A Study of Design Method of Process and Layout of Parts and Facilities for Cell Production

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1 A Sudy of Design Mehod of Process and Layou of Pars and Faciliies for Cell Producion Mizuki Ohashi Graduae School of Engineering, Maser Degree Progra Nagoya Insiue of Technology, Nagoya, Japan Tel: (+81) , Eail: Masahiro Arakaa Graduae School of Engineering Nagoya Insiue of Technology, Nagoya, Japan Tel: (+81) , Takui Wada Graduae School of Engineering, Docor Degree Progra Nagoya Insiue of Technology, Nagoya, Japan Tel: (+81) , Eail: Keia Sugiura Graduae School of Engineering, Docor Degree Progra Nagoya Insiue of Technology, Nagoya, Japan Tel: (+81) , Eail: Absrac. In he curren producion environen, diversificaion of cusoer needs prooes he developen of ne producs and he producion of various ypes of producs. These phenoena can resul in facories requiring flexible producion syses in order o produce any ypes of producs ih a shor lead-ie. Cell producion syses are ordinarily inroduced for assebly processes ih a sall nuber of orkers. Because cell producion syses are effecive for flexibly producing any ypes of produc such syses require a reconsrucion of he process line and layou of he faciliy ihin a shor cycle. Hoever, process and ork designs are required in order for orkers o easily anage jobs because uliple anipulaing orks are assigned o every orker in cell producion syses. In his sudy, e develop a oal design syse for he processing and layou of pars and faciliies for cell producion ih high produciviy. The developed ehod is consruced fro hree ypes of design ehods based on a aheaical odel: process design, design of faciliy layou, and design of he layou of pars on he ork desk. In his paper, e discuss he characerisics of process and ork design in prooing he produciviy of cell producion. Then, e develop he ehods for process design, layou design of he faciliie and layou design of pars in he oal design syse. Nuerical experiens are perfored o evaluae hese design ehod including he developed algorihs. Keyords: Cell producion, Process design, Maheaical odel, Layou of Par Levelizaion 1. INTRODUCTION In he curren producion environen, diversificaion of cusoer's needs prooes a shorened developen cycle of ne producs. Many facories have inroduced cell producion syses in order o flexibly anufacure uliple ypes of producs. Ordinarily, cell producion syse denoes a producion syse coposed of a sall nuber of orkers or a single orker in a sall area (Iauro, 2002, Sakadue, 2004). Here, orker or a single orker, require he anipulaion of uliple ypes of jobs. I is knon ha cell producion is effecive for reducing he nuber of orkers and for flexibly anufacuring uliple

2 ypes of producs. Therefore, if he process line for cell producion syses can be auoaically consruced, he process line igh be flexibly reconsruced ihin a shor ie in order o anufacure ne producs. On he oher hand, cell producion syse requires orker's skill and raining for he design of an effecive process line ha includes orkers ho can anipulae uliple ypes of jobs. Therefore, consrucing an analysis odel for an effecive process line is difficul. We consider ha if process design, design of faciliies layou, and design of pars locaion are all inegraed, he process line could be flexibly reconsruced for cell producion syses ihin a shor ie because he resuling designs ould be quickly revieed. We sugges ha hese designs should be auoaically perfored and evaluaed for he ne process line o be effecively designed ihin a shor ie. In his sudy, e propose he ehods and algorihs for resolving he process design, faciliies layou, and pars locaion probles for he cell producion lines of uliple ies. We consruc an inegraed syse ha cobines hese designs and explain he syse in his paper. In addiion, e propose he ehods for resolving he process design and pars locaion probles. A nuerical experien is conduced for evaluaing he perforance of he proposed ehod and he developed algorih. 