Dynamic models for production control and scheduling.

Transcription

1 Unversdade de São Paulo Bbloteca Dgtal da Produção Intelectual - BDPI Departamento de Engenhara de Produção - EESC/SEP Comuncações em Eventos - EESC/SEP 2013 Dynamc models for producton control and schedulng. Mexcan Internatonal Conference on Artfcal Intellgence - MICAI, 12., 2013 Cdade do Méxco, Méxco Downloaded from: Bbloteca Dgtal da Produção Intelectual - BDPI, Unversdade de São Paulo

2 th Mexcan Internatonal Conference on Artfcal Intellgence Dynamc Models for Producton Control and Schedulng A Bref Revew Julana Keo Sagawa Industral Engneerng Department Federal Unversty of São Carlos - UFSCar São Carlos, Brazl e-mal: julana@dep.ufscar.br Marcelo Sedo Nagano Industral Engneerng Department Unversty of São Paulo - USP São Carlos, Brazl e-mal: drnagano@usp.br Abstract Aglty may be an mportant compettve advantage n many marets. In order to acheve t, the dynamcs of the manufacturng systems must be consdered. Control theory supports the development of dynamc models for producton and nventory control. Ths paper dscusses some dynamc models of producton control specfcally appled to schedulng and shop floor control. A comparatve and crtcal analyss of the models s presented and drectons for future wors are provded. Control theory; schedulng algorthms; shop-floor orented systems; producton control I. INTRODUCTION In most manufacturng envronments, the producton system s always subjected to dsturbances of several sources, such as changes of demand and customer requrements, machne breadowns, urgent jobs, absenteesm, fnancal fluctuatons, and so on. In order to be compettve, the companes must be able to qucly respond to these uncertantes wthout a large penalty n cost. In other words, "Agle companes [...] are strong n ther adaptablty to changng condtons n the producton envronment" [1]. System Dynamcs & Control Theory, orgnally come from Mechancs and Electroncs, provde a range of tools for modelng and analyzng dynamc systems that can be sutably appled to producton plannng and control of manufacturng systems. As nown, some of the frst wors n ths feld was developed by [2]. Snce then, several other models have been developed to approach dfferent levels of the producton plannng herarchy or the analyss of supply chan dynamcs. After a broad lterature scannng, few models were found focusng on schedulng and shop floor control, that s, the lower levels n the plannng herarchy. Thus, the am of ths paper s to present a short revew of these wors,.e., to dscuss some dynamc models of producton control appled to schedulng and shop floor control. The scope of the revew manly ncludes publcatons of the last ffteen years. A comparatve analyss of the models s carred out and some drectons for future wor are provded. II. LITERATURE REVIEW AND PRESENTATION OF THE MODELS As already mentoned, a reasonable number of models to control the dynamcs of producton systems have been developed. A comprehensve revew s presented n [3]. These authors have dentfed two areas of applcaton of control theory to producton-nventory systems. The frst one approaches the supply chan dynamcs and related topcs, such as the bullwhp effect. The developments n ths area were labeled as "horzontal extensons" of the determnstc models of producton-nventory systems [3]. One of the frst wors n ths area was developed by [4]. In ths, an nventory order based producton control system was consdered to have three fundamental system parameters: producton delay tme (.e. producton lead tme), the tmeto-adjust nventory, and demand averagng tme. Smlarly, [5] consdered three man elements whle modelng manufacturng systems: forecastng, lead tmes and replenshment rules (or order polces). In the mentoned wor, expressons n the frequency doman to represent manufacturng lead tmes and replenshment rules are presented. In general, demand forecast represents the feedforward path of these systems, whle wor-n-process and nventory level are usually transmtted as feedbac nformaton. In some systems, the order polcy s the control element. Followng ths lne of reasonng, several models are developed and mprovements were proposed to the exstng models [6-8]. Most of these models amed at fndng an optmum order polcy to reduce the bullwhp effect,.e., the varatons n the nventory levels. The second area of applcaton focuses on "herarchcal