

with cittce knowcedge of optimization (Fceischmann et ac. [15]).

(9)

Lista de Figuras ... i

Lista de Tabelas ... ii

Lista de Abreviaturas ... iii

1. Introduoão ... 1

606 ' !(& ! ... 3

608 .$ ! !! ' ... 4

60806 .$ ... 4

60808 .$ ! !% )/1 ) ! ... 4

60S , # 5 ' !! ' ... 4

2. O Contexto ... 5

806 "% ! ... 5

808 ) !! & . " ... 8

3. Problemas de Dimensionamento de Lotes e Sequenciamento ... 10

S06 # &' ... 10

S08 . , " 3 !! ) ... 10

S0S " ! ! & ! ... 11

S0T . " " #! # " # ; ! 3 % ) ... 12

S0Q . " !) " #! # " # ; ! (& #) " # ... 12

S0H 3 !! 1 ) ' 1 "& ' ... 14

4. Estudo de Caso: Planejamento da Produoão de Impressoras ... 16

T06 , ... 16

T08 # &' ... 16

T0S , " " ) ... 18

T0S06 E" ! 2 ! 5 ! ... 18

T0T U6... 20

T0T06 ' ! ,& ! ! 'A ! 1 "& ! ... 22

T0Q U8... 23

T0H # ! ! ! ... 25

T0M !& ! . ! ... 30

(10)

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Figura 5 ) !! % &' "% !! ! ! . " # #, "% 000000 7

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Tabela 22 # ! ! " ! % H % ! "% !! !B S #- ! " #&1 & 000000000000 SH

(13)

iii

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W 00000000000000000000000000Keccogg Pcanning System

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#&1 & ! , # ! ># ) !

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(14)

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set,up costs and set,up times

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% # # ! (&@#) ) " )&! ! "% ! set,up

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(15)

1

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1.1 MOTIVAÇÃO DA PESQUISA

" ' " ! ! % . " % , " ' % &' "% !! ! %

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1.2 OBJETIVOS DA DISSERTAÇÃO

1.2.1 Objetivo geral

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1.2.2 Objetivos específicos

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1.3 ORGADIZAÇÃO DA DISSERTAÇÃO

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(19)

5

CAPÍTULO 2

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% ) ! ! " 5 # ! # "% ! ) #! & " " ? % " % 1 ! " # , " 1 # 0

3 " " # , " 1 # "% !! ! ? ) ) 5 % &! # #! ! #- !

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2.1 A EMPRESA

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(22)

8

2.2 O PROCESSO PRODUTIVO E O PROBLEMA

% &' "% !! ! # ) D! # " # , " % ) ) )& "% !! 34 IIn

Circuit BoardO (& ? " #- ! : ISurface Mount TechnocogyO 1 " % " (& # !

" # , " & " ) , " # # , ! (& % ! ) # " ! " ! ) "% # # !

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#! ' " #& : IPcated Through HoceO ! ! 3: IIn Circuit TestOB #

) "% # # ! ># ) ! " ! ! % ! ) # ! " #& " # # % ) 0 # " # % )

! ,& % " # , " 1 # . " # , "B ! % ) !B !% ! !

># ) ! " )E# ) ! ! % ! ) # ! # &" ) ) ' % ! ) ) #1 ,& #

% & 1 # I ,& TO0

Figura 4 &G , " !&" % ) !! % & 0 Fonte: ,& ! I899HO0

G ! " & ! #- ! )# , ) " # 1 # ! 1 G/ ! " # , "0 3 #- % !!&

) % ) )# , % &5 ! T % ! 1 # ! "% !! I ,& QO0 ! "% !

changeover # ! #- ! 6 8 " # 6H9 899 " #& ! " 1&#' ) %

(23)

9

ISingce Minute Exchange DieO " #&1 & #G& B &" . - # ) " #- !

: % ,& ! L8VN ) #1 ,& ' " (& # ! G # 5 ' % !B % " #

&' " #& #' "% changeover% #- . ! ?)# ) % " (& ! '

" )- I ) % ) O % ! # # " " " ) ! $ " # ! $&! B 1 ) # &"

" - ! "% #- " 0

Figura 5 ) !! % &' "% !! ! ! . " # #, "%

3 #! D! " # , " 1 # % , , % ) !! % &' B &" 5 (& !

% ! # ! % !!& " " ) % ) #! % &5 " ! . " # !! % 0

?" !! B ! % ! " # , ! % ! 1 # ! ) # !0 # B

% , " ' % &' " # , " ? "% E#) ! ?, % ! "% !

" #&1 & ) # 0

! ! # " ) " * " # )& % 5 B % & B "%

!% #/ % & # B )&! ! (& )&! ! "% ! set,up changeover !

" #/! ) ! 1 " ) ! ) " #, #- ! !% #! ! % % ) !! 0

! % ) !! " #&1 & % ! " % % . " " #! # " # !

! (& #) " # % &' 0 !! 1 1 &" ! & " ! ) !! ) !

1 "& ! # & 0 4 &G J Y ! \ LHNB )- J Y ! \ L8MN Y ! \ LS7NB %

G "% B " 1 "& 'A ! " " ) ! % % . " ! " #! # " # !

! (& #) " # " ) " !% ) ! ) " start,upsBchangeoversB " #- "/# " !B

!) - # &" & !set,ups% % / " % . " !smacc bucket big bucket0 Demanda Montagem SMT Almoxarifado (Carcaças) Inserção

Manual Linha-1

(24)

10

CAPÍTULO 3

S0

;

:

R: 3 D

4;

:

; :

<

3 :

! ) %/ & . &' - ! C ) " , " % . " ! " #! # " #

! ! (& #) " # % &' B . " ) " ! ?, ! ! &' !! ! " !0 ^

&" 1 ) " + ! ?, 1 "& ' " " ) ' ! ,& ! !

% ! &" !!&# ) # % . " ! & # !! !! ' 0

3.1 IDTRODUÇÃO

1 #) . #,@#) & ' B ! " ! " #! # " # !

