Decision Support for the Dynamic Reconfiguration of Machine Layout and Part Routing in Cellular Manufacturing

Transcription

1 Decson Support for the Dynamc Reconfguraton of Machne Layout and Part Routng n Cellular Manufacturng Hao W. Ln and Tomohro Murata Abstract A mathematcal based approach s presented to evaluate the dynamc cellular reconfguraton problem n a CM system. The model developed s a mult-obectve Goal Programmng problem that smultaneously consders performance n machne utlzaton nter-cellular part movements and machne reallocaton. The mert of the approach presented n ths paper s the utlzaton of meta-goals to represent decson-maers preferences and to ensure the meta-goals can effectvely gude the underlyng model to reach a soluton that best satsfes decson-maers preferences. Ths approach sgnfcantly mproves decson-support capabltes and t s crtcal for the development of decson-support systems. A hypothetcal numercal example s provded n ths paper to verfy the strength of the presented approach. Index Terms Machne Layout Cellular Manufacturng Decson Support Optmzaton I. INTRODUCTION Ths paper s focused on dscussng the development of a mathematcal model based decson-support approach to solve the dynamc machne layout confguraton problem presented n Cellular Manufacturng (CM). CM s a paradgm derved from the concept of Group Technology (GT) [] where the ey dea s to mprove producton performance by groupng parts wth smlar producton flows and groupng machnes wth the rght mx for producng a partcular famly of parts wthn a cell. Prevous study and mplementaton of CM n actual manufacturng systems have confrmed mprovements n producton effcency end product qualty and part flow control on wor-floor. It s generally accepted that CM s most sutable for medum producton volume and medum product mx systems []. In our study we emphaszed on the problem that producton demand fluctuates dramatcally and that the machne layout and part routng of the CM system must be dynamcally adusted to ensure the overall effcency of the system. Further our study concentrates on the ncorporaton of Decson-Maers (DMs) preferences nto the mathematcal model so that the Manuscrpt receved January. Ths wor was supported by AENHI <-8764> and n part by the Japan Socety for the Promotonal of Scence (JSPS). H. W. Ln s a vstng researcher wth the School of Informaton Producton and Systems Waseda Unversty ta-yushu Fuuoa Japan (phone: ; fax: ; e-mal: h.ln@urena.waseda.p). T. Murata s a professor wth the School of Informaton Producton and Systems Waseda Unversty ta-yushu Fuuoa Japan (e-mal: tomohro.murata@waseda.p). correspondng optmal soluton that best satsfes the preferences can be effectvely found. Ths mechansm would pave the way for a better desgned decson-support tool as t sgnfcantly mproves the qualty of analyss nteractons between DMs and the underlyng decson model. II. BACGROUND The classcal problem of settng up a CM system manly focuses on determnng the optmal allocaton of machnes to each cell and the routng of parts between the producton cells. In general the optmal obectve was to elmnate Exceptonal Elements (EE) [3]. EE are classfed nto exceptonal machnes and exceptonal parts. Exceptonal machnes refer to the machnes wthn a cell that are only utlzed by a few of the parts assgned to that cell. Exceptonal parts however refer to those parts that must be routed through more than one cell to complete ther producton. Exceptonal machnes and exceptonal parts are nversely related to each other but they both have negatve effects on the performance of the overall CM system. Excessve exceptonal machnes requre sgnfcantly hgher machne nvestment and usually they would experence lower utlzaton levels. Excessve exceptonal parts dramatcally ncrease materal handlng costs and nter-cellular dependency. Intra-cell part movements are performed manually over a close dstance one unt at a tme. Inter-cell movements though parts are usually moved n lots and navgates over a relatvely longer dstance usng costly materal handlng resources and