2. INTEGRATED SYSTEM FOR PROCESS DESIGN ON CELL PRODUCTION 2.1 Effeciveness of inegraed syse for process design Because cell producion syses are ordinarily consruced for uliple anipulaing job he efficiency of he producion syse depends on orker's skill and experience. This characerisic of cell producion syses denoes ha he conen of he jobs and anipulaing oveens included in such jobs require faciliaion in order o enhance syse produciviy. In order o faciliae he conen of he jobs and oveens included in such job a designer asked ih he consrucion of a producion syse is required o copleely and efficienly generae he os successful condiion for he aciviies in he operaion of orker such as anipulaing he oveen of orker sequencing job assigning jobs o ork cener locaing par and designing he faciliies layou. If ne producs ere inroduced ihin a shor cycle in facories for uli-ie producion, i ould be pracical and effecive for he facory anager o reconsruc he process line and evaluae he perforance of he designed line using he inegraed syse of process design, faciliies layou, and pars locaion. Maheaical odels are consruced in order o resolve he probles reaed in hese sub-syses. Oherise, opial algorihs are developed for resolving he probles. Because he aheaical odels or he opial algorihs can use daa fro he coon daabase of he inegraed syse differen sub-syses can be inegraed. The coplex anipulaion of orkers and coplex locaion of pars and faciliies are ordinarily odified in order o easily operae he cell producion syse based on he experience and skill of is orkers. Therefore, he aheaical odels or he opial algorihs are developed by considering characerisic easures in order o faciliae he conen of he jobs and oveens included in such jobs. By developing he aheaical odel and opial algorih i ould be expeced for an inegraed syse o be effecive hen consrucing a significan process line ihin a shor ie. 2.2 Characerisics of inegraed syse for design of process line Our inegraed syse is consruced fro hree subsyses: (1) process design ha includes job sequencing, (2) faciliies layou, and (3) pars locaion. A coon daabase based on engineering-bom (e-bom) is consruced in order o inegrae hese sub-syses. Figure 1 shos a scheaic diagra for he inegraed syse developed in his sudy. Work eleens are assigned o ork ceners by considering he precedence relaionship of such ork eleens aied a levelizaion for ixed producion (Monden, 2006) in subsyse (1). Then, in subsyse (2), he layou of he faciliies is consruced by considering he ork eleens assigned o he ork ceners by subsyse (1). In subsyse (3), he pars used for he ork eleens are locaed on he desk of each ork cener aied a reducing useless oveen and orker isake. Daa fro he coon daabase are used o execue hese subsyses. Here, daa fro he coon daabase are coposed of daa for ork and produc inforaion as e- BOM. The folloing secions explain he aheaical odel and opial algorih for resolving he proble reaed in each subsyse. Process Design Design of Faciliy Layou Design of Pars Layou The coon daabase Work Inforaion Produc Inforaion (e-bom) Figure 1: Scheaic diagra for consrucion of inegraed syse developed in his sudy

3 3. PROCESS DESIGN PROBLEM 3.1 Characerisics of process design proble for cell producion We consider he process design proble here ork eleens are assigned o uliple ork ceners in order o anufacure uliple differen producs. The condiions of his proble are assued o be as follos: (1) The nuber of orkers is equal o or greaer han o, (2) The precedence relaionship of he ork eleens is predeerined ih regard o all produc (3) The operaion ies of he ork eleens are predeerined. We consider o ypes of operaions in order o consruc a ixed producion line for cell producion. One operaion is here ork eleens are assigned o ork ceners aied a generaing a line balance for each produc in order o enhance he produciviy of he ixed producion line. We call his operaion, Operaion (a). Figure 