! (& #) " # ! ) !! 1 ) !0 ) !! 1 ) ' 1 "& 'A ! " " ) ! ! ! " !

! #) # ! " . - ! ) # ! ) " " )- J Y ! \ L8MNB Y ! \ LT9N !A !

) " G J W ""! L6SNB 4 - " et ac0LVN0 !! ) !! 1 ) ' 1 ) # # " #

. #,@#) " % " # B !! "B &" (& ' " + % ) 0

"% " # ' ! " ! " #! # " # ! ! (& #) " # "

% . " ! # &! ! ! % " ) "% # - ! ) " 1 5 " #

#1 " 'A ! (& ! ! 'A ! ! 1 # ! ". # ! & ' 0 % ) 'A ! "

# F! ! & " !B # F! ! 1&# ' B # F! ! ) % # ! B 1 . ) !

1 , # !B 1 . ) ! 'A !B 1 . ) ! ,& # F! ! " # ! ! #) # !

" !)-" ##et ac0L6QNB 5 et ac0L8QNB # L8HNB : et ac0LSSNB : ! J .

LSTNB # et ac0L8SN 4 Z#et ac0 L7N !% ) " # 0

3.2 ABORDAGEM CLÁSSICA

. , " ) !! ) B # & B % # $ " # % &' ! (& #) " # !

(25)

11

" # ! ! # , 0 ! ! ! # ! ?! ) )& % # $ " #

# ) !! ! " ! I O0 " 5 " # ! ! " #- ! !

! (& #) " # ? 1 0 !! 1 " B ? # ) !! (& ! #1 " 'A ! % # $ " # #,

% 5 I O ! $ " - ! " #/ "? I O " ! ,& " #/ )&

I! (& #) " # O I 2 " #et ac, LSMNO0 !! " " # B ". ! ) % ) ! % & !

% !! " ! # & " # !% !B # ! " # ' # ! 1 # ! #/ !

% # $ " # B (& % % # ! # ! % &' 0

! " 'A ! " ' " # #1 " 'A ! ! ' ) % )

! (& #) " # % 'A ! " " 3- # J L69N . &" " % , " '

# " ! % # , ) !A ! % # $ " # % &' ! (& #) " # !

% 'A ! #/ )- 1 . ) 0

" ! ?(& ! & & ! % & "& D#/ ) #! ! 'A !

% ) @#) # ) #1 ,& ' ! !0 ! &' " % " software ) " )

3 ; P ! " ! " % (& # ! #! E#) ! , & ) "% G

" I D O0

". ! $ . ! # # " % ) 'A ! % ) !B % . " " #! # " #

! ! (& #) " # "& D#/ # " ) . !1 ' ! ) #! ! " % !(& ! !

I4 - " et ac0LVNO0

3.3 PRIMEIROS ESTUDOS

,&# G J W ""! L6SNB ! % " ! ! & ! " % # $ " # % &' # (& !

1 " #! # " # ! # ) " ) " " " "% ) # /#&

" #! # " # ) #>" ) I < Economicac Order QuantityO ! " ! 'A !

) % ) B " # ) #! ! ) # - 5 # % # $ " # #1 # 0

". # % ) % # $ " # % &' < 1 " # ! & 5 (& !

!% B % ! ! ! " % ) 'A ! # "% ! ! " ! ! . ) # 'A !

!&% " # ) # /#& ) "% ! # " # !0 ! ) #$&# !% )/1 ) ! & 'A ! " &

% ) . " 0 1 )& ! ) # ! % ) " (& # &" #F" ) #

#! ! ) #! ! "& # " # I , ! L87NO0

, ! L87N " ,- .\ L6TN " ! ! 'A ! ) % ) " ) #! ' ?!

(26)

12

&" )& ! B &" 1 #>" # # 1 @#) # &" )& ! ? (& ! 1 5 8

& " ! #! " !" "% B (& ? 1 ! ) " # "% !!/ I " ,- .\B L6TNO0

# # B !! " ) " <B ; ? ".?" &" " " "% ) # /#& B #

!!&" " # ! ) # - 5 # % # $ " # #1 # B ?" ! D 0

" &' " ) " , " Y ,# J Y- # LSVN # ! " &" !

#E" ) <B (& !&. "% " % / ! !) ! ) #! " #

#E" ) B % " # ! &' % . " " "% % # " 0 # # B !! % . "

# ) #! " ! ) % ) I G J W ""! L6SNO0

3.4 PROBLEMA

DE

DIMEDSIODAMEDTO

DE

LOTES

CAPACITADO

% . " " #! # " # ! ) % ) I3; O ? &" G #! % . "

Y ,# J Y- #B % ! ! ! 'A ! ) % ) " ) #! ' 0

% . " " #! # " # ! ) % ) ) " ) % ) ) #! # % !

! " "% % # " B ! ) "% ! " !&.% . " ! " #! # " #

! # ) % ) !0 ! % . " ! " #! # " # ! # ) % ) ! $ 1 "

. ! # ! & !0 ! ! % . " ! % " ! 1 "& ! " " ) " # ) "

% . " ) " #- " ! )& ! ! ! " "% % # " I )- J Y ! \

L8MN ) %/ & M0T % &" 1 "& ' ) "% ) # !! % . " O0

". ! % . " ! ) " ) % ) ) #! # & # D) % ) ! % !! " ! ! !

" "% % # " B ! % . " ! " #! # " # ! ) " ) % )

set,up! # % # # ! ! 'P,hard ! . ) # 'A ! ! " ! I4 # J K # !! LMNOB % ! % "

! &5 ! % . " " )- 9D60 I )- J Y ! \ L8MNO0

3.5 PROBLEMA DISCRETO DE DIMEDSIODAMEDTO DE

LOTES E SEQUEDCIAMEDTO

! # ! % # , " % # $ " # ! (& #) " # " ". # job,

shop ) " " &5_ D ? 5 J ; !! L68N0 ! ! ! . ! " # "? ; !! L89N

% #) # &" % # % &' 0 ! &' ! ! #, &" % ) " #

(27)

13

1 G # ! " (& # ! ! (& #) " # job,shop % &" % # 1 G % &' 0 .$ ?

#) # " - % # 0 ! ?, ? $&! 1 ) % 1 " ! ) # !