often through a complex routed factory floor. Hence t s generally accepted that the overall costs of nter-cell movements are sgnfcantly hgher than ntra-cell movements. Further when parts are assgned to be processed on multple cells then producton schedules between these cells must be synchronzed n order to reduce Wor-In-Progress (WIP). Ths type of nter-dependency between the cells s dffcult to manage and t often prevents each cell operatng at an optmal condton. Conventonally the layout confguraton of a CM system s consderably statc. In general the average demand of each product s predcted over a relatvely long foreseeable future and that the cell layouts are planned accordngly once off. In [] Groover has dscussed a smple clusterng approach to determne a cell formaton for processng all the products n consderaton. Ths method however only analyzed the producton routng relatonshp of each part and t does not consder the effects of demand varatons between parts. In

2 [4] Defersha and Chen appled mathematcal based approach to analyze the cell confguraton problem. The problem s however NP-hard and thus the calculaton tme s generally long even for a relatvely small problem. oon Bulga and Betas [5] have proposed a lnearzaton approach that mproves evaluaton tme by elmnatng non-lnear relatonshps n the model. As reported n [6] and [7] heurstc approaches have also been attempted to mprove calculaton tme wth slghtly comprsed result qualty. In a volatle maret the demands for each product s subectng to sgnfcant fluctuatons over relatvely short tme ntervals. Inherently the CM based machne layout must be reconfgured dynamcally to ensure the producton floor s used optmally for producng the overall demands of the system at dfferent producton perods. Ths type of problems have been tacled by [8] and [9] wth satsfyng results. In our study we have notced that whle plannng for each reconfguraton DMs must convey real-tme stuaton and be allowed to specfy ther performance preferences for the new cell confguraton. These preferences must be concsely ncorporated to the model n order to fnd the correspondng soluton that best satsfes the scenaro at tme. Ths problem has not been actvely addressed n prevous studes and t s the man contrbuton of ths study. In ths study the performance factors consdered are the utlzaton level of each machne the number of nter-cell movements for each product and the number of machnes to reallocate. The authors of ths paper have developed a Goal Programmng (GP) [] model to evaluate ths mult-obectve cell reconfguraton problem. Further the concepts of meta-goal [] s appled to convey DMs preferences and to buld the necessary nterface between DMs and the underlyng model. Ths mechansm s sgnfcantly mportant for the development of decson support systems. III. PROBLEM DEFINITION AND MODEL FORMULATION The problem consdered n ths study assumes that producton order of each part n the upcomng producton perod has been determned. The cell reconfguraton model s then appled to determne a cellular formaton that would optmally produce the parts. The soluton of ths model ndcates what machnes are allocated to each cell but t does not provde the actual arrangement of machnes wthn a cell. Machne arrangement n each cell s determned by the producton sequences of the parts that are assgned to a cell and ths s not wthn the scope of ths study. It s also assumed n ths study that the machnes can be reallocated economcally. In each plannng perod the demand for each part fluctuates dramatcally. Hence by reallocatng the machnes t s expected that ntercellular materal handlng would be dramatcally reduced and that the resources saved from materal handlng ustfes the resources that are requred to perform the reallocaton of machnes. Overall the model consders three obectves whch are mnmzng nter-cellular part movements maxmzng machne utlzaton and mnmzng machne reallocaton. Ths mult-obectve problem s modeled usng the GP technque. Inter-cellular part movement s nversely proportonal to machne utlzaton and machne