Integrated Mixed-Model Assembly Line Balancing with Unskilled Temporary Workers

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1 Integrated Mxed-Model Aembly Lne Balancng th Unlled Temporary orer Dongoo m, Jnoo Par, Ilyeong Moon To cte th veron: Dongoo m, Jnoo Par, Ilyeong Moon. Integrated Mxed-Model Aembly Lne Balancng th Unlled Temporary orer. Shge Umeda; Maaru Naano; Hajme Mzuyama; Hronor Hbno; Dmtr rt; Gregor von Cemn. IFIP Internatonal Conference on Advance n Producton Management Sytem (APMS), Sep 2015, Toyo, Japan. IFIP Advance n Informaton and Communcaton Technology, AICT-460 (Part II), pp , 2015, Advance n Producton Management Sytem: Innovatve Producton Management Toard Sutanable Groth. < / _38>. <hal > HAL Id: hal Submtted on 10 Jan 2017 HAL a mult-dcplnary open acce archve for the depot and demnaton of centfc reearch document, hether they are publhed or not. The document may come from teachng and reearch nttuton n France or abroad, or from publc or prvate reearch center. L archve ouverte plurdcplnare HAL, et detnée au dépôt et à la dffuon de document centfque de nveau recherche, publé ou non, émanant de établement d enegnement et de recherche frança ou étranger, de laboratore publc ou prvé. Dtrbuted under a Creatve Common Attrbuton 4.0 Internatonal Lcene

2 Integrated Mxed- Model Aembly Lne Balancng th Unlled Temporary orer 1 Dongoo m, 1 Jnoo Par, and 1 Ilyeong Moon 1 Department of Indutral Engneerng, Seoul Natonal Unverty, Seoul , orea E-mal: moon@nu.ac.r, Fax: Abtract. Th tudy extend a ngle-model aembly lne balancng problem to an ntegrated mxed-model aembly lne balancng problem by ncorporatng unlled temporary orer, ho enhance productvty. An nteger program that mnmze the um of total ortaton cot and alare of lled permanent and unlled temporary orer thn a pecfc cycle tme. The propoed model are baed on partcular feature of a real-orld problem ncludng multaneou agnment of lled permanent and unlled temporary orer a ell a precedence retrcton for the ta. eyord: nteger programmng, lne balancng, mxed-model aembly lne, hojna. 1 Introducton An aembly lne a flo-orented producton ytem typcal of ndutral te that produce large quantte of tandardzed commodte, but t alo mportant for producer of lo volume dvere or cutomzed product. If only one product manufactured, then all or pece are dentcal and the ytem called a ngle model aembly lne. The name of other aembly lne depend on the type of ntermxed unt. The dfferent aembly lne type, decrbed by dfferent geometrc hape, are characterzed n Fgure 1. A mult-model aembly lne produce a equence of batche contanng unt of only one tem or a group of mlar tem th ntermedate etup operaton, herea a mxed-model aembly lne produce dfferent tem n an ntermxed equence. Dependng on aembly lne type, ngle, mxed, and mult-model veron of aembly lne problem hould be appled and tuded. The aembly lne balancng problem (ALBP) ued to earch for the optmal agnment of aembly ta to taton under precedence and addtonal practcal contrant. Bryton (1954) ntroduced the dea of lne balancng n h graduate the. The frt paper on the ALBP a publhed n Among the famly of ALBP, the mple aembly lne balancng problem (SALBP) the bet non. Aembly lne balancng reearch ha tradtonally focued on the SALBP that feature ome retrctng adfa, p. 1, Sprnger-Verlag Berln Hedelberg 2011