% # $ " # % &' ,# " ! ! 'A ! ! (& #) " # " ". # job,shopB

(& % + # . % &' 0 "? # , # " ! &' B #

# # B , # ! &' &" % # % &' 0

" ! ?, # !! # % # , ) !A ! ! (& #) " # # % . "

" #! # " # ! ) % ) ? !&. ! macroperíodos !! % . " "

microperíodo!0 !! "B "D! % . " !) " #! # " # !

! (& #) " # I ; O I # ! et ac0 LTNO0 ! % . " B ! % / ! % ! # " )&

& ' I & # ! & - !O % !! ? )- " smacc bucket. & ) ) /! ) !! !

% . " ! ? % ! #' ! 'A ! % &' ` & & # a0 ! !microperíodo!! %

% &5 % # ! &" % & % % / 0 # ! % . " " ! /! ) B ) !A !

% &' ` & & # a % % / ! " # ! ?! % " !! ) @#) set,

up # ) & # 0 !! " B "D! % &' " ! &" % & " &" F# )

& # ) ) 5 # % . " " #! # " # ! ) " set,up ) # /#& I3 ; O

I G J W ""! L6SNO0

! " - #' ; ) " % . " ! ! (& #) " # " & # J G L6VN

! @D % % . " ! (& #) " # ! I4 O0 4 ? # " (& ! +

" , " " " ) ; (& # ! % . " " &" " (& # ) " "%

)&! set,up % # # ! ! (&@#) 0 !! ) + . ! &' !

% . " % % . " ! (& #) " # " &" " (& # 0

# J G L6VN % " (& @#) ; 4 0 ! " ! % " !

! " !" ! % . " ! ! ! #! E#) ! 1 " #!1 " !0 # # B % ) ' 4 ?

" ! # $ ! " #! E#) ! ) " % &) ! #!Bset,up! #, ! & 5 ' ) % ) B

#(& # (& ; ! ?(& " ! #! E#) ! ) " "& ! #!B . G & 5 '

) % ) "% ! set,up# "& ! ,# 1 ) !0

" , " % . " ! " ! ) "% G ! ) " % . " ) % )

! (& #) " # " #! # " # ! ) " )&! ! set,up % # # ! ! (&@#)

"% ! set,up # D#& ! ) " ) ) /! ) " #& #' set,up &" % / %

& ! #) # ! " ! & ! ) " " &% J ,#&!! # L6MNB .! J - &" L8NB

; . et ac. L86N \ L8TN0 !! ! % . " ! ! ) #! ! D- I4 # J K # !!

LMNO0 !! B ?)# ) ! ) " branch,and,cutB " 5 ' & " - & /! ) ! ) "

(28)

14

3.6 CLASSIFICAÇÃO E REFORMULAÇÃO

! ?, ) !! 1 ) ' ! % . " ! " #! # " # ! "& D " "

#/ ! ! " ! 1 "& 'A ! ! 'A ! % ! # " )- J Y ! \ L8MN ?

, # B ! (& % " ) # " # % !(& ! ) ) " % % . "

" #! # " # ! (& ! "0 ?" !! B ) !! 1 ) ' ! ! % . " ! % ! #

1 "& 'A ! " " ) ! ! ,& ! ! % % . " ! ! " !0

' ! ,& ! ! 'A ! 1 "& ! ! ! ?, ! & 5 ! #

! # " # ! . - 0 ) !! 1 ) ' ) ! % . " ! " #! # " #

! % " (& !! ) !! % . " ! % !! ! ! ?! 1 "& 'A !

% A !B 1 "& 'A ! ! # !B 1 "/ ! ! ,& ! ! . #! socvers

, " ' # ! 0 " #! # , " &! ) !! 1 ) ' 1 "& ' B

Y ! \ LT9N % ! # !) ' @! % . " ! "& D #!0 ! ! % . " ! !

) !! 1 ) ! I! ,&# &" . (& % ! # ! & ! " ! "% # ! ) # !

% . " OB 1 "& ! "% " # ! % ) "% 'A ! ! "% #- 0 1 "& ' ?

, # "% E#) B % ! % " (& ! ! % . " ! % ) ! % !! " ! 1 " #

! ! " softwares ) " ) ! ) " P 3 ; P I4 &G J Y ! \ LHNO0

1 "& 'A ! " " ) ! " ! " #! # " # ! ! (& #) " #

#) & # changeovers start,ups% " ! ! ! " Y ! \ LS7N0

,&#! . - ! ) " W " ] J )- , L67N % ! # " 1 "& 'A ! # !

% % . " " #! # " # ! ! (& #) " # 0 ?! G '

, #, # .&!) D! " # . #!cower bounds &5 # !% ' .&!) , "

branch,and,bound0

! 1 "& 'A ! " " ) ! ! ,& ! ! (& ! "

" #! # " # ! ! (& #) " # % ! # " % G " 'A ! ) !) ) # G 0 ! !

! , # ! " ! "DF# ) I ! (& ! $ ! " . ! # ) #- ) " # O 1 # " #

% ! " ! "& D "0 ) "% ! ' % . " ! "& D " " &" ) #$&#

% . " ! "DF# ) , , ! % ! 'A ! &# 1 5 ) " (& ! &' !! !

% . " ! % !! ! " software! ) " ) ! , " ' # D ! ?!

1 "& 'A ! " " ) ! #! ' ! ,& ! ! I Y ! \ LT9NO0

' ! ,& ! ! % % ) # 1 "& 'A ! " ! 1 !0 ! ! ?, ?