reallocaton. It s expected that DMs understand ther operatonal envronments and have clearly dstngushable preferences on the attanment level of each obectve. The model must accurately convey these preferences and effectvely determne the correspondng optmal soluton for the system. In ths study the nterface between the DMs preferences and the model s establshed based on the concept of meta-goals. A. Meta-Goals In general classcal GP models use weghtng factors and normalzaton to represent the relatve mportance of each orgnal goal and solve the mmeasurablty problem respectvely. These technques alone are unable to concsely and accurately portray DMs fulfllment preferences for decson problems that consst of relatvely hgher number of goals especally. By applyng the concept of meta-goals [] ths problem can be effectvely addressed. The man dea behnd meta-goal s the smultaneous cogntve evaluaton on the degree of attanments for orgnal decson goals consdered n a GP model. In a Meta-GP model a meta-goal s represented by approprate constrant functons and target parameters for the undesred devatons of the orgnal goals. In ths study three meta-goals have been formulated to represent the DMs preferences on the achevement of the cell reconfguraton model. Each meta-goal offers a unque way of expressng and manpulatng the overall achevement for a partcular class of the orgnal decson goals. These decson goals are classfed based on the obectves of optmzng nter-cellular part movements machne utlzaton and machne reallocaton. Through the use of these meta-goals t elmnates the needs to drectly manpulate the underlyng orgnal GP model when the desred operatonal preferences of the DMs are modfed whch nherently renforces the elmnaton of human error. Furthermore meta-goals allow DMs to more swftly dentfy an overall pcture on the strengths and the weanesses of the partcular cell formaton under consderaton. Meta-goal targets can then be adusted accordngly to setup the requred condton for fndng a soluton wth better overall performance wth respect to all the preferences consdered. B. Modulated GP Model wth Meta-Goals The dynamc cell reconfguraton model s ntended to be evaluated by Lngo optmzaton solver released by Lndo Incorporated []. The basc structure of the model can be categorzed nto four maor groups whch are varable type declaraton constrant functon orgnal goal functon and meta-goal functon components. The type declaraton group s for declarng the data type and range lmtaton for each varable. The constrant functon group ncludes equatons that convey physcal nter-relatonshps between the decson varables and operatonal parameters of actual decson problems. The orgnal functon group s for specfyng the performance obectves of the model. Lastly the meta-goal functon group s for specfyng equatons that convey DMs preferences on the fulfllment level of the orgnal goal functons. Inherently the system must automatcally dentfy the approprate constrant functons orgnal goal functons and meta-goal functons to be ncluded n buldng a complete model that specfcally portray the correspondng

3 preferences. Ths feature s enabled by the Sub-model and Logc control functonaltes that are supported by Lngo. The cell confguraton model s formally defned below. Decson model ndces and basc sets: Indexng nteger for parts Indexng nteger for machne types Indexng nteger for producton cells P = { p p p 3... p... p I} Set of parts to be produced I s the total number of dfferent parts to be produced M = { m m m 3... m... m J} Set of machne types avalable J s the total number of dfferent machne types C = { c c c 3... c... c } Set of producton cells to be reconfgured s the maxmum number of dfferent cells Decson model parameters: Total unt n demand for part D T Total unt of machne(s) avalable for machne type mn S Mnmum unt of machne(s) requred n cell max S Maxmum unt of machne(s) allowed n cell W Total unt of producton tme avalable for every machne O Represents f operaton of part on machne type s requred value mples requred and mples