Prceedings f the 2010 Internatinal Cnference n Industrial Engineering and Operatins Management Dhaka, angladesh, January 9 10, 2010 Cmparative Study between Mixed Mdel ssembly Line and Flexible ssembly Line ased n Cst Minimizatin pprach F.. Rajput, Z. Othman, and. Suhail Schl f Mechanical Engineering Universiti Sains Malaysia, 14300 Nibng Tebal, Pulau Pinang, Malaysia bstract Mixed Mdel ssembly Lines are widely used t prduce different mdels as per custmer s demands. The Sequencing is an imprtant factr fr an efficient use f Mixed Mdel ssembly Lines. We reslved the sequencing prblem in favr f minimizing the ttal cst and keeping unifrm usage f each part and cst mdel is presented. T get merits and demerits between Mixed Mdel ssembly Line and Flexible ssembly Line, a cmparisn is dne, cncerning sequencing prblem. The utcme f this research suggests best sequence, which gives cntinued cnsumptin f parts and cst saving as well, reducing cycle time wuld prvide higher prductin. Keywrds Mixed mdel assembly line, Flexible assembly line, Cst mdel, Sequencing, Cycle time. 1. INTRODUCTION In this era f business, manufacturers must be able t prduce multi-mdel f the prducts, in rder t meet custmer demands. Different mdels f a prduct ften require different cycle times fr assembling. Frm a flexible assembly system pint f view, different mdels are assembled in different prcessing times and in separate assembly lines althugh, multiple prductin lines might nt be feasible, ecnmically [1]. Therefre, fr reducing csts, different mdels f the prduct must ften be prduced n the same line. T bserve the effect f different parameters n ttal cst f finished gds, a cmparisn is carried ut between mixed mdel assembly line (MML) and flexible assembly line (FL) based n a cst minimizatin apprach. The bjectives f this research are as fllws; The main bjective f this prject is t present the cst mdel and cmpare the perfrmance f MML and FL with respect t cst savings. Csts are included, rdering cst f parts, hlding cst f parts, line setup cst fr each mdel, hlding cst f finished gds, penalty cst fr late delivery f finished gds. The secnd bjective is t keep the cnstant cnsumptin f each part in the assembly line. 2. Previus related wrk Cst ptimizatin fr mixed mdel assembly system is cncerned with parameters f mdel size, cycle time, jb sequence, and wrk statin. nalysis f these parameters acquiesce the cst slutin effectively - Variable cycle times gives lesser hlding cst f manufactured prduct [1]. Hyun et al. [2] presented paper regarding minimizatin f the ttal utility wrk, thrugh keeping a cnstant usage f parts and minimizing ttal setup cst. genetic algrithm (G) was designed t find near-paret ptimal slutins fr the prblem. The results expsed that the prpsed G was exceptinally result-riented and that was als implicated fr diverse setup cst. Miyazaki [3] cmpared inventry cst f parts between pull systems and parts-riented prductin systems. The parts riented system indicates fewer inventry csts with larger variatin f parts demand, larger prductin stages and higher safety stck level. One year later, Sarker and Pan [4] wrked t minimize the ttal cst f the utility time and idle time, which ccurs due t different line parameters, such that launch interval, statin length, starting pint f wrk, upstream walk and peratin sequences f the mixed mdels. The result indicates that pen statin system prvides minimum ttal cst than clsed-statin fr a given line length. Pesenti and Ukvich [5] and Meyr [6] wrked n scheduling f multiple prductin lines. They suggested that
multiple prductin lines yields minimizatin f large prductin, setup, inventry, and penalty csts. number f authrs presented varius cst mdels. s Heike et al. [1] analyzed inventry hlding cst, which was affected by the cycle time. ut the researchers did nt highlight the penalty cst fr late delivering f finished gds and als rdering cst f raw materials. In rder t minimize the setup cst within MML, a cst mdel was presented by researchers (2, 7). ccrding t Tyta Prductin System (TPS), each type f mdel prduces within ne assembly line and average cycle time is cnsidered fr each mdel [8]. ut, in this research, cycle time is varied fr each mdel t bserve the effect n ttal cst - Variatin f cycle time wuld indicate the effect n cnsumptin f parts. In the current research, ne assembly line is assumed t assemble the mdels within MML with zer length and n setup is required [9]. While in FL, different setup is required fr different mdels. nd, t bserve the effect f cycle time n cst, the cycle time is varied fr each mdel [1]. The abve researchers gave the idea f MML with setup/change ver cst. ut the current research gives a unique idea with zer setup fr MML. Saving csts is the main prblem in manufacturing industries. s, Pesenti and Ukvich [5] and Meyr [6] prpsed multiple prductin lines - multiple prductin lines can reduce penalty csts, but here, a critique can be made, in