" ! 1 ) # ! ) "% + ! ?, G ' # 0 " !) ' % ) #

(29)

15

! ! (& #) " # % "DF# ) % ! ! " 2 # $ J 2 # ! LSQN #(& #

(& " 3 # # # L66N @"D! 1 "/ ! ! ,& ! ! % ! " !" % . "

"& D " F# ) D" (& # 0 !! F " , B &" ! & % # F! (&/" ) B . D!

&' "% ) "%& ) # % .&!) ! &' C " % &" % . " ) " Q #!

? SH % / !0 " &" ! & % &" 1 . ) ,& B # et ac. L8SN " &"

! ?, - & /! ) % ! &' ! % . " " " (& # ! % ! ! (& !

) "% - !0

& ! ?, ? ! , , ' ! ! % . " !) " #! # " #

! ! (& #) " # 0 !! % " (& ! % . " % !! ! 1 "& ) " % . "

# ) " #- " ! )& 0 ! 1 "& ' B # # # B ) !) "& % ) " &" #

#F" #!0 !! 1 " B % (& ! 1 "& ' # % !! ! & 5 % !

% ) ! ? # ) !! ! # , " ! (& G) & " ) # " ! ! 'A !

G #! " # I # ! J W # LSHNO0

1 "& ' " " ) % . " !) " #! # " # !

! (& #) " # % # # ! (&@#) ) " )&! ! "% ! set,up I ; O % !

1 ?! #!1 " ' ! # . " ) G $ # ) " $ # ! "%

I: :YO I " # et ac0 LS9NO0 ! ! 1 5 " &! % , " ' #E" ) % ! &'

! % . " 0

. ) # 'A ! !% )/1 ) ! )&! " 5 # " # B % . " " #! # " #

! "& D " ) " ) % ) ) #! # )&! ! set,up !! ) ! % ! 1 "&

! " "% % # " I # \ et ac0 LSN % &" 1 "& ' " ! 1

% , " ' # % !! % . " O0

% . " ) % ) " #! # " # ! ! (& #) " # ! "& E# ! "

#- ! % ! # @# ) ! % ! # # ! ! & ? % carge bucket, "& D" (& # !B

F# ) #/ B "& D "B ! ) " #/! ) 0 !! . , "B ! ! #! % " !

% &5 ! " ) macro período0 ! (& #) " # ) ! " # "

-! (&@#) ) ' ! ! % &' " ) micro período0 ". ! ! $ !!&#

% ! # # ! !! ' B ! % . " ? % &) !)& # & I # et ac0

L8SNO0 ?" !! B ! ! % . " ! % ) ! ! " # ! % 1 "& ' I )- J

Y ! \ L8MNO0 " " " ) , # " # % % ! 1 5 &! ) !! 1 ) '

% ! # " Y ! \ LT9NB #! ' ! ,& ! ! 'A ! 1 "& ! % !

(30)

16

CAPÍTULO 4

T0

:

3 *

;

:

4.1 METODOLOGIA

! ?, % !(& ! & 5 % ) # &' . - 1 ! & ) ! 0 ! 1 ! !

# ! # ! % ) !! ! * 1 # ' ! # " # #! &" # % !(& ! B )

!B # ! ! ! & , ' ! !& ! ) #) &!A !0

% . " ) #! ! " " # " - " #- ! (&@#) ) ' !

% &' # ! #- ! " #&1 & "% !! !B !% # % # ! " #& #'

% # " # " # % ! ! " ! ! " # )&! % !!/ 0

!! 1 " 1 ! # ! ! # & ! &# A ! ) " , &% 1 ) ) "% ! % ?)# ) !

!% #! ! % % ) !! % & % # % #) % ! 1 ! (& # 1 " #

% # $ " # % &' 0

" ! ,& 1 " % !(& ! ! . - ! %&. ) 'A ! 1 # ! !!&#

" #! # " # ! ! (& #) " # % &' " #- ! " #&1 & % ! (&

% " !! " ! # " # &" " " " ) (& + #) # 0

) ! # ! ! ! ) & $&# " # ) " ! # " # !

" " " ) 0 !! 1 " % " D! ! & & ' ) "% . ! ! ) "

! ?, " , " % % ! 1 " !& % ) . !&,

"% " # ' % ) 0

. - . #, ".?" " % " # ) B % " # !! " &" !

! ! @" ) % ) !! % &' % % ! ' &" "? # % &' 0

4.2 IDTRODUÇÃO

% ) !! " # , " "% !! ! ? 1 # ! ! ,& # ! ) # 'A !* "D! 4

(31)

17

" #&1 & 0 # F! 1&#) # " &" ! ! " % &' ) % ) 8 & # !B H - !

) B & # H ! ! " # 0

! "% ! &# ! % &' ) "% !! ! 1 #) ! " 1&#' ! #- !

" #&1 & 0 ! "% ! set,up % # " % & #- " #&1 & #

% & ! 1 . ) 0 # # B # - ) #!&" "% ! ! ,# 1 ) ! # ) % !

"% !! !B (& ) ) 5 set,up % # # % & B # ! (&@#) 0 ! ! "

% &' % ! # ? ) % ) B & ! $ B % !!& ) % ) 1 # % &' B (&

) ) #) @#) ! % & ! % )& ! ! % &' 0 ! "% ! changeover

% # # ! #- " #&1 & ) #! ' ! "% ! % ! ! % " #& #'

&5 " 1 #) " ) % ) !% #/ % % &' &" % / % & 0

! ! #1 " 'A ! % " ! ! ! # ! : . ! H 6T !% ) " # 0

" ' " " #! # " # ! ) # "% # ! ! & ?

) #! ' ! (& ! ! ,& #' 0 ". ! ) #! ' ! $ % ! # " "& !