3 aumpton. Hoever, t may offer a lmted reflecton of complex real-orld lne balancng. A comprehenve reve of ngle-model ALBP and related oluton procedure a provded by Scholl and Becer (2006). Fg. 1. Dfferent veron of an aembly lne Over tme, the need of cutomer gro dvere and competton among manufacturer tremendouly ncreae. The ntallaton of a mxed-model aembly lne one of the bet repone to th challengng tuaton, and th methodology ha already been dely adopted by ndutry manufacturer ho can ue t to meet the dverfed demand of ther cutomer thout mantanng large nventore or a trng of aembly lne. The mxed-model aembly lne orgnated th Toyota, hch developed the concept of mxed-model producton n the 1960 n repone to problem created by lne changeover. The prncple of the mxed-model aembly lne qute mple. Hoever, degnng the proce and ytem qute dffcult. Th tudy deal th the mxed-model ALBP. In th paper, e preent a mathematcal formulaton for a mxed-model ALBP th a cot-orented objectve to reduce neffcency n a manufacturng proce, hch e reach by conderng the employment of unlled temporary orer. A thorough reve of the latet publcaton dd not ndcate that a mathematcal model ha been ued to olve a mxed-model ALBP that account for the agnment of unlled temporary orer, hch mae up a ey component of th tudy, to obtan balance that mnmze potental or overload. Although Coromna et al. (2008) condered ue of temporary orer, they dd not account for ntegrated aembly lne balancng. Ther objectve a to mnmze the number of unlled orer. Moon et al. (2009) tuded an ntegrated ALBP, but they dd not conder reducble ta tme through cooperaton of permanent and temporary orer. Moon et al. (2014) a ey reference of th tudy and they developed an nteger program that mnmze the um of total annual ortaton cot and annual alare of lled and unlled orer thn a predetermned cycle tme. Lmtaton of ther or that the model can be adopted only for a ngle model aembly lne. Th tudy extend to an ntegrated mxed-model aembly lne balancng problem. The organzaton of th paper a follo: In Secton 2, a mathematcal model for the ntegrated mxed-model aembly lne balancng tuaton th unlled temporary orer ntroduced. In Secton 3 computatonal experment conducted for the developed mathematcal model. Secton 4 provde concluon of th reearch.

4 2 Mathematcal Model Th tudy tre to balance a mxed-model aembly lne th unlled temporary orer. Unlled temporary orer can only perform a ubet of all ta requred to manufacture an tem, o they cannot be agned alone to any ta. Hoever, they can reduce operaton tme of completng ta by cooperatng th lled permanent orer. A a reult of th teamor, the number of ortaton needed for performng all ta can be decreaed. Hoever, there a trade-off beteen the alare of unlled temporary orer and the operaton cot of ortaton. Avalable ll et for each orer can dffer. A a reult, both ta and orer hould be optmally agned. Salare of orer and operaton cot of ortaton can be reduced under an effcently degned ortaton. The goal of lne balancng to mnmze cot, and t equvalent to mnmzng the um of the ortaton cot and the alare of lled permanent and unlled temporary orer. To olve the ndutral problem ued n th tudy, the follong aumpton ere made for the mathematcal model: (1) A lled permanent orer cannot be agned to more than one ortaton. (2) Slled permanent orer hould be agned to ta dependng on the ortaton ta et. (3) Unlled temporary orer cannot be agned alone to any ta. (4) The operaton tme of ta can be reduced by agnng an unlled temporary orer to a ta. (5) At mot, one unlled temporary orer can be agned to each ta to reduce operaton tme. (6) Operaton and reducble tme for producton are fxed and non. (7) Demand durng the plannng perod are fxed and non. (8) Precedence contrant determne the equence n hch the ta can be proceed. (9) There a lmt on the number of orer ho can occupy each ortaton. Ung thee aumpton, th tudy preent a mathematcal model for an ntegrated mxed-model ALBP reflectng operaton ung unlled temporary orer. The follong notaton preented folloed by a decrpton of the objectve functon and contrant. Indce:, ta (, = 1, 2,, I ) product type ( = 1, 2,, ) ortaton ( = 1, 2,, S ) lled permanent orer ( =1,2,, ) j j

5 Parameter: C C u D o r P(, j, ) T OC cycle tme upper lmt of total operaton tme of each ortaton number of dfferent product that requre ta demand of product operaton tme for ta for product hen performed by a lled permanent orer reducble tme for ta for product hen performed by a lled permanent orer and an unlled temporary orer together et of ta par ( ) for product uch that there an mmedate precedence relatonhp beteen them et of avalable ta that can be agned to lled permanent orer operaton cot of a ortaton, j SS alary for lled permanent orer SU n M alary for an unlled temporary orer upper bound of the number of orer ho can be agned to a ortaton a uffcently large number The follong to addtonal parameter are calculated th the above parameter, and Equaton (1) and (2) are ued for calculaton of thee added parameter. o r aggregated operaton tme for ta under demand rate hen performed by a lled permanent orer aggregated reducble tme for ta under demand rate hen performed by a lled permanent orer and an unlled temporary orer together o r D o 1 D 1 D r 1 D 1 (1) (2) Decon Varable: F number of ortaton to be ued n the aembly lne

6 X Y Z A 1, f ta for product performed by lled permanent orer at ortaton 0, othere 1, f lled permanent orer agned to ortaton 0, othere 1, f an unlled temporary orer agned to ta at ortaton 0, othere 1, f ta agned to ortaton 0, othere Objectve Functon & Contrant: S I S Mn OC F SS Y SU Z (3) Subject to S X (4) X A, (5) 1 1 S X M o, (6) 1 1 I S X 0 (7) 1, T 1 1 S ( X X j) 0 (, j, ) P(, j, ) (8) 1 1 I Z X, (9) 1 1 o X r Z C (10) I u o X r Z C, 1 1 (11) S Y 1 (12) 1