2 shos he scheaics diagra for Operaion (a). If orker ravel ie is negleced, he line for cell producion could be regarded as a linear ype for he process design (Rekiek e al., 2005). If operaion ie balancing ere generaed aong orkers in he line for each produc, produciviy ould be enhanced in he ixed producion line because he operaion spare ie could be reduced in he ork ceners. When operaion ie line balancing is generaed for each produc, he designed process line is no influenced by he differen producion proporions. Maerial Operaion Tie Produc B Work eleens of differen producs Produc A Produc Cycle Tie of Produc A CT (Produc B) CT (Produc C) Produc A Produc B Produc C Figure 2: Scheaic diagra for design of process line by line balancing each produc for ixed producion line Furherore, he proposed process design includes an assignen ehod for orks in order o reduce in-process invenory beeen ork ceners. We call his operaion, Operaion (b). Figure 3 shos he scheaics diagra for Operaion (b). When he operaion ie a he ork cener for pos-processing is larger han ha a he ork cener for pre-processing, an in-process invenory is generaed in fron of he ork ceners for pos-processing, as shon in Figure 3. We propose assigning ork eleens o ork ceners so ha he operaion ie of he ork ceners for pos-processing can be saller han ha of he ork ceners for pre-processing. We propose an assignen ehod ha considers Operaions (a) and (b) siulaneously. Operaion ie Figure 3: Scheaic diagra for design of process line ha includes assignen of jobs for reducing invenory beeen ork ceners 3.2 Maheaical odel Work ceners 3 The aheaical odel ha includes Operaions (a) and (b) is consruced as follos: Paraeers i:work eleen (i {1,2,,I}), k:work cener (k {1,2,,K}), l:produc (l {1,2,,L}), i:average operaion ie of ork eleen i, d i:operaion ie dispersion of ork eleen i, h il: The paraeer is equal o 1 hen ork eleen i is included in Produc l. Oherise, he paraeer is 0, M:Large posiive nuber. Variables: u i:work cener o hich ork eleen i is assigned (u i {1,2,,K}) δ i k:when ork eleen i is assigned o ork cener he variable is equal o 1. Oherise, he variable is 0. η kl:when he operaion ie of ork cener k-1 is saller han he operaion ie of ork cener k ih regard o Produc l, his variable is equal o 1. Oherise, his variable is 0. a kl:difference beeen operaion ies of ork cener k and he axiu operaion ie of a ork cener before ork cener k ih regard o Produc l. When operaion ies of ork cener k is equal or saller han he axiu operaion ie of a ork cener before ork cener k ih regard o Produc l, his valuable is 0. In addiion, a 1l is equal o 0. σ kl :When a kl is a posiive nuber ih regard o Produc 0

4 l, his variable is equal o a kl. Oherise, his variable is 0. Objecive Funcion: L Min C ax l l=1 L K Min σ kl s.. l=1 k=1 L C ax,l δ ik h il i K δ ik = 1 k=1 I l=1 i=1 (1) (2) l (3) i (4) k + M(δ ik 1) u i i, k (5) u i K(1 δ ik ) + k i, k (6) u i u j i j (7) a 1l = 0 l (8) I a kl = (δ ik h il i δ ik 1 h il i ) i=1 k=[2,k] l a kl M η kl l (10) η kl 1 + a kl l (11) M M(1 η kl ) + a kl σ kl l (12) σ kl a kl + M(1 η kl ) l (13) σ kl η kl M l (14) 0 σ kl l (15) This proble is reaed as a uli-objecive proble. Equaions (1) and (2) are objecive funcions. Equaion (1) denoes he su of he axiu operaion ie in all ork ceners for each produc ih regard o all producs. Equaion (2) denoes he su of he oal difference of operaion ies beeen ork ceners for each produc ih regard o all he producs shon in Figure 3. When he operaion ie of he ork cener for pos-processing is larger han ha of he ork cener for he pre-processing of a produc, he difference in operaion ies beeen he ork ceners is calculaed in Equaion (2). Equaion (3) denoes he consrain equaion ha calculaes he axiu operaion ie in all he ork ceners for each produc. Equaion (4) denoes he consrain equaion here ork eleen i is alays assigned o a single ork cener. Equaions (5) and (6) denoe he consrain here u i is equal o k hen ork