this case, setup cst is higher, because different mdels are prduced with different setups and this is als kind f flexible system. On ther hand, in real life, demand is nt remained same, s if demand is just fr ne r tw mdels then ther lines vestiges idle and labrs and equipments are als becme idle as well and this idle resurces are induced fr higher carrying cst r hlding cst. 2.1 Prblem identificatin Over the last decade, researchers have been wrked within MML and they have been slved MML prblems by using different techniques. We studied different papers regarding t keep cnstant parts cnsumptin and t minimize the cst fr MML. Mstly, researchers discussed fr keeping cnstant parts cnsumptin with sequencing prblem [9-16]. ut, in this research study, we reslved the sequencing prblem in favr f saving cst prductin sequence is directly prprtinal t prductin cst, as sequence is cntrllable activity and prper sequencing prvides cntinue cnsumptin f each part and ultimately prvides better cycle t fulfill the marketing demands, withut backlg demand and hlding cst [8,17]. 3. n industrial example n autmbile firm is situated in Malaysia, cnsist f MML and FL, prducing tw mdels f car in MML and tw mdels in FL. Its prductin planning department dispatches the schedule t bdy shp, paint shp and assembly shp. The prductin planning data cnsists f sequence and prductin quantity, the sequence and prductin quantities are illustrated in the fllwing Table 1. These different sequence are, and with same prductin quantity but different jb rders were tested in simulatin experiment. The prduct has an internatinal Market, the demand f mdel is cnstant, while demand f mdel is randmly changed. nd als demand f mdel is higher than mdel. MML is equipped with verhead cnveyr t deliver parts and autmated guided vehicles t mve partially assembled units n the line, an electr-cating painting line, a machine and a welding shp which bradly ccupy rbts. While in FL, mdels are line in, manually, parts and subassemblies are either made in huse r purchased frm dmestic and freign vendrs. In this research, lcal vendr is cnsidered fr delivering the parts n zer lead time basis [18]. 4. Mdeling prductin line Simulatin prgram was develped fr MML and FL, and simulatin was carried ut thrugh MTL prgramming methd - MTL is a sftware package, which culd simulate and analyze the data [19]. T get steady result, simulatin was run till 2000 days fr bth MML and FL. In case f FL, line changever r setup is required, prductin line was simulated with cnsidering three different prductin line statuses. Status 0, in which finished prcessing a mdel type and setup nt dne yet, status 1, in which finished prcessing a mdel type and setup dne fr new mdel and status 2, in which unfinished prductin f a mdel type. The simulatin began with n wrk-in-prcess (WIP) in the system. 5. Cst mdel T calculate the different type f cst in MML & FL, the cst mdel is develped. These csts are cmputed by
MTL prgramming and by mathematical frmulatins. T check the cst is either crrect r nt, a cmparisn is made between cdes & mathematical frmulatins. The result shws similarity by prgramming and mathematical frmulatins. This shws that develped prgram can predict the different csts. The cmparative results are shwn in Table 2. Table 1: & prductin quantity Jb rders 1 4 6 4 6 4 6 2 6 9 6 9 6 9 3 8 12 8 12 8 12 4 10 15 10 15 10 15 5 12 18 12 18 12 18 6 14 21 14 21 14 21 7 18 27 18 27 18 27 8 20 30 20 30 20 30 9 24 36 24 36 24 36 10 28 42 28 42 28 42 T determine the day, in which csts are repeated, least cmmn multiple (L.C.M) is carried ut between daily wrking time and cmpletin time f a cycle f the sequence. The btained L.C.M is 13, it is als examined that after every 13 th day, each csts are repeated. T cmparing the result, a prgram and cst mdel frmulatin is develped till 13 th days. nd t determine, hw many times cycle f the sequence is repeated in 13 th day. This technique will give apprpriate slutins abut hlding units r backlg units. Fr this, we develped the relatinship between; 1- Day after which sequence f mdels is repeated. 2- Time left per day. 3- Ttal time in which ne cycle f sequence is cmpleted. fter assuming these parameters, we fund exact time in which sequence f the mdels is repeated. Mathematically, nc = d * TL TL t (1) 5.1 verage rdering cst f parts Parts are delivered n zer lead time basis, whenever parts are required then rdered as per prductin demand, rdering cst f parts is calculated mathematically as; GC = OS * (2) G i G i ( t) = GC (3) G i ( t) G i ( a) = (4) d 5.2 verage hlding cst f parts It is experienced that there is very much flexibility n parts cnsumptin fr different mdel. ecause the rder is placed, when inventry f parts dn t meet the prductin, s each day s ending stck f parts is different and it culd nt be determine thrugh the frmula. Therefre, t determine the hlding cst f parts, it must be simulated till 13 th days.