otherwse L Average producton lead-tme of part on machne type f part s not to be operated on machne type I Represents the ntal machne layout confguraton I machne unts of machne type allocated n cell utlse γ Meta-goal obectve that represents the DMs preference on machne utlzaton level move γ Meta-goal obectve that represents the DMs preferred number of nter-cellular part movements for part alloc γ Meta-goal obectve that represents the DMs preferred number of machne reallocatons for machne type Decson model varables: A Represents f part s assgned to operate on machne type that s allocated to cell mples assgned mples otherwse R Represents f part has any operatons performed n cell mples at least one operaton of part s performed n cell mples otherwse N Represents the new cell confguraton number of unts of machne type to be allocated to cell ntra X Total number of ntra-cell movements for part n cell nter X Total number of nter-cell movements for part Y Y + Represents how much producton tme capacty s underutlzed and over-utlzed for machne type n cell respectvely n out Z Z Represents how many unts of machne type s to be moved nto and moved out of cell respectvely utlse utlse η μ Respectvely slac and surplus varables of the meta-goal that represents the utlzaton level preference of all machnes move move μ η Respectvely slac and surplus varables of the alloc alloc meta-goal that represents the number of nter-cellular part movement preference for part η μ Respectvely slac and surplus varables of the meta-goal that represents the number of machne reallocaton preference for machne type Decson model functons: SUBMODEL DATATYPE_DECLARE: A { }; () N Integer; () R { }; (3) DATATYPE_DECLARE s for explctly declarng data type and range for varables that are not default postve real numbers as assumed by Lngo. In the model A s for representng the assgnment of parts and that R s for representng the process routng of each part. Both A and R can only tae a logcal value of ether true or false and these values are represented by a bnary number of or respectvely. N s for representng the allocaton of machnes n cells and snce each machne can only be consdered as an ndvdual unt N s declared as a real nteger number by (3). SUBMODEL ALLOCATE_MACHINES: J N S ; (4) = J = mn max N S ; (5) N T ; M (6) = ALLOCATE_MACHINES defnes the machne allocaton constrants for the model. Equaton (4) and (5) specfes the mnmum and maxmum number of machnes that must be assgned to a cell respectvely. Equaton (6) specfy that for each machne type the total number of machne unts allocated to all of the cells s less or equal to the number of avalable machne unts. SUBMODEL ASSIGN_PARTS: = I + A D L Y Y = A = O ; P M (7) + = (8) N W; M ASSIGN_PARTS specfes part assgnment constrants and utlzaton goal functons for the dynamc cell reconfguraton problem. Equaton (7) specfes that a vald operaton step of a part must be entrely assgned for producton on the correspondng machne type of a sngle

4 cell. In ths equaton A apples a constrant that the entre producton demand of a partcular operaton of a part s only assgned for producton n a sngle cell. Ths approach would reduce the needs to synchronze producton actvtes between multple cells and thus reducng the complexty of ntercellular schedulng actvtes. Further as the entre lot of parts has the same producton path t sgnfcantly mproves producton traceablty for every product produced n the system. Equaton (8) s a goal functon that specfes worloads for producng the part demands must be less or equal to the producton capactes. The purpose of the goal functon s to detect and mnmze over-utlzaton and under-utlzaton of the avalable resources. SUBMODEL INTRA_INTER_MOVES: J ntra = ntra ; ntra ntra nter ; = X = A D ; P X R P () X R X = ; P () X = R D P () INTRA_INTER_MOVES apples functons to detect the ntra-cellular and nter-cellular part handlng movements. Equaton (9) calculates the number of ntra-cellular part handlng movements for a partcular part n a partcular cell. Equatons () and () are formulated to