eleen i is assigned o orksaion k. Equaion (7) denoes he consrain equaion for he precedence relaionship of o ork eleen i and j. Here, Equaion (7) indicaes ha ork eleen i precedes ork (9) eleen j. Because here is ordinarily a precedence relaionship in uliple ork eleen uliple equaions relaed o Equaion (7) are prepared. Equaions (8) o (15) denoe he consrains for calculaing σ kl hen he operaion ie of ork cener k is larger han he axiu operaion ie beeen he firs ork cener and ork cener k-1. In his sudy, he objecive funcion in Equaion (2) is odified as a consrain equaion using he axiu value of he funcion in order o resolve he uli-objecive proble. 3.3 Nuerical experien A nuerical experien is conduced o evaluae he perforance of he proposed process design using a aheaical odel. Gurobi Opiizer (Ocobersky Co., Ld.) is used o resolve he aheaical odel. Three producs are assued o be anufacured in he process line: Producs A, B, and C. The nuber of ork ceners is assued o be five. The aoun of ies produced for Producs A, B, and C is 100, 220, and 100, respecively. These producs are assued o be siilar. The nuber of ork eleens for Producs A, B, and C is 11, 11, and 13, respecively. Table 1 liss he operaion ies of he ork eleens for hese producs. Figure 4 shos a diagra of he precedence relaionship of he ork eleens. The ork eleen nubers shon in he preceding relaionship are idenified ih he ork eleen nubers lised in Table 1. Produc A is a core produc. Produc B is a produc ha uses several alernaive pars in Produc A. Produc C is a produc consruced by adding pars o Produc A. We copare o process lines in he Pareo soluions obained by he aheaical odel: he process line here he iniu value of he su of he axiu operaion ie in all he ork ceners for each produc is obained (e call his line, Process design 1 ), and he process line here he iniu value of he su of he oal difference of he operaion ies beeen he ork ceners for each produc ( Process design 2 ) is obained. Wih regard o Process design 1, he su of he axiu operaion ie in all he ork ceners for each produc is 71.0, and he su of he oal difference of he operaion ies beeen he ork ceners for each produc is Wih regard o Process design 2, he forer funcion is equal o 74.0 and he laer funcion is equal o 0.0. Figures 5 and 6 sho he disribuion of he operaion ies of Process designs 1 and 2, respecively. Figure 7 shos he siulaion resuls of he produciviy for boh designed lines. Arena (Rockell Co., Ld.) (Kelon e al., 2007) is used for he siulaion. The copleion ies of all producs is calculaed by a siulaion under differen lo sizes. ( ) indicaes ha one lo size for Producs A, B, and C is equal o 50, 110, and 50, respecively.

5 Copleion ie Operaion ie Operaion ie Rando indicaes ha single producs are randoly hron in he line. In addiion, Figure7 shos a coparison of he lines ih and ihou buffers beeen ork ceners in he siulaion. A siulaion is conduced ih 100 rials. Bars denoe he average of he copleion ies for he producion of all producs obained fro all rials. The resuls indicae ha Process design 1 could produce all ies ihin a shorer copleion ie han Process design 2. Hoever, he difference of he copleion ie beeen Process designs 1 and 2 is several percenages of he copleion ies for boh process designs. In addiion, he copleion ies for boh process designs are shorer han he copleion ie calculaed ih convenional ehods in he previous sudy (Wada e al., 2014). Because line balancing for levelizaion is considered for boh process line e believe ha he copleion ies calculaed a differen lo sizes are siilar o each oher. The line ih buffers requires a 20% shorer copleion ie han he line ihou buffers. Wih regard o he lines ih buffer he averages of he oal in-process invenories are 20.8 and 10.0 a Process designs 1 and 2, respecively, hen single producs are randoly hron in he lines. Alhough he values of he in-process invenories for boh process designs are sall, saller in-process invenories are preferred because orkers