Journal of Chemical and Pharmaceutical Research, 2014, 6(5): Research Article

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1 Available online Journal of Chemical and Pharmaceuical Research, 204, 6(5): Research Aricle ISSN : CODEN(USA) : JCPRC5 Cells formaion wih a muli-objecive geneic algorihm Jun Gong *, Xiuyang Chen and Sen Zhang 2 Deparmen of Sysems Engineering, Norheasern Universiy, Shenyang, China 2 School of Auomaion and Elecrical Engineering, Universiy of Science and Technology Being, Being, China ABSTRACT The problem of how o form dynamic cells based on changing producion requiremens wih muliple planning horizons and muliple objecives was discussed. A nonlinear muli-objecive mahemaical model of dynamic cell formaion was buil by weighing he hree objecives, including oal cos in he process of cell manufacuring and formaion, maximum deviaion of wor load from available capaciies of machines, and oal number of iner-cell moves. Using adapive niche echnique, penaly echnique, double roulee wheel mehod, and reserving elie sraegy, reserving elie-based random weigh muli-objecive geneic algorihm was designed for he complicaed combinaion opimizaion model. The model and algorihm were analyzed by a numerical example. The compuaional resuls demonsrae ha he proposed geneic algorihm is effecive. eywords: Cell formaion; Cellular manufacuring; Muli-objecive geneic algorihm INTRODUCTION Nowadays, cell manufacuring is adoped by companies of worldwide as one of he advanced producion modes. I produces and processes he componens and combines he flexibiliy of worshop producion and he high efficiency of flow producion. Many researches show ha, cell manufacuring has he advanages of he invenory of wor in process is less, he response ime of order form is shorer, he floor space is smaller, logisics quaniy is smaller, he ime for equipmen o adjus is shorer and he cos of producion is lower[-2]. For all hese aspecs, cell manufacuring is supposed o be he promising and viable producion mode. Many documens did researches on cell grouping efficiency, he cos and he flexibiliy of cell formaion. However, producs in oday s mares have he feaures lie life cycle and he ime of delivery is shoren, he diversificaion of variey and he indeerminism of demand. Reduce o he necessiy for cell manufacuring o wor in a dynamic and changing environmen. In he environmen of changing demand, he quaniy demand of differen produc is changing in no ime. And he inerior collocaion of cell manufacuring needs adjusmen. Because of he change of demand, he cell manufacuring designed for he manufacure requiremen of former planning horizon may no be he opimal cell manufacuring sysem for he curren planning horizon. In oher words, he configuraion of cell manufacuring sysem is ou of dae. The research for his issue in our counry on he sage is blan. Now, some foreign academics pu forward ha he inerior collocaion should be adjused due o he dynamic change of manufacure requiremen ha is he formaion of muli-objecive dynamic cells [3-4]. Consequenly adap o he demand of changing mare, and preven he ou of dae of cells. Acually, he demand of changeable mare hrough dynamic regulaion o he inerior collocaion of cell manufacuring of each plan period is developed o exploi he decomposiion algorihm o forma dynamic cell [5-6]. The opional manufacure pah and sochasic producion requiremen is considered o build he uncerainy dynamic cell mahemaic model and used simulaed annealing mehod o solve he problem. The dynamic change of mare 70