% . " ! % ) !B ! &! # # " ! %&. ) 'A ! ) # /1 ) ! I )- J Y ! \

L8MNO0

" # " #! ? % " # " # % ) # #, ! & # !b

!! 1 " @"D! ! " # % & # ) % & 0 E" ! # ) "

)&! &# ! (& B ! (& # ) !% #/ B "% # ) !! % % &5 )&!

set,up ! % & ! # ! #- ! ! " #/! ) !0 ! ! 1 " !% # . 5 ! %

#, #- ! # &! ! !% #! ! % % ) !! ! % ! # ! " . ! # ! ' T0H0

" # % " &% & ! (& &backcogging% " # (& "% ! % ! #

&" " #/ ! ' ! & ) # 0

! )& ) # ! ! ) % ) % # $ " # B D! ) #

#1 " 'A ! ) # ! + & ) % ) B !! 1 " "D! ) % )

1 # ) " #F" - ! 1 ! % &' I )- J Y ! \ L8MNO0 % E"

) % ) !% #/ B % # # "% ! # ! B ? !& B % # B !) #

"% ! downtimeB # &%'A ! " #& #' % , " "% !% #/ 0

" #& #' % , " % ! % ?D " # % &" - 5 # % # $ " #

#, % 5 0 ! & 5 L6N % ! # &" ! ?, ) ' " 5

% $ ! " #& #' % # " #- ! " #&1 & 0 !! " # B !! .

-) #! ! "% ! % ?D " # ! " #& #' ) ' " 5 ! ! #

- 5 # % # $ " # 0 ! !B % !& 5B ) #! " " % "% !% #/ %

" #&1 & ! "% !! ! # !macro período!0 !! 1 5 ) " (& ) % ) !% #/ %

(32)

18

% . " ) % ) " #! # " # ! ! (& #) " # ! "& E# ! "

#- ! % ! # @# ) ! % ! # # ! ! & ? % carge bucket, "& D" (& # !B

F# ) #/ B "& D "B ! ) " #/! ) 0 !! . , "B ! ! #! % " !

% &5 ! " ) macro período0 ! (& #) " # ) ! " # "

-! (&@#) ) ' ! ! % &' " ) micro período0

3 #! "D! ! #/ ! % # $ " # % % / !* % / !macro micro0 % /

macro . #, &" "@! % # $ " # #(& # (& % / micro! !&" &" & #

% &' 0 #! ' ! set,up % " (& "% !% #/ % % &'

! $ & 5 " !& ) "% & 0 !! 1 " B ? % !!/ (& ! #- ? ! % !

"% !! ! % &5 ! % #- % & # 0

4.3 MODELAGEM MATEMÁTICA

.$ (& % % ! ? # , ) !A ! #/ ) ) " - 5 # 8 " ! !

#/ % # $ " # % ) # )- 1 . ) 0 ! (& #1 & #) " # 1 " #

% # $ " # % &' # % " ! " !B % # B "% ! " #& #'

% , " G % & ! ) #! ! # " 0 ! !B % !& 5B &5 "

) % ) !% #/ 1 #) &" % / % & 0

. &D! B % # B &" " " " ) % . " , " #! # " #

! ! (& #) " # ! "& E# !0 ! 1 # ) " # % ! # " \ L8TNB # # #

,&" ! ! 'A ! 1 " ) !) # ! % # D " ! % CG " + "% ! 0

" " " ) 1 "% " # # P ! 67099098 (& & 5 #,& , "

! 0 ! ! G "% ! % ) 'A ! " ! " #,& , " ! % " !

#) # ! " &? et ac. L6HN0

! ?, ' ! ,& ! ! 1 "& ' ! 'A ! % " & (&

" %& !! ! G )& % P " "% - . 0

4.3.1 Parâmetros e variáveis utilizados

3 #! D! = 1, … , % ! "% !! ! )&$ ! ! % &' " !

! (&@#) ! " _{= 1, … ,} #- ! % ! " #&1 & # @# ) ! )# , ) " # %

(33)

19

macroperíodos (& ! !&. ! " = 1, … , & # !B ) " microperíodos0 3 "

) #! (&@#) #F" microperíodos ! 1 G B % D! - microperíodos ) ! !

) " (& # % &' 5 0 &" % & 1 ) % ! % &5 %C! &"micro

período ) ! B # ) set,up" # # ! #- ) " # " " # # 0

^ ! ,& # # ' % 1 "& % . " *

Parâmetros

"% &# % &' "% !! % # #- I" #O

)&! &# % &' "% !! % # #- I c &# O

)&! &# ! ) , " "% !! % &" macroperíodo %

& I cO

)&! set,up "% !! % # #- I cO

"% changeover "% !! % # #- I" #O

"% set,up "% !! % # #- I" #O

)&! changeover "% !! % # #- I cO

" # , , "% !! % # macr período I&# O

) % ) !% #/ % % &' "% !! ! # #- I&# O

) % ) !% #/ % #- # macroperíodo I&# O

"/# " % &' % "% !! % # #- I&# O

! (& # ) "% !! % # #/) % # $ " # I&# O

! (& ! ,& #' % "% !! % I&# O

"% " #& #' % # % #- I" #O

Variáveis de decisão

(& # ! (& "% !! % 1 # macroperíodo I&# O

(& # "% !! ! % % &5 ! # #- # microperíodo

! set,up0 = 1! #- ! % % % % &5 "% !! !

(34)

20

= 1 ! - changeover # #/) microperíodo # #- !

% % % % &5 "% !! ! % 0 I = 0) ! ) # O

= 1 se há " #& #' % # % , " # macroperíodo

microperíodo # #- B = 0B ! # 0

4.4 O MODELO_1

U6 % ! # ! ,& # 1 "& ' # ) *

%&'&%& ( ∑ ∑+ * _{+ ∑ ∑ ∑ (}0 * / ₊ ₊ ₎ _I9O

!0 *

+ ∑ ∑0 / ₌ _{+ = 1, ∀ ∈} _I6O

34+ ∑ ∑0 / = + ∀ ∈ 2, . . , , ∀ ∈ I8O

≥ ∀ ∈ , ∀ ∈ ISO

∑ ∑ (* / + + ₎_≤ _{− ∑}/ _{∀ ∈ , ∀ ∈} _ITO

∑ `

;4 = 1 = 1, = 1 (5)

∑/_{; `=4} = 1 = 1, = 2 (6)

∑ `

;4 = 1 = 2, = 1 (7)

∑/

; `=4 = 1 = 2, = 2 (8)

(35)

21

≤ ( 34− ) ∀ ∈ , ∀ ∈ , ∈ I69O

∑* + ≤ ∀ ∈ , ∀ ∈ I66O

∑* = 1 ∀ ∈ , ∈ I68O

≥ _{C 34}+ − 1 ∀ &, ∈ , & ≠ , ∈ , ∈ 2, … , I6SO

∈ E , ∈ E, ∈ F0,1G, ∈ F0,1G, ∈ F0,1G I6TO I6QO I6HO I6MO I6VO

.$ U6 I9O ? " # " 5 ! )&! ! % &' B ! (& B set,ups

changeovers0 )&! % &' 1 @# ) " ! ! #- ! ₍ _{= ∀ , )}B )&!

% &' ! # # % ! !) 1&#' .$ 0 ! ! 'A ! I6O

I8O ! ) # ! " % . " ! % # $ " # % &' 0 ! ! " # " ) #! '

1 &G " ! #, - 5 # % # $ " # 0 I ,& HO0 (& ! A !

"% ! ! .&!) " #& #' &" . " #/ ! ' B " # D! ?!

! ' ISO (& ! (& ! ,& #' ! !% 0 ! ' ITO " # (&

! " C ! "% ! % &' B changeover set,up !% ) % )

!% #/ B (& % !& 5 ? &5 % "% ! " #& #' % # 0 ! ! 'A ! IQOB

IHOB IMO IVO ! . ) " ) @#) &" " #& #' % # % #- # &"

% / % ?D " # 0 ! ' I7O " (& # "/# " ! % &5 % #-

% / ) ! ) set,upB & ! $ B % % ' % " #&1 & &" # % & 0

! ' I69O ) ) 5 3 ; % ! # " G J W ""! L6SN , # (&

% &' &" "% !! " " # % / !C % ) ! #- !

% % # #/) & # 1 # (& % / 0 3 " " ! &" % "% !! % !

% &5 % % / B ! ' I66O ? # &5 % " # ) % ) !% #/ %

micro período # ! " !0 3 " 1 # & #/) ) % / #- !

, # 5 . ! ) B ! ' ? " # ?! ! ' I68O0 ) # G #

(36)

" \ L8TN0 !

!0

Figura

4.4.1 Adioão de desiguald

! ?, '

(& !! # " I

; 0 !! " @"D! ! ! ,& #

' ! ! ,&

' ) % )

% / B !! (& # )

" # 0

+ ∑ ∑ (HI

JKI)

/

0 _≥

34+ ∑ ∑ (0 / _JH_KII) ≥

! ! 'A ! % ! # !

changeover !&.! & " !

22

! ! 'A ! I6TOB I6QOB I6HOB I6MO I6VO " # "

Figura 6 ! ' , . ) #! ' 1 &G

igualdades e restrioões reformuladas

! ,& ! ! 'A ! 1 "& !

U8O % !! ! G )& " " # "% % &

,& # ! 'A !*

! I67O I89O % 4 &G J Y ! \ LHN

!% #/ # % / ? " & ,& + (& #

) # ! (& % / # ! "

= 1, ∀ ∈

∀ = 2, … , ∀ ∈

# ! " I86O I88O % ! # " 1 "& ' "

! ' I6SO U60

" # " "/# !

U6 % "

&" " 5

LHNB ? % !

# % &5 #

! " & ,& +

I67O

I89O

(37)

23

≤ − ₃₄ ∀ ∈ , ∀ ∈ , ∈ 2, … I86O

≤ ∀ ∈ , ∈ , ∈ I88O

! ! ,& ! I8TO I8QO ! ) # ! ) " 1/) &' !% ' .&!)

! % ! Y ! \ LT9N0

≥ L A1 − ∑0 LB ∀ M ∈ 1, . . , , ∀ ∈ I8SO

L34≥ L A1 − ∑0 LB ∀ M ∈ 2, . . , , ∀ ∈ I8TO

4.5 O MODELO_2

U8B % # B % ! # ! ,& # 1 "& ' *

%&'&%& ( ∑ ∑+ * + ∑ ∑ ∑ (0 * / + + ) I8QO

!0 *

+ ∑ ∑0 / ₌ _{+ = 1, ∀ ∈} _I8HO

34+ ∑ ∑0 / = + ∀ ∈ 2, . . , , ∈ I8MO

+ ∑ ∑ (

HI

J_KI

)

/

0

_≥

_{= 1, ∀ ∈}

_I8VO

34

+ ∑ ∑ (

_JHI

KI

)

/

(38)

24

≥ ∀ ∈ , ∈ IS9O

≥ _L A1 − ∑0 _L_{B ∀ M ∈ 1, . . , , ∈} _IS6O

L34≥ L A1 − ∑0 LB ∀ M ∈ 1, . . , , ∈ IS8O

∑ ∑ (* / + + ₎_≤ _{− ∑}/ _{∀ ∈ , ∈} _ISSO

∑ `

;4 = 1 = 1, = 1 ISTO

∑/

; `=4 = 1 = 1, = 2 ISQO

∑ `

;4 = 1 = 2, = 1 ISHO

∑/_{; `=4} = 1 = 2, = 2 ISMO

≥ A − ₃₄B ∀ ∈ , ∈ , ∈ 2, … , ISVO

≤ ( 34− ) ∀ ∈ , ∈ , ∈ IS7O

∑* + ≤ ∀ ∈ , ∈ IT9O

∑* = 1 ∀ ∈ , ∈ IT6O

(39)

25

≤ ∀ ∈ , ∈ , ∈ ITSO

≥ 0 , ∈ E, ∈ F0,1G, ≥ 0, ∈ F0,1G ITTO ITQO ITHO ITMO ITVO

U8B !! " ) " U6B .&!) " # " 5 )&! ! % &' B ! (& B set,

ups changeovers0 (& ! 1 +! ! 'A !B U8 ? 1 " % ! ! 'A !

U6 ) !) # ! ! 'A !0 ! ! 'A ! I8VO I87O , # " # " # +

" # % ) % ) #! B ! 'A ! IS6O IS8O " # " (& ! (& ! #

% / % ) !! !&% " # #! " microperíodos !&.! (d # ! ? ! (&

# ) % &' "0 # " # ! ! 'A ! IT8OB ITSO " # " ) @#)

changeovers ! " # ! - & ) @#) set,ups# " !" % / # ) set,

up# % / % ) !! 0 ! ! ! (& changeover % ! # " "/# !

≥ 0 ≥ 0 I ! 'A ! ITQO ITVOO0 !! G ' !C ? "/# !

! I # !O (& ) "%A " ! % E" ! ! I. # !O (& % ! # " ! !

! # " I ! 'A ! I8MOB I8VO ! 'A ! ITSOB ITTOO0

4.6 ADÁLISE DOS DADOS

! G "% " #! &" ! & ' % # $ " # % &' # T % !

1 # ! "% !! ! " ! ! &! ! ! "& # " # " #! # !B ) !

! (&@#) ! " 8 #- ! " #&1 & 0 ! !& ! % % ! ! ! ) "% ! ) " &

! ?, % # $ " # % &' "% ! ! & 0

! ! % ! # ! 1 " ) ! ) " #, #- !B , # ! ?)# ) ! !% #! !

% % # $ " # % &' 0 (& ! A ! ! , ? ) B ! ! )&! ! % ! # !

1 " "& % ) ! % &" ) #! # σ " # # D! B % # B % % ) #

% ! # ! ! , # !0

"% &# % &' I: . 6O 1 . ?! # ! ) % ) # " #

) #- " #&1 & "& % ) % G % & " ) #- 0 #- 6

% ! # % & "? M8[ #(& # (& #- 8 % ! # % & "?

MQ[0 ! G 1 . ?! # ! - ! C ) % & 0 3 " !

% ! % & ! - ! C ) ! ) !% # " # ! Q[ "? B ) #! &D!

(40)

26

Tempo unit. (min.) ; #- 6 ; #- 8

"% !! 6 9BQQ 9BT7

"% !! 8 9BQS 9BTH

"% !! S 9BSQ 9BS7

"% !! T 9BTQ 9BTM

Tabela 1 : "% &# % &' "% !! % j# #- c

3 " "% ! ! & # % ! # ! )&! ! ! ) , " 1 " - B ! " D

! (& )&! &# ! ) , " I: . SO ) " ! # % G " " # Q[ ! )&! !

&# ! 1 . ) ' I: . 8O0

Custo unit. (U$) ; #- 6 ; #- 8

"% !! 6 699 669

"% !! 8 79 7Q

"% !! S M9 HQ

"% !! T MQ M9

Tabela 2 3&! &# % &' "% !! % j# #- c

Custo unit. Estocagem (U$)

"% !! 6 Q

"% !! 8 Q

"% !! S S

"% !! T T

Tabela 3 3&! &# ! ) , " "% !! % j &"macro período% &

set,up ) 1 # 5 &" & # % &' 0 !! 1 " B ? # ) !! &" "% %

! 5 ! . ! " ? % " . #) % &' , # 5 1 " # ! " (& # !

" ) #- 0 & B changeover ? "% # ) !! % ) #1 ,& ' #-

% ) % ! "% !! 0 3 " (& # % " ? % " ! 1 #) "

&" % "% !! % & B "% set,up I: . TO changeover I: . HO

".?" ! 1 #) "0 ) @#) ! set,up! changeover! &5 " ) % )

(41)

27

Tempo .

(min.) ; #- 6 ; #- 8

"% !! 6 S9 89

"% !! 8 89 8Q

"% !! S 8Q S9

"% !! T 88 89

Tabela 4 : "% set,up "% !! % j# #- c

)&! set,upI: . QO 1 ! " ) " ! # )&! % &# % &5

"% !! ! % &" % / % % ) # "% set,up0 ! ".?" ? 1 " )&!

(& "% ! & 5 % ! " ! &! )&! ! changeoverI: . MO0

Custo .

(U$) ; #- 6 ; #- 8

"% !! 6 M08STBSH V0769B99

"% !! 8 H0V6HB68 V0S68BQ9

"% !! S M07MSBQ8 H0HH8BQ9

"% !! T H0H6HBV9 Q07Q9B99

Tabela 5 3&! set,up "% !! % j# #- c

(min.) ; #- 6 ; #- 8

"% !! 6 899 889

"% !! 8 6V9 899

"% !! S 6H9 6V9

"% !! T 6V9 899

Tabela 6 : "% changeover "% !! % j# #- c

changeover ? ) &" % "% !! % & % # " !" #-

" #&1 & 0 !! 1 " B ! # ) !! ! ! ! 5 " # . #) B )

" (& # ! " #&1 & I)- " ! , , ! " #&1 & O #)- " # ! . #) ! ) " !

" ? !D% " ! # ) !! ! + % &' " # % & 0 % ) " # ! "

(42)

28

Custo

(U$) ; #- 6 ; #- 8

"% !! 6 860M9SB97 8H0MS9B99

"% !! 8 890TTVBSH 8T07SMBQ9

"% !! S 8S0789BQH 6707VMBQ9

"% !! T 670VQ9BT9 6M0VQ9B99

Tabela 7 3&! changeover "% !! % j# #- c

! ! " # I: . VO % ! # " ! % ! ) ! % "% ! ) # +

" #&1 & % & ! ># ) ! (& ! ! ! # # ! 0 ! ! ! " ! #

1 " ) "% " # )&"% ! # % # & 0 ) "% ' !& " ) "

& ) # % ! ! ) " " ! - ! # C% ) T070

Demanda (unid.) / 6 / 8

"% !! 6 6Q0999 690999

"% !! 8 6T0999 6Q0999

"% !! S 6S0S99 670999

"% !! T 6S0Q99 6Q0999

Tabela 8 " # , , "% !! % j# macro período t

! ! ) % ) # micro período I: . 7O 1 " $&! ! ?!