approaches" or "vertcal extensons" [3] of the models. Ths area comprses mult-echelon models where the product structure tree or bll of materals (BOM) s used as an nput matrx for the producton-nventory system. As nown, the bll of materals s a herarchcal representaton of the assembles, subassembles, components and parts that form a product. Some authors that wored on ths vertcal approach are [9-12], among others. In the dynamc models, besdes the BOM, these authors also employed the nput-output analyss. Accordng to [3], "nput output analyss models present the opportunty to transform one set of resources nto another set usng effcent mathematcal language". The man objectve / /13 $ IEEE DOI /MICAI

3 of these models s lot szng optmzaton,.e., defnng batch szes and the optmum moments to start ther producton n tme. In the lterature revew presented by [3], there are only a couple wors approachng Operatons Schedulng and shop floor control [1], [13]. Lately, a few more models have been developed for these applcatons. These models are the focus of ths paper and wll be dscussed wth some detal n the followng subsectons. The model presented by [1] wll be also ncluded n the dscusson, snce t was consdered relevant n ths subarea. A. The Lever Heurstc for Adaptve Producton Schedulng (Model 1) A computer-aded producton schedulng and control system s proposed by [14]. In ths system, an average processng tme and lever heurstc (APT-LVR) s ntegrated wth a closed-loop feedbac control scheme, as shown n Fg. 1. The jobs are rescheduled based on smulaton and reapplcaton of the heurstcs to the updated boundary condtons of the problem. The smulaton module employed by the mentoned authors s named THOCPN-CS and was developed usng Petr nets. The necessary steps to run the system, as presented n [14], are reproduced as follows. 1. Manually assgn possble manufacturng resources (e.g. operators/machnes) to each stage, and hence form a tas-resource matrx (TRM). 2. Schedule the jobs by the APT-LVR heurstc. 3. The smulaton module wll smulate the executon of the jobs, and the bottlenec stages wll be dentfed. Human schedulers may reallocate operators/machnes n stages accordngly, to smooth producton flow. 4. Reschedule the jobs by the APT-LVR heurstc. 5. Repeat steps 3 and 4 n the offlne producton schedulng phase untl a satsfactory producton schedule s obtaned. 6. Delver the producton schedule to the shop floor and swtch the control loop from the smulaton model to the shop floor. 7. If any dsturbance occurs on the shop floor, swtch the control loop bac to the smulaton model, and go bac to step 3 f operators/machnes reallocaton s necessary, or go bac to step 4. The heurstc developed by the authors s an extenson of Johnson s algorthm. Bascally, m machnes are grouped nto two vrtual machnes several tmes, and Johnson s algorthm s appled to obtan a set of sequences. The lever concept comes from an analogy wth the moment of punctual forces appled on a beam. A flow lne wth m machnes s modeled as a lever, as shown n Fg. 2. On ths lever, the counter, Ctr, s regarded as a fulcrum. Each machne acts as a force wth magntude of d j, where d j s an array wth the dfferences between the processng tmes of the jobs on machne j and the average of all processng tmes (APT). The dstance between machnes s of one unt. The counter s used as an auxlary varable to splt up the machnes nto two groups. As t moves along the beam, the sum of the moments n each sde of the counter s calculated. Each of these sums correspond to an arrays assocated to each vrtual machne. Johnson s algorthm s thus appled to these arrays to generate a sequence. The sequence wth best performance s chosen. The proposed heurstc was appled to benchmar data for performance assessment. In addton, a case study was carred out n a company that manufactures wndows and doors. In ths company, 1396 jobs should be processed on a fve-stage flow shop n one day. The researchers clamed that an mprovement n productvty of 1,49% was obtaned, whch corresponds to processng 20 addtonal products daly [14]. B. A Schedulng Heurstc Based on the Dstrbuted Arrval Tme Controller (Model 2) The Dstrbuted Arrval Tme Controller, DATC [15-16] s a schedulng model where an ntegral controller s used to determne the arrval tmes of parts. In ths model, shown n Fg. 3, the schedulng s processed accordng to the just-ntme logc, where both earlness and tardness from due date are penalzed. The closed loop system teratvely adjusts the arrval tme of a gven part so that t may be completed as close as possble from ts due date. The completon tme of the parts s calculated by a shop floor smulaton module based on the arrval tmes of each teraton and the gven processng tmes of the parts. Fgure 2. The lever concept for an m-machne flow lne [14]. Fgure 1. A computer-aded producton schedulng and control system [14]. Fgure 3. Structure of the Dstrbuted Arrval Tme Controller [16]. 39