7 I X M Y, (13) 1 1 I Y Z n (14) 1 1 S X 1,, (15) 1 1 X F,, (16) X, Y, Z, A {0, 1} (17) The objectve functon (3) mnmze the um of the total ortaton cot and the alare of lled permanent and unlled temporary orer. Contrant (4) enure that every ta hould be performed by one lled permanent orer at one ortaton. Contrant (5) ndcate that the ame ta for dfferent product hould be agned to the ame ortaton. Contrant (6) prevent ncontency of can be greater than zero hen not zero. Contrant (7) prevent lled orer o X hch from beng agned to a ortaton th a ta that the orer cannot complete accordng to the lled permanent orer' avalable ta et T. Contrant (8) enure that the precedence relatonhp beteen ta are condered for product. Contrant (9) enure that an unlled temporary orer can be agned to ta only hen a lled permanent orer alo agned to ta. Contrant (10) repreent the total operaton tme under condton of a demand rate of each ortaton that maller than a pecfc tme. Contrant (11) repreent the total maxmum operaton tme to manufacture product at each ortaton; t maller than the pecfed upper lmt. Contrant (12) guarantee that a lled permanent orer agned to exactly one ortaton. Contrant (13) demand that a ta agned to a lled permanent orer at the ortaton; can be 1 hen a lled orer agned to a ortaton. Contrant (14) retrct the number of total orer to one ortaton to prevent overcrodng. Contrant (15) enure that the ame ta for dfferent product type agned to the ame orer. Contrant (16) are ued to decde the total number of ortaton needed. Contrant (17) demontrate the bnary nature of the decon varable. X 3 Computatonal Experment The mathematcal model a olved th FICO Xpre-IVE veron 7.3. Computatonal experment ere conducted th an Intel(R) Xeon(R) 3.5GHz proceor th 16GB RAM on the Mcrooft ndo Server 2008 R2 operatng ytem. Ta precedence equence dagram of a tet problem are hon n Fgure 2. Salare of lled

8 orer and ther avalable ll et are hon n Table 1. Demand rate of Product 1 and Product 2 are ame n th problem. Reducble tme for ta of each product type are organzed n Table 2. Table 3 ho the oluton of the tet problem. Only to ortaton are needed f three unlled temporary orer are employed n th problem. More experment ll be done n the future reearch. Fg. 2. Ta precedence equence dagram for 9 ta and 2 product Table 1. Avalable et and alare of lled permanent orer (9 and 14 ta) Ta orer Poble Ta Salary $3, $4, $3, $4, $3, $3,000 Table 2. Reducble tme and alare of unlled temporary orer Number of ta 9 Ta Reducble tme Product 1 Product Salare of unlled temporary orer $1,500 Table 3. Soluton of a tet problem Ta equence o r o r Cumulatve ortaton tme Temporary orer O

9 O O Concluon Moon et al. (2009) ntroduced the ntegrated ALBP, and th tudy extend ther dea to the mxed-model aembly lne and conder multaneou agnment of lled and temporary orer. In the producton lne decrbed heren, the lled orer have multple competence and commenurate alare; unlled temporary orer are agned to help them. A mathematcal model a developed by nteger lnear program for the ntegrated mxed-model ALBP and the model a degned to mnmze total cot, ncludng thoe aocated th operaton of ortaton and the alare of lled permanent and unlled temporary orer for a pecfed cycle tme. Due to the complexty of the problem, heurtc procedure are needed to olve the problem and t ll be done n future reearch. Reference 1. Bryton, B.: Balancng of a contnuou producton lne. M.S. The, Northetern Unverty, Evanton, IL (1954) 2. Coromna, A., Pator, R., Plan, J.: Balancng aembly lne th lled and unlled orer. Omega, 36, pp (2008) 3. Monden, Y.: Toyota Producton Sytem (2011) 4. Moon, I.., Logendran, R., Lee, J.H.: Integrated aembly lne balancng th reource retrcton. Internatonal Journal of Producton Reearch, 47, pp (2009) 5. Moon, I.., Shn, S.H., m, D..: Integrated aembly lne balancng th lled and unlled orer. IFIP Advance n Informaton and Communcaton Technology, 438 (1), pp (2014) 6. Scholl, A. and Becer, C., State-of-the-art exact and heurtc oluton procedure for mple aembly lne balancng. European Journal of Operatonal Reearch, Vol. 168, p , 2006.