operae in sall areas of cell producion syses. These resuls sho ha he proposed aheaical odel ha considers levelizaion generaes preferable process lines for ainaining produciviy ih differen lo sizes. Table 1: Operaion ie of ork eleens for anufacuring producs No. indicaes ork eleens nuber. Ave. and Sd- Dev. denoe average and sandard deviaion, respecively Produc A Produc B No. Operaion ie No. Operaion ie Ave. Sd-Dev. Ave. Sd-Dev Produc C (Produc A + No.16,17,18 ) Figure 4: Diagra for precedence relaionship of ork eleens Figure 5: Operaion ies of Process design Produc A Produc B Produc C Work cener Figure 6: Operaion ies of Process design Produc A Produc B Produc C Work cener Process design 1 Process design 2 No buffer Buffer No buffer Buffer ( ) 2 Rando Figure 7: Siulaion resuls for produciviy of boh designed lines

6 4. PARTS LOCATION PROBLEM 4.1 Proble characerisics In his secion, he proble of deerining he locaions of he pars is discussed by considering he ork eleens ha use he pars a each single ork cener afer he ork eleens have been assigned o he ork ceners. In his proble he pars are locaed on he desk aied a iniizing he oveen of he orker s hands hen picking up he pars in order o enhance produciviy a each ork cener. In addiion, he locaion of he pars is calculaed in order o avoid losing such locaion by considering he process order of he ork eleens assigned o each ork cener. The issues included in he pars locaion proble are as follos: (1) Miniizaion of he oveen of he orker s hands hen picking up he pars. (2) Reducion of issing he locaion of he pars hen picking up he pars. The locaion of he pars is considered o be he desk a he ork cener. The raveled disance of he orker s hands hen picking up he pars is iniized in order o resolve issue (1). The differen pars are locaed close o each oher hen he pars are coninuously used, according o he order of he ork eleen in order o resolve issue (2). We consider ha he orkers could reduce issing and isaking he pars hen picking up he coninuously a nearby locaions in he order of he jobs. In his sudy, a aheaical odel is consruced in order o resolve he pars locaion proble ha considers boh issues. In he odel, issue (1) is adoped as he objecive funcion and issue (2) is adoped as he consrains relaed o he disance beeen he locaions of he pars of coninuous ork eleens. 4.2 Maheaical odel Consrucion of aheaical odel Figure 8 shos a scheaic diagra of he odel used o resolve his pars locaion proble. The pars are assued o be locaed a he cells in he grid on he desk in he odel. The desk is regarded as a single ork cener, and a single orker operaes he ork eleens on he desk. The aheaical odel is consruced as follos: Paraeers: i, j: The coordinaes of he cells for locaing he par : The pars nuber, : The ork eleen nuber ha coincides ih he order nuber of he ork eleen, n : The nuber of par o use, d i, j: The disance beeen he ork area and cell (i, j). Variables: η i,: When par is locaed a cell (i, j), he variable is equal o 1. Oherise, he variable is 0, δ : When par is used for ork eleen he variable is equal o 1. Oherise, he variable is equal o 0, p i, : When δ and η i, are boh equal o 1, he variable is equal o i. Oherise, he variable is 0, q i, : When δ and η i, are boh equal o 1, he variable is equal o j. Oherise, he variable is 0. Objecive Funcion: i j Min d i, j i, n s.. i j i, 1 i M( i, 2) pi, (16) (17) i, (18) pi, ( i, p i, M p i, M i, M 2) i i, (19) i, (20) i, (21) j M( i, 2) qi, i, (22) qi, ( i, q i, M q i, M i, M 2) j i, (23) i, (24) i, (25) x p p i, i, i,, 1 (26) y q q i, i, i,, 1 i, j,,, k, s, i ax (27) x L i, i, j,,, k, s, j ax (28) y L i, (29) Equaion (16) denoes he objecive funcion and iniizaion of he oal raveled disance of he orker s hands o pick up he pars. Equaion (17) indicaes ha every par is locaed a a single cell. Equaions (18), (19), (20), and (21) denoe he consrain equaions ha cause p i, o be equal o i hen δ and η i, are boh equal o 1. In addiion, Equaions (22), (23), (24), and (25) denoe he consrain equaions ha cause q i, o be equal o j hen δ and η i, are boh equal o 1. Equaions (26), (27), (28), and (29) denoe he consrain equaions here he desire is for he differen pars o be locaed close each oher hen he pars are used coninuously according o he order of he ork eleens. Here, he absolue values included in Equaions (26) and