determne f a part s to be routed through a certan cell n order to complete ts producton. Based on ths routng nformaton Equaton () s used to determne the number of nter-cellular part handlng movements for each part. SUBMODEL MT_MOVEMENTS: n out I + Z Z = N ; M (3) MT_MOVEMENTS conssts of a goal functon to specfc the machne movement obectves. Equaton (3) ndcates that t s best to eep the machne formaton unchanged n order to save machne reallocaton resources. Due to demand fluctuaton however machne movements are performed to mprove producton effcences. In (3) the number of machnes of a partcular machne type movng nto a cell or movng out of the cell s determned. SUBMODEL OBJECTIVE_FUNC: J J I + Mn Y + Y + X nter = = = = = J n out Z Z = = + ; P M OBJECTIVE_FUNC defnes an obectve functon (4) for the underlyng GP model. A hgh weghtng factor s assgned to mnmze over-utlzaton varable as demand fulfllment s most prortzed. A moderate weghtng factor s assgned to the machne reallocaton varables as ther magntude scale s consderably smaller than the other factors. The obectve functon s merely the mnmzaton of the sum of the undesred devatons. The soluton obtaned wth respect to ths obectve functon would be used as a performance reference pont and would provde tradeoffs + (9) (4) gudance for the DMs. Thus the DMs would gan better understandng of the model and thus formulate better meta-goals to search for the preferred fnal soluton. SUBMODEL MG_UTILISE: utlse utlse Y ) + η μ = γ ; (5) M MG_UTILISE s used to defne a meta-goal functon (5) that represents the DMs preferred fulfllment level for the orgnal machne utlzaton goal. Ths meta-goal allows DMs to specfy an under-utlzaton level commonly accepted for every machne n the system. SUBMODEL MG_INTERMOVE: = move move move η μ γ R + = ; P (6) MG_INTERMOVE s used to defne a meta-goal functon (6) that represents the DMs preferred fulfllment level for the orgnal part movement goal. Ths meta-goal allows DMs to specfy a unque maxmum number of nter-cellular movements allowed for each part produced n the system. SUBMODEL MG_MTMOVES: = n out alloc alloc alloc η μ γ Z + Z + = ; M (7) MG_MTMOVES s used to defne a meta-goal functon (7) that represent the DMs preferred fulfllment level for the orgnal machne reallocaton (both movng nto and out of each cell) goal. Ths meta-goal allows DMs to specfy the unque maxmum number of machne movements allowed for each machne type n the system. CALC: If scenaro {OBJECTIVE_FUNC model}: Assgn Parts INTR_INTER_MOVES MT_MOVEMENTS OBJECTIVE_FUNC) ELSE-If scenaro {MG_UTILISE model}: Assgn Parts INTR_INTER_MOVES MT_MOVEMENTS MG_UTILISE) ELSE-If scenaro 3 {MG_INTERMOVES model}: Assgn Parts INTR_INTER_MOVES MT_MOVEMENTS MG_INTERMOVES) ELSE-If scenaro 4 {MG_MTMOVES model}: Assgn Parts INTR_INTER_MOVES MT_MOVEMENTS MG_MTMOVES) END IF The CALC secton bulds the fnal model for analyzng the cell reconfguraton problem correspondng to a partcular scenaro. In the current model four scenaros are supported. The frst scenaro s to evaluate the problem usng the OBJECTIVE_FUNC mnmzaton obectve functon and thus obtan an ntal soluton that serves as a performance tradeoffs reference pont for DMs. The other scenaros are to evaluate the problem wth respect to the meta-goals. Each meta-goal represents a preferred fulfllment obectve for the orgnal goals and they are descrbed as per sub-model secton above under MG_UTILISE MG_INTERMOVES and MG_MTMOVES headngs respectvely.