c = 4 13 H ( t) H ( t) (5) i i = 1i = 1 i c H i ( t) H i ( a) = (6) d 5.3 verage set up cst In case f FL, setup is required fr each new mdel. Setup cst S j (t) fr mdel j type at the end f t th day, can be calculated with the relatin f nc cycle f assembled mdels and setup cst f mdel j type. Mathematically, the equatin is written as; S j ( t) = m j * nc * S j (7) 5.4 verage hlding cst f finished gds verage hlding units F j (a) prductin CP ; f j type per day { j =, } are calculated with the cnsideratin f ne cycle CP F j ( a) = 2 (8) F j ( t) = F j * F j ( t) (9) F = j ( t) F ( t) j = 1 j (10) The fllwing ntatins are cnsidered t cmpute the discussed csts. c Hi (t) = Cumulative hlding cst f parts i type at the end f t th day {i = P1, P2, P3, P4} G i = Ordering cst f parts i type {i = P1, P2, P3, P4} c Fj (t) = c S j (t) = Cumulative hlding cst f finished gds j type at the end f t th day { j =, }. Cumulative Set up cst fr mdel j type at the end f t th day { j =, }. CP = One cycle prductin. OS = Ordering N. f parts in nc cycle. G i (a) = verage rdering cst f parts i type per day. H i (a) = verage hlding cst f part i type per day. nc = Six sequence cycles (6 times schedule f the mdels is repeated in a derived average day). mj = Mdel f j type line in - in different time. GC = Ordering cst f parts in nc cycle. d = verage day (13 th day after this each cst is repeated) TL = Time left per day TLt = Ttal time in which ne cycle f sequence is cmpleted
6. Results and discussin Reslving sequencing prblem regarding cst minimizatin and keeping unifrm cnsumptin f parts, results are as fllws, which shws, hw cst becmes higher r lwer n the basis f discussed parameters. Table 2: Cmparisn between mathematical frmulatin & prgramming Csts y mathematical frmulatins y prgramming Ordering cst f parts 126.92 126.92 Set up cst 6.46 6.46 Hlding cst f finished gds 1040 1040 Hlding cst f parts -- 42.96 Effect f different parameters in MML & FL 6.2 Cycle time 15-20 at cnstant demand fr MML The average ttal cst fr MML at cycle time 15-20 fr each mdel is shwn in Table 3. Maximal cst ccurs at jb rder {1} f sequence pattern, where prductins are 52000 at demand 80000. nd minimal cst ccurs at jb rder {2} f sequence pattern, where prductins are 53332 at demand 80000. Hence the best sequence pattern is and its jb rder {2}. Table 3: verage ttal cst fr MML cycle time 15-20 at cnstant demand Csts Prductins Demands 4 6 173525 53334 80000 6 9 173527 52000 80000 6 9 173519 53332 80000 6.3 Cycle time 15-20 at randm demand fr MML While Table 4, at randm demand indicates that maximal cst ccurs at jb rder {3} f sequence pattern, where prductins are 53336 at demand 50505. nd minimal cst ccurs at jb rder {6} f sequence pattern, where prductins are 52500 at demand 50240. Therefre, feasible sequence pattern is alng with its jb rder {6}. Table 4: verage ttal cst fr MML cycle time 15-20 at randm demand. Cst ($) Prductin Demand 14 21 28301 52500 50240 18 27 33036 53501 50061 8 12 35964 53336 50505 6.4 Cycle time 25-30 at cnstant demand fr MML The belw Table 5 shws cst status at cnstant demand and cycle time 25-30, the maximal cst ccurs at jb rder {10} f sequence pattern, where prductins are 34109 at demand 80000. nd minimal cst ccurs at jb rder {10} f sequence pattern, where prductins are 34019 at demand 80000. Here sequence pattern is and its jb rder {10}. Table 5: verage ttal cst fr MML cycle time 25-30 at cnstant demand Cst ($) Prductin Demand 6 9 299243 33334 80000 28 42 299155 34019 80000 28 42 299113 34019 80000