4 As t can be seen, each part has an embedded controller that computes the devatons of the expected completon tme from the due date and adjusts the arrval tmes based on the accumulated devatons. For ths reason, the controller of DATC s classfed as an ntegral one. The completon tmes are calculated by the smulaton module accordng to a frstcome-frst-served (FCFS) dspatchng polcy, whch s appled n each teraton based on the current arrval tmes. The arrval tme of -th part n dscrete tme doman can be wrtten as n t 1 a = [ d ( m) c ( m)] + a (0) = z ( m) + a (0), m = 0 where a (t), p (t), c (t), d (t) and z (t) refer to arrval tme, processng tme, completon tme, due date and devaton from completon tme about due date of -th part, respectvely, and s the control gan for -th part. In the proposed model, the schedulng objectve s to mnmze the Mean Squared Devatons of completon tmes from due dates (MSD), as follows: (1) 2 MSD = ( d c ) / n. (2) Accordng to [16], the ntegral controller of DATC wors as a search engne that replaces the heurstcs used n the tradtonal models. However, t s mportant to hghlght that the controllers are dstrbuted on part enttes and computaton of devatons and adjustment of arrval tmes n part enttes taes place wth lmted global nformaton, snce each controller s ndependent of the other ones, as can be seen n (1). The response of the model depends on the relatonshp between processng tmes and due dates. If the due dates are nfeasble, that s, f they are too close to each other and cannot be smultaneously met due to nsuffcent resource capacty, then the trajectory of arrval tmes converges to a steady-state value, regardless of the ntal values of arrval tmes. On the other hand, the trajectory converges to dstnct values of d - p when due dates are feasble. The DATC was appled to statc sngle machne schedulng problems wth nown optma, n order to evaluate ts performance n ths context. The bggest values for the average percentage devaton from the optmum soluton were around 5%. C. An Automatc Producton Control System Based on a Contnuous Flow Model (Model 3) An Automatc Producton Control (APC) system based on flow models n contnuous tme s presented by [1], [17]. Accordng to them, a flow model s advantageous snce control theory offers many more methods for contnuous models than for dscrete ones. The mentoned authors propose a flow-orented stochastc job shop model based on the funnel model and the theory of logstc operatng curves. They represent the wor-n-process (WIP) of a wor centre wthn a flow networ n contnuous tme as n (3). t 1 m = 0 mwp + j = 1 [ out [ out order,max, = mwp order,max, j out out order, loss, (0) + extn order, loss, j ], ] p where mwp (t) = mean wor-n-process of centre at tme t, mwp (0) = ntal mean wor-n-process of centre, extn (t) = cumulatve external nput of centre untl tme t, out order, max, j (t) = cumulatve potental outflow of upstream centre j untl tme t, out order, loss, j (t) = cumulatve potental lost of outflow due to empty upstream centre j untl tme t, out order, max, (t) = cumulatve potental outflow of centre untl tme t; out order, loss, (t) = cumulatve potental loss of outflow due to empty centre untl tme t, and p j, = fracton of total output from centre flowng drectly to centre. All these varables (except p j,, whch s dmensonless) are expressed n number of orders. As t can be seen n the rght sde of (3), the momentary wor-n-process of wor centre depends on ts ntal nventory, ts cumulated external nput, the actual cumulatve nput of ts upstream wor centers flowng to and ts own actual cumulatve output untl tme t. In smple terms, the wor-n-process of each wor centre on tme t s a result of the dfference between the nput flow and the output flow, summed to the ntal WIP. Thus, the second term and the summaton n the rght sde of (3) represent the nput flow, whle