5 IV. NUMERICAL EXAMPLE A hypothetcal example s appled to here to demonstrate the applcaton of the dynamc cell reconfguraton model formally defned n Secton III. It s assumed that the manufacturng frm consdered n ths example has a weely fxed nterval plannng perod. In total there are worng mnutes avalable per machne n operaton. The data sets and varous parameter values of the hypothetcal problem are summarzed below. Decson solutons wll also be presented for the orgnal OBJECTIVE_FUNC model and the meta-goal models whch are the MG_UTILISE MG_INTERMOVES and MG_MTMOVES models. Data sets for the numercal example: = p p p p p p p C = c c c c c P { } { 3 4 5} M = { m m m m m m } D = { } mn max S = {} S = {88888} T = {666666} L = Table below summarzes the ntal cell layout confguraton and producton routes for each part consdered n the example. The data s expressed as duplets. For each duplet the number before the colon ndcates how many unt of a machne type s assgned to a cell. The values after the colon ndcate what parts are assgned to the machne type that s located wthn the partcular cell. Table. Intal cell confguraton and producton routes Intal Setup C C C 3 C 4 C 5 m :P :P P m :P :P 5 P 7 :P P m 3 :P P :P :P 6 P 7 m 4 :P :P 5 P 7 :P 4 :P 6 m 5 :P :P P 4 :P 6 P 7 m :P 4 :P 6 P 7 In the ntal analyss the model s solved usng the OBJECTIVE_FUNC model. Correspondng soluton of the model s summarzed n Table and t s the optmal setup for cell confguraton and producton routes when all obectves are consdered wth equal mportance. It s assumed now that the DMs have some specfc preferences to satsfy. Frstly ths numercal example consders a meta-goal where each machne type n each cell must not have more than 5 of unutlzed producton mnutes. Secondly the example consders that each unt of parts should be allowed a maxmum number of nter-cellular movements of {}. Fnally t s consdered that every machne type should not have more than a maxmum of reallocatons. The solutons for these three problem setups are summarzed n Table 3 Table 4 and Table 5 respectvely. Table. Soluton of the OBJECTIVE_FUNC model New Setup C C C 3 C 4 C 5 m :P ---- : P P m :P P 4 :P 3 P 5 : P 7 m 3 :P : P 3 P 5 P 6 P m 4 :P :P 4 :P 5 P 7 :P 3 m : P P :P 3 P 6 P 7 m : P :P 6 P 7 Table 3. Soluton of the MG_UTILISE model New Setup C C C 3 C 4 C 5 m : P 3: P P 4 m : P P :P 7 : P 4 P 5 m : P P 3 P 5 P 6 P m 4 : P 3 : P 6 : P 4 P :P 5 m 5 : P : P P 6 P :P 4 m : P 4 P 6 P Table 4. Soluton of the MG_INTERMOVES model New Setup C C C 3 C 4 C 5 m : P P 4 : P m : P : P 7 : P P 4 : P 5 m 3 : P 3 P : P 5 P : P m 4 : P 3 P : P 7 : P 4 : P 5 m 5 : P 3 P : P 7 : P P m : P 6 P 7 : P Table 5. Soluton of the MG_MTMOVES model New Setup C C C 3 C 4 C 5 m :P : P P m : P 3 P 5 P 7 : P P m 3 :P ---- : P 5 P : P 3 P 6 m : P 3 P 5 P 7 : P 4 : P 6 m : P P 4 3: P 3 P 6 P 7 m : P 4 :P 6 P 7 V. RESULT ANALYSIS AND DISCUSSION The performance of the CM system when dfferent meta-goal s appled n the model s analyzed n ths secton. The soluton obtaned from Secton IV s used as the bass of ths analyss. As mentoned earler machne utlzaton nter-cellular part movement and machne reallocaton are the three obectves consdered n ths study. It s attempted to verfy here that when a DM has a specfc preferred achevement level for these obectves hs/her preference can be represented by a meta-goal and that a correspondng optmal soluton would be found by the model MT Cell Cell Cell3 Cell4 Cell5 A. Under-utlzed machne capacty B. Inter-cellular movements for parts MT.5 MT.5.5 Cell Cell Cell3 Cell4 Cell5 Cell Cell Cell3 Cell4 Cell5 C. Machne(s) movng nto each cell D. Machne(s) movng out of each cell Fgure. Performance for MG_UTILISE model

6 Frstly let s analyze the MG_UTILISE model where satsfyng machne utlzaton s consdered the most mportant. In Fg. varous performance parameters for the MG_UTILISE model are depcted usng bar graphs. It can be observed n Fg..A that every machne type has an under utlzaton level that satsfy the DMs preference and that other obectves are mnmzed provded that the DMs preference s met. In Fg..B to Fg..D t can be clearly observed that nter-cellular part movements and machne reallocaton are strongly compromsed n order to satsfy the machne utlzaton meta-goal. In order to satsfy the part nter-cellular preferences MG_INTERMOVES model s appled. The correspondng performance parameters are summarzed n Fg.. It can be observed n Fg..B that nter-cellular movements for every part are sgnfcantly reduced. In order to acheve ths preferred performance level however more exceptonal machnes are needed and that machne utlzaton and machne movements