2 requiremen is considered o design he flexibiliy cell manufacuring frame and he dynamic cell manufacuring hrough saic soluion and dynamic recurrence. Much mea-heurisic arihmeic is exploied o solve he formaion of dynamic cel and compared he efficiency of he arihmeic hrough simulaed analysis [7]. The opional process roue, operaing sequence, machine capaciy, woring load, operaing cos, producion arrangemens cos and some oher facors are considered, hen se up dynamic cell formaion mahemaic model and designed a wo-sep geneic algorihm based on heurisic mehod o solve his model[8-0]. The sudies above rarely consider each cell s capaciy uilizaion rae afer he formaion of cell. I no only lead o he big differences beween each cell s uilizaion rae and cause huge wase, bu also he formaion of cell iself is a complex muli-objecive opimizaion problem. These sudies are jus form he cell by single arge and simple weighing each arge. Or see oher arge excep cos as consrain o form cell. I is very difficul o design an opimal cell manufacuring sysem because he imporan facors were no disposed a same ime. Under he circumsances of dynamic manufacure requiremen, his ex hins abou he quesions abou opional process roue, woring abiliy of faciliies and so on. Build he dynamic cell manufacuring sysem ha can adjus he inerior collocaion by he demand of mare hrough balancing he oal cos, he bigges difference beween faciliy s load and capaciy and he oal number of imes ha pas move across he cell during he process of formaion of cell manufacuring. 2. Decision model for he formaion of dynamic cell 2. Relevan parameers B is he producion lo; D j is he demand for componen j in he plan period ; of he componen j by faciliy. A is he amorizaion cos of faciliy ; one hour of faciliy ; S is he insallaion charge of faciliy ; is he minimum quaniy of equipmen of a cell; W 2 is he maximum quaniy of equipmen of a cell; available capaciy(hour) of faciliy ;, = Componen j s process can be done by faciliy ; 0, Ohers; 0, λ = Firs plan period;, Ohers α ij P ij is he processi s ime O is he processing charge of W R is he unloading cos of faciliy ; β is he 2.2 Decision variable X is he number of faciliy ha disribue o cell during plan period ; Y is he number of faciliy ha add o cell a he beginning of plan period ; Z is he number of faciliy ha unload from cell a he beginning of plan period ;, V ij = During he plan period, componen j s process i was done by he faciliy in cell ; 0, Ohers; 2.3 Decision model In order o form he cell manufacuring sysems ha have superior performance, we need 3 arges: oal cos is minimum, he uilizaion rae of equipmen is maximized and he number of componens move across he cell is minimized. So, based on he adequae consideraion of mehods abroad o he formaion of cel his ex is he firs o build a mahemaic model for he formaion of muli-objecive dynamic cells. I can be described by he followed muli-objecive nonlinear programming model (MDCFP): Where Min {f (X), f 2 (X), f 3 (X)}, () T L T L T L J I j ( X ) = X l A + ( SYl + R Zl ) + D jpijovijl, = I = = = I = = = I = = j= j= f (2) 702

3 f 2 max T L T L J I X = β l j ij ijl (3) = = = I = j= i= j ( ) X D P V ; I j i+, jl i= = = S. X V V. (4) L I= = ijl α V ijl =, i, j, (5) ij + Yl Zl = X l,, 2,..., ; (6) l, = T J I j β X D P V,, (7) Y l ij ij ij j= i= { ( X l X l, ),0}, { ( X X ),0}, l = max, l = max l, l, Z W l (8) l (9) X l W2, =, (0) V = 0, i, j,, () ij X, Y, Z, V 0, (2) l l l l Formula () is he overall objecive, minimize (2)~(4) and ge he hree suboals. Formula (2) is he oal of purchased cos of equipmen, equipmen operaing cos and cos of equipmen configuraion of each plan period; Formula (3) show he larges deviaion beween each equipmen s load and capaciy. I is nonlinear ineger expression; Formula (4) expresses he oal number of componen move across he cell. Formula (5) shows ha cerain operaion of a componen only can be arranged o he only equipmen o produce and process; formula (6) is he balance equaion of he oal number of equipmen. Formula (7) shows ha producion capaciy of each cell during every plan period ha can saisfy he manufacure requiremen. Formula (8) shows he amoun of equipmen ha add o cell I a he beginning of plan period, i is decided by he differences beween he amoun of equipmen in cell I during he curren plan period and he former plan period. Formula (9) shows he amoun of equipmen disassembly from cell I a he beginning of plan period. Formula (0) limis he maximum number and he minimum number of each cell. Formula () and (2) shows he decision variable s 0- consrain and he nonnegaive ineger consrain. 3. Algorihm design This research uses advanced random weigh muli-objecive geneic algorihm o forma he muli-objecive dynamic cells. In his algorihm, chromosome coding is designed o be a code form of a muli-module wo-dimension ineger marix. I also uses he adapive niche echnology, he penaly echnology; double disc be mehod and reserve essence sraegy. In geneic algorihm, crossover and muaion are wo very imporan geneic operaors. We need o use special crossover operaor and muaion operaor because chromosome in his ex is muli- module wo-dimension ineger marix, and is coded forma is very special. Sep Randomly choose one chromosome as paren populaion. Sep 2 Randomly choose one nonzero elemen m from marix 703 M o solve his problem (i and j are respecively represen is line number and column number). Sep 3 Randomly choose a posiive ineger from 0 o ( is he amoun of he ypes of equipmen). When parameer α ij =, give s value o m or go bac o sep 2. Sep 4 Randomly choose a posiive ineger l from 0 o L(L is he amoun of cells). Give l s value o he elemen which is in he line j and column i of marix C. Sep 5 Randomly choose a posiive ineger w from o W z. Give w s value o he elemen which is in he line and column l of marix N l. Sep 6 The end of muaion operaion