6.5 Cycle time 25-30 at randm demand fr MML t randm demand and cycle time 25-30, in Table 6, the maximal cst ccurs at jb rder {10} f sequence pattern, where prductins are 33939 at demand 51223. nd minimal cst ccurs at jb rder {10} f sequence pattern, where prductins are 34019 at demand 49681. Table 6: verage ttal cst fr MML cycle time 25-30 at randm demand Cst ($) Prductin Demand 28 42 103748 33939 51223 28 42 100230 34019 49681 18 27 99143 33913 49364 6.6 Cycle time 15-20 at cnstant demand fr FL In FL, there is reasnable setup time require. Cycle time and setup time induce fr lesser prductin. It is nted frm ur experiment, penalty cst fr late delivering the finished gds is fund maximal. If we take a lk at fllwing table, which shws the effect f cycle time at cnstant demand. Table 7 shws that maximal average ttal cst ccurs at jb rder {9} f sequence pattern, where prductin quantities are 50003 at demand 80000. nd lwer cst ccurs at jb rder {10} f sequence pattern, where prductin quantities are 51842 at demand 80000. Hence the best sequence pattern is and its jb rder {10} fr cst saving. Table 7: verage ttal cst fr FL cycle time 15-20 at cnstant demand Cst ($) Prductins Demands 28 42 195237 50003 80000 28 42 185209 51840 80000 28 42 185199 51842 80000 6.7 Cycle time 15-20 at randm demand fr FL t randm demand, Table 8 indicates that maximal cst ccurs at jb rder {6} f sequence pattern, here prductins are 50003 at demand 50184. t jb rder {4} f sequence pattern, the ttal average cst is fund minimal, where prductins are 49656 at demand 49504. S the best sequence pattern is and its jb rder {4}. Table 8: verage Ttal cst fr FL cycle time 15-20 at randm demand Cst ($) Prductins Demands 28 42 2839 50003 50020 14 21 3762 50003 50184 12 18 2318 49656 49504 6.8 Cycle time 25-30 at cnstant demand fr FL t cnstant demand and cycle time 25-30, the Table 9 shws maximal average ttal cst ccurs at jb rder {10} f sequence pattern, where prductins are 32667 at demand 80000. nd minimal average ttal cst ccurs at jb rder {10} f sequence pattern, where prductins are 33430 at demand 80000. The mre feasible sequence pattern is and its jb rder {10}.
Table 9: verage ttal cst fr FL cycle time 25-30 at cnstant demand Cst ($) Prductins Demands 6.9 Cycle time 25-30 at randm demand fr FL The Table 10 shws that the ttal average cst at randm demand is high at jb rder {10} f sequence pattern, where prductin quantities are 113031 and demand 48700. nd minimal cst ccurs at jb rder {10} f sequence pattern, where prductins are 33430 at demand 49833. The best sequence pattern is and its jb rder is {10}. Table 10: verage ttal cst fr FL cycle time 25-30 at randm demand Cst ($) Prductin Demand 7. Cnclusin and future wrk The cmparative study between MML and FL was cmpleted with the sequencing prblem. real industrial data was used t demnstrate the sequencing prblem and with the bjective f minimizing cst and keeping cnstant cnsumptin f each part. Our prpsed cst mdel demnstrates in favr f saving cst. Fllwings are the main cntributin f the current research; 28 42 307951 32667 80000 28 42 302982 33434 80000 28 42 302936 33430 80000 28 42 113031 32667 48700 24 36 107549 33324 49832 28 42 105839 33430 49833 The cmparative study gives the merits and demerits f MML & FL. Merits g t MML, because MML is nt dependent n setup time and mre mdels prduce n ne single line. It is als bserved that the best sequence pattern and its jb rder, depends n prductin and demand quantity. The best sequence yields cntinue cnsumptin f parts and minimize the verall cst. Maximum cycle time is als a factr fr higher cst. Cnstant demand and randm demand was set, accrding t planning hrizn f cnsidered cmpany. It is ntified that cnstant demand induced fr higher cst than randm demand. The literature study shws that n previus wrk has been published t cmpare the experimental result f MML & FL based n cst minimizatin apprach. This research successfully demnstrates the cmparative study fr MML & FL based n cst minimizatin apprach. Hwever, this wrk can be extended, fllwing are sme recmmendatins fr the future wrk. Reductin f lead time fr delivering the imprted material. Multiple mdels might be cnsidered fr ptimizatin. cknwledgment This research wrk was supprted by Universiti Sains Malaysia (USM), under IGS scheme. References 1. Heike, G., Ramulu, M., Srensn, E., Shanahan, P., Minzadeh, K., 2001, Mixed Mdel ssembly lternatives fr Lw-Vlume Manufacturing: The Case f the erspace Industry, Internatinal Jurnal Prductin Ecnmics, 72, 103-120 2. Hyun, C.J., Kim, y. and Kim, Y. K., 1998, Genetic lgrithm fr Multiple Objectives Sequencing Prblems in Mixed Mdel ssembly Lines, Cmputers Operatins Research, 25, 675-690.
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