are compromsed Cell Cell Cell3 Cell4 Cell5 Cell Cell Cell3 Cell4 Cell5 MT MT Cell Cell Cell3 Cell4 Cell5 Fgure. Performance for MG_INTERMOVES model Lastly let s assume the DMs preferred to have a maxmum of two machne reallocaton for each machne type. It s demonstrated n Fg. 3 that ths preference can be acheved but at the prce of ncreased nter-cellular movements for parts as depcted n Fg. 3.B Cell Cell Cell3 Cell4 Cell5 Cell Cell Cell3 Cell4 Cell5 MT MT Cell Cell Cell3 Cell4 Cell5 MT MT In ths study the models are solved on a Dell computer system wth a Pentum Dual Core.6MHz CPU. Usng the global optmzaton extenson on Lngo lengthy calculaton tme s requred to evaluate each model. However t has been observed that hghly vald local optmal solutons for a problem sze smlar to the ones consdered n the numercal example would be found n between to mnutes. Thus by relaxng the global optmzaton tolerance a balance between result qualty and calculaton tme can be obtaned. VI. CONCLUSION In ths paper a mathematcal optmzaton based approach has been presented to evaluate the dynamc cellular reconfguraton problem n a CM system. The mert of the approach s to mprove the nterface between end users and the mathematcal model. Usng the concept of meta-goal DMs preference can be ncorporated nto the model and that a correspondng optmal soluton that closely satsfes the DMs preferences can be evaluated wth acceptable calculaton lead tme. In ths study t has been demonstrated that a sngle meta-goal s appled n each scenaro. Our future study wll consder the smultaneous consderaton of multple conflctng meta-goals preferred by multple DMs. Hence the approach can be utlzed n group decson-analyss envronment. Based on ths approach t s ntended that a web-based decson-support system wll be developed to enable onlne group decson-mang actvtes. REFERENCES [] Ballaur A. (985). An nvestgaton of part famly/machne group formaton n desgnng a cellular manufacturng system Ph.D. Thess Unversty of Wsconsn Madson WI [] Groover M.P. Automaton Producton Systems and Computer Integrated Manufacturng Prentce-Hall Internatonal Edtons 987 [3] Shafer S.M. ern G.M. and We J.C. (99). A mathematcal programmng approach for dealng wth exceptonal elements n cellular manufacturng Internatonal Journal of Producton Research Vol.3 Iss [4] Defersha F. and Chen M. (6) A comprehensve mathematcal model for the desgn of cellular manufacturng systems Internatonal Journal of Producton Economcs [5] oon S.A. Bulga A.A. and Betas T. (9). Integrated cellular manufacturng systems desgn wth producton plannng and dynamc system reconfguraton European Journal of Operatonal Research [6] Solmanpur M. Vrat P. and Shanar R. (4). A mult-obectve genetc algorthm approach to the desgn of cellular manufacturng systems Internatonal Journal of Producton Research 4(7) [7] Splopoulos and. Sofanopoulou S. (3). Desgnng manufacturng cells: A staged approach and a tabu search heurstc Internatonal Journal of Producton Research 4() [8] Chen M. and Cao D. (5). A robust cell formaton approach for varyng product demands Internatonal Journal of Producton Research 49(8) Fgure 3. Performance for MG_MTMOVES model [9] Chen M. (998). A mathematcal programmng model for system reconfguraton n a dynamc cellular manufacturng envronment Based on the analyss provded above t can be concluded that n a reconfgurable CM system the obectve value of nter-cellular part movement s nversely proportonal to machne utlzaton and machne reallocaton. Further t s verfed that the model presented n ths paper enables DMs to express ther unque preferences usng meta-goals. It s further demonstrated that optmal soluton that best satsfy the preferences can be effectvely evaluated. Annals of Operatons Research [] Schnederans M.J. (995). Goal programmng: methodology and applcatons. The Netherlands: luwer Academc Publshers Group [] Rodrguez Ura M.V. Caballero R. Ruz F. Romero C. (). Meta-goal programmng. European Journal of Operatonal Research 36 () 4-49 [] Lndo Inc. Last Updated th June 8 accessed 5th September 9