last term n bracets refers to the output flow of wor centre. Accordng to [1], although the parameters of ntal wor-n-process, external nput and potental cumulatve output of each wor centre are relatvely easy to determne, the relaton between losses n utlzaton (out loss, ) and the momentary WIP level cannot be easly defned. In order to overcome ths ssue, the funnel model and the derved theory of logstc operatng curves are appled. The funnel model states the relatonshp among the wor n process of a system, ts performance (n terms of producton rate or throughput rate) and ts mean range (or lead tme). The mean range s related to the mean runout tme of the wor centre. "The ncomng orders, measured n hours of wor content, form a stoc of pendng lots, whch have to flow through de funnel outlet. The dameter of the outlet can be descrbed as the capacty of the wor system, whch s adjustable wthn lmts" and determnes the actual performance of the system [1]. Accordng to the theory of the logstc operatng curves [18], the output of a wor centre s ndependent of the mean wor-n-process as long as every wor system has a buffer of pendng orders at all tmes. If so, the performance of the system s equal to ts capacty. Losses n producton wll occur only f the buffer s further reduced, due to nterruptons n materal flow. Also, the range decreases n proporton to the WIP untl the physcal mnmum s reached. Beyond ths pont the range cannot be further reduced because t s lmted by the sum of the operaton tme and the transport tme, whch s the mnmum range. The deal WIP mnmum represents the WIP level necessary to run the system, consderng that the arrvng orders do not have to j, (3) 40

5 wat and the materal flow s not nterrupted. Consderng (3) and both the aforementoned theores, the flow of wor n a wor centre may be represented as n (4). mwp t 0 extn t 0 = mwp + per ( mwp j = 1 ), j (0) + per ( mwp 1 ) mot where per j (mwp j (t)) s the output performance of a center j for a gven level of mean wor-n-process. The performance s measured n terms of throughput rate, and ts value s taen from the logstc curve. Actually, the term per j (mwp j (t)) represents a specfc operatng pont of the wor centre j n relaton to ts characterstc logstc curve of performance. In order to adapt (3) to the contnuous tme doman and use control-theory elements, the dmensons of the varables must be converted from number of orders nto wor content (e.g. hours). Ths converson s done by means of the mean order tme of the wor centers (mot), whch appears n (4). The transton probabltes are used snce (4) represents a job shop confguraton. These probabltes can be easly calculated wth the ad of a common materal flow matrx (MFM) obtaned by usng real data from the job shop. As nown, ths matrx shows the quanttes of the materal or the number of orders that flow from a wor centre to another. To obtan the transton probabltes, the matrx must be normalzed. Based on the presented equatons, a job shop model wth two controllers was developed: a baclog controller and a WIP controller [1], [17], as shown n Fg. 4 and Fg. 5. The baclog of a system may be defned as the dfference between the planned sum of wor and the actual output. Thus, n ths case, the planned performance s the reference varable whereas the capacty s used as a correctng varable. "The essental tas of a wor system s to allocate the requred performance to process the system load" [1]. In the proposed system, the dfference between the actual and the planned performance s ntegrated over a tme nterval, resultng n the above-mentoned baclog. In most producton systems, capacty can be ncreased or decreased n dfferent sze steps and a reacton tme s requred. Ths reacton tme was ncluded n [19]. Thus, the capacty nstallaton and de-nstallaton s represented n the model by envelope curves, as seen n Fg. 4. j j p j, mot jdt (4) Fgure 5. Concept of the automatc WIP controller [1],[17]. The man tas of the WIP controller s "to set the system to an operatng pont on the operatng characterstc curve that was defned wthn the scope of producton plannng" [1]. The reference varable s the planned WIP, and the controller adjusts the nput rate of the producton system based on the dfference between the actual and the planned WIP, as shown n Fg 5. In the model presented n [1], the baclog and the WIP controller were combned, as can be seen n Fg. 6. Ths combnaton s