4 Afer he crossover operaion and muaion operaion, we ge a chromosome may no saisfy formula (7) and (0), and need o use formula (4) and (5) and he penaly echnology o correc i. 4. Calculaion and analysis The algorihm above can be realized by programming wih Malab, and he mass simulaing calculaion can be done by Penium IV wih 52M memory. Boh of hem have good effec. Now we will give you a small-scale simulaion example o explain he model and applicaion of his mehod. In cerain machinery manufacuring enerprise, here is a job shop o produce several ypes of componens. This ex chooses 7 ypes of componens, he job shop can open 3 cells a mos, and each cell can accommodae 5 equipmen a mos and can accommodae 2 equipmen a leas. This enerprise does he dynamic formaion of cell manufacuring sysem according o he plan of he following wo monhs afer he nex monh. The manufacure requiremen and he basic daa of echnology are shown in he able. Table. The manufacure requiremen and he basic daa of echnology in living example Demand Process Componens Plan period Plan period M3 or M2 M6 M M2 or M5 M4 or M M5 or M3 M4 or M M3 or M2 M or M4 M M2 or M4 M M6 M M or M4 M M2 or M4 M6 Tae componen 3 as example, from able we can ge he producion informaion of componen 3, and componen 3 doesn need o be produced in plan period. 500 should be produced during plan period 2, and 2 processes are needed o produce componen 3. The firs process can be done by equipmen 5 for.85s or equipmen 3 for 2.43s. The second process can be done by equipmen 4 for 3.47s or equipmen 6 for 2.70s. The cos parameers of differen equipmen s during he producion process are shown in able 2. The ype of equipmen Table.2 The cos parameers of equipmen in he living example Buying expenses (en housand) Operaing cos (per hour) Insallaion charge (en housand) Table.3 Non-dominaed disaggregaion Removal cos (en housand) Toal cos(million) Maximum difference (hour) Toal number of movemens

5 Use he algorihm of his ex and wrie he simulaion program, we can ge he non-dominaed disaggregaion in able 3. From able 3, we can clearly disinguish he quaniaive and qualiaive relaionship of he 3 conflic arges. For example, componen s oal degree of move across he cells is increase wih he decrease of oal cos of producion, bu here is no secure relaionship beween he differences beween equipmen load and capabiliy and he oal cos of producion. The wide spreading non-dominaed disaggregaion provides he sufficien gis for designer o consider he oal cos, he rae of equipmen uilizaion and he oal number of componen move across he cells, and o mae he arge rade-off decisions. CONCLUSION The formaion of dynamic cell manufacuring is one of he hoes opics in he field of advance producion operaions. This ex discusses he problem of he formaion of dynamic cell. Through rade-off beween 3 arges which are he oal cos of he formaion of cell manufacuring, he maximum difference beween equipmen load and equipmen capabiliy and he oal number ha componens move across cells. The decision is made for he formaion of dynamic cell manufacuring, and lasly pu forward he random weigh muli-objecive geneic algorihm based on he essence reenion sraegy. This ex also analyzes he dynamic relaionship beween he 3 arges and loos for he non-dominaion disaggregaion by doing he simulaions for living examples. REFERENCES [] Wemmerlov U, Johnson D J. Inernaional Journal of Producion Research, 997, 35 () :29~ 49. [2] Wemmerlov U, Johnson D J. Inernaional Journal of Producion Research, 2000, 38 (3) : 48~507. [3] Wemmerlov U. Inernaional Journal of Producion Research, 989, 27 (9) : 5~ 530. [4] Shafer S M, ern GM, Wejj C. Inernaional Journal of producion Research, 992, 30 (5) : 029~036. [5] Adil G, Rajamani D, Srong D. Inernaional Journal of Producion Research, 996, 34 (5) : 36~ 380. [6] Rajamani D, Singh N, Anejay P. Inernaional Journal of Producion Research, 990, 28 (8) : 54~ 554. [7] Sanaran S. Mahemaical Compuer Modeling, 990,3 (9) : 7~ 82. [8] Sofano P. Inernaional Journal of Producion Research, 999, 37 (3) : 707~ 720. [9] Aronlunala N, Mousapha D,Wilson L. European Journal of Operaional Research 2006, 7 (3) : 05~ 070. [0] Chen M. Annals of Operaions Research,998, 77 () : 09~