7 (27) are convered o linear equaions using indicaor variables. L i-ax and L j-ax are he axiu disances beeen he differen pars used in he coninuous ork eleens. These disances are predeerined o be consan nubers. Because here is a radeoff relaionship beeen he oal raveled disance of he orker s hand and he axiu disances beeen he differen pars of he coninuous ork eleen Pareo soluions can be generaed by resolving he aheaical odel under he condiion ha differen nubers are predeerined as he axiu disances Nuerical experien A nuerical experien is conduced o evaluae he perforance of he aheaical ehod. Table 2 liss he pars used for he ork eleens according o he order of he jobs. The ork eleen nubers correspond o he order nuber of he jobs o be processed. Gurobi Opiizer (OcobersSky Co., Ld.) is used o resolve he aheaical odel. Li-ax and Lj-ax are predeerined o be he axiu lengh of he area of he grid. They indicae ha he disance beeen he pars of he coninuous ork eleens are no considered in his experien. Figure 8 shos he resuls obained fro he aheaical odel. The sybols locaed in he cells in he grid indicae he locaions of he par and he filled circle denoes he cener of he ork area. All cells denoe he candidaes of he locaions of he pars sough by he aheaical odel. Par e is locaed a he neares cell fro he ork area because his par is used he os. Par a is locaed a he farhes cell fro he ork area because his par is used he leas. Figure 8 shos ha he axiu disance beeen he differen pars used coninuously corresponds o he disance beeen Pars a and d. The value of he objecive funcion is These resuls denoe ha he nuerical odel could generae he appropriae resuls for his proble. Table 2: Lis of pars used for ork eleens according o job order Work eleens Pars nuber d e e c b d a b e c 4.3 Geneic algorih d a b e Model for geneic algorih When e aep o resolve large-size probles for he pars locaion, he aheaical odel can be difficul o use because i requires long copuaional ie. Therefore, e develop a Geneic algorih o resolve largesize probles. Siilar o he previous secion, he objecive funcion is he oal disance raveled beeen he pars locaions and he ork area. The oal raveled disance is adoped as he finess of he algorih. The locaion candidaes are prepared on cells in he grid on he desk in order o seek he opial locaions for he differen pars hen consrucing he aheaical odel Chroosoe represenaion A chroosoe is an array of pars nubers locaed on he cells. The eleens of he chroosoe array are assigned o he cells in he grid, as shon in Figure 9. When no par is assigned o he cell, he eleens ha correspond o he locaions are equal o zero. This assignen of chroosoe eleens o cells is adoped in order o effecively locae he pars close o he ork area in differen chroosoes. The populaion is equal o 100 individuals. The axiu generaion is 100. A o-poin crossover is used as he crossover process. The uaion process is used hen child chroosoes are idenical o each oher a he crossover process. In he uaion proces a sapping process for nubers a o arbirary eleens of he chroosoe and a shifing process fro he arbirary eleens of he chroosoe are execued a arbirary ies by he generaion of differen chroosoes. In he selecion process for he nex generaion, elie and roulee selecions are used o choose 25 and 75 individual respecively. c Work area Figure 8: Resuling layou for pars calculaed by aheaical odel