"& % ) ' % & % ) % ) # " # ) #- " #&1 & 0

; #- 6 ; #- 8

Capacidade: (min/turno) S9H 8V6

Tabela 9 3 % ) !% #/ % % &' "% !! # #- c% micro período

) % ) macro,perídoI: . 69O 1 $&! # " ) #! ' ! "% !

% ! ! % " #& #' % # 0 " #& #' ! #- ! " #&1 & " # "% !

1 #) ! % #- 0 !! 1 5 ) " (& ) % ) !% #/ % #- macro período

! $ 1 #) &" % / % & 0

Capacidade:

(43)

29

; #- 6 6VQ8H 6VQVH

; #- 8 6VQQH 6VQ8H

Tabela 10 3 % ) !% #/ % #- c# macro período t

"/# " % &' I: . 66O ? &" ! ?, & 5 % "% ! % !

) #) ) # " !) 0 ! ! ' 1 5 ) " (& ' &" #- % !! !

) "% #! % &" % &' "/# " 0

Lote mínimo (unid.) ; #- 6 ; #- 8

"% !! 6 699 899

"% !! 8 899 699

"% !! S 899 699

"% !! T 699 699

Tabela 11 ; "/# " % &' % "% !! % j# #- c

! (& # #/) - 5 # % # $ " # I: . 68O ? " # ) " &"

(& # % % ) # 8 ! " # ! % &' 0 # # B "% ! # " # ?" ! #/

! (& ! ,& #' ) " ! ?, &' )&! !0 !! 1 " B ) D! +

(& % # $ " # !% #! . # " # " # # % 5

% ! 0 !! "B ! " ) #! ! ! (& ! # ) ! ) " % E" !

# 0

Estoque inicial (unid)

"% !! 6 QH8H

"% !! 8 HSQ7

"% !! S TH9T

"% !! T T9QH

Tabela 12 ! (& # ) "% !! % j# #/) % # $ " #

! (& ! ,& #' I: . 6SO % # (& % ! F " - B & 'A ! !

(44)

30

Estoque de seguranoa (unid)

"% !! 6 6Q99

"% !! 8 6TS9

"% !! S 6Q69

"% !! T 6H89

Tabela 13 ! (& ! ,& #' % "% !! % j

"% "? " #& #' % # % #- I: . 6TO ? &" % E" (& &5

) % ) !% #/ % &' # ! micros,períodos " #- ! " #&1 & b # # # B

! ! ) #! % % " % # $ " # # ! ! " ! !% #/ !0

; #- 6 ; #- 8

Tempo de Manutenoão

(min):

79 689

Tabela 14 : "% " #& #' % # % #- c

4.7 RESULTADOS OBTIDOS

% ! # D! # !! C% ) " #- ) ' C " ! # ! #- ! " #&1 &

" # ! % " " #! # " # ! ! (& #) " # ! "& E# ! "

" (& # ! % !0 % # % &' ! % ! # # ) % ) B & ! $ B

!) # # D! "% ! set,up!Bchangeover! "% ! " #& #' % # 0 1 #

. ?"D! )&! "/# " 1 . ) ' 0

!& 1 # ) &" % # # , % &' ) # ) !A ! #/ ) B

I) " % G "% B (& # % &5 ! ) " ) "@!O #/ % ) # I) " %

G "% B (& " #- ! (&@#) ! ! # ! #- ! " #&1 & "% !! !O0

" 5 ! ! ! ) "%& ) # ! ) #! # micro período ) " ! # &"

% / (& # &" & # % &' B & ! $ B H - !0 3 " 1 . ) 1&#) # " 8

& # ! % ! ,&# ! . B "D! 68 & # ! % ! " # 0 "@! ? ) #! ) "

# TV & # !0 " B % # B .&!) " # % # $ " # 8 " ! ! % &' B

(45)

31

# ) & ,@#) B " #& #' % # # ? ! %& " - !

1 G !0 " # D! B % # B # "% (& " #& #' ! 5 0

G "% " (& ! B ! ) #! ! ! # ! & # 6 I = 1O & # 8S I ` = 23O

& # 8T I ` + 1 = 24O & # TV I = O0 !! ' ? % ! # # ! ! 'A ! ISQOB

ISHOB ISMO ISVO0 3 . " ) " - " " # " #& #' % # & #

- 5 # % # $ " # 1 " (& - $ " # # #' % !!/ # % &' 0

! : . ! 6Q 6H % ! # " % # macro % &' ! 8 " ! !0 ! % #

) #! ! ! ! (& # ) " # 0 % ! # "D! (& (& # , ,

! % &5 % % "% !! (& # ! ) B !% # ! (&

! ,& #' % % & #, "@!0

MÊS 1

(unidades) _{Estoque Inicial Produoão Demanda Estoque Final}

Impressora 1 QH8H 69VMT 6Q999 6Q99

Impressora 2 HSQ7 689SH 6T999 TS7Q

Impressora 3 TH9T 6TH9S 6SS99 Q79M

Impressora 4 T9QH 6S9S8 6SQ99 SQVV

Tabela 15 # " ) % &' % "@! 6

MÊS 2

(unidades) _{Estoque Inicial Produoão Demanda Estoque Final}

Impressora 1 6Q99 69VMT 69999 8SMT

Impressora 2 TS7Q 689SH 6Q999 6TS6

Impressora 3 Q79M 6TH9S 67999 6Q69

Impressora 4 SQVV 6S9S8 6Q999 6H89

Tabela 16 # " ) % &' % "@! 8

% # , , ? - #/ % ) # # ! . ! 6M 6V0 % ! # "D! (&

# ) !A ! ) ' ! (&@#) % &' "% !! ! # ! #- ! " #&1 &

I: . 67OB ) " ".?" ) !A ! " #! # " # ! ! % &' !% #