8 The oal raveled disance Figure 9: Chroosoe represenaion and relaionship beeen cells and chroosoe eleens Nuerical experien In order o evaluae he effeciveness of he developed algorih a nuerical experien is perfored. Fir he proble of he en ork eleens and five pars lised in Table 2 is resolved by he developed algorih in order o copare ih he resul obained by he aheaical odel. The oal raveled disance calculaed by he developed algorih is 14.89, and i is he sae as ha calculaed by he aheaical odel. Alhough he resuling locaions of he pars are differen fro hose obained by he aheaical odel, boh resuls sho he sae characerisic relaionship beeen locaions and pars. Table 3: Relaionship beeen pars and ork eleens Pars Work eleens Pars Work eleens a 5, 30, 47, 48 g 4, 11, 13, 14,19, 25, b 6, 9, 26, 33, 43 35, 37, 39, 42, 45 c 8, 10, 24, 27, 38 d 18, 40, 49 h 15, 41 e 1, 17, 20, 21, 28, i 7, 12, 22, 31, 46 29, 34, 36, 44 j 2, 3, 16, 32 f 23, 50 Second, he developed algorih is perfored for large-size probles in order o invesigae he characerisics of he resuls as bi-objecive funcions of he oal raveled disance and axiu disances beeen he differen pars used in he coninuous ork eleens. The proble of 50 ork eleens and en pars is used. Table 3 liss he relaionship beeen he pars and ork eleen nubers. The ork eleen nubers correspond o he order of he jobs. When he developed algorih resolves he proble as a bi-objecive proble differen consan values are deerined for he nubers of L i-ax and L j-ax. Here, boh nubers indicae disance beeen differen cells. Figure 10 shos he pars locaions calculaed by he developed algorih hen boh L i-ax and L j-ax are equal o 3 or 5. This figure shos ha pars g and e are locaed a he neares locaions fro he ork area in boh condiions. When boh L i-ax and L j-ax are a large nuber, he oal raveled disance is a value saller han ha obained under anoher condiion. Figure 11 shos Pareo soluions calculaed under differen condiions for L i-ax and L j-ax. This figure denoes he radeoff relaionship beeen he oal raveled disance and axiu disance in he axis direcion beeen differen pars used in he coninuous ork eleens. When axiu disance in he axis direcion beeen differen pars is equal o 2, no soluion is obained. These resuls indicae ha his proble is required o be calculaed as a bi-objecive proble and he developed GA is effecive for resolving he proble. (a) L i-ax=l j-ax=3 Figure 10: Resuling pars locaions calculaed by he developed algorih CONCLUSION (b) L i-ax=l j-ax= The axiu disance in he axis direcion Figure 11: Pareo soluions obained by he developed GA In his sudy, e proposed aheaical ehods and algorihs for resolving process design and pars locaion probles for he cell producion line of uli-ie producion. We consruced an inegraed syse ha cobines hese designs. The resuls of he nuerical

9 experien shoed he effecive perforance of he proposed ehod and developed algorih. In a fuure sudy, he characerisic operaions based on orker's skill and a corresponding experien ill be analyzed, and he ehods ill be odified o consruc a process line ha ill include he characerisic operaions in he cell producion syse. The developed inegraed syse ill be adoped o consruc a process line in real facories. In addiion, opial algorihs ill be developed for hese probles in order o calculae large-scale probles. ACKNOWLEDGMENTS This ork as suppored by he Gran-in-Aid for Scienific Research (C) (15K01186) fro he Japan Sociey for he Prooion of Science. REFERENCES Iauro, H.(2002) Cell Producion Syse Nikkan Kogyo Shinbun, LTD,p (in Japanese). Kelon, W.D., Sadoski, R.P. and Surroc D.T. (2007) Siulaion ih Arena, Corona Publishing Co. LTD (in Japanese). Monden, Y. (2006) Toyoa producion syse Diaond Inc., (in Japanese). Rekie B. and Delchabre, A. (2005) Assebly Line Design, Springer, pp Sakadue, Y. (2004) Why is coninuous iproveen process required afer cell producion syse is inroduced?, IE Revie Vol.45, No.2, p.6-13 (in Japanese). Wada, T. and Arakaa, A. (2014) A Sudy of Process Design for Manufacuring Line aied a Levelizaion and Produciviy on Mix Producion, Proceedings of he Asia Pacific Indusrial Engineering & Manageen Syses Conference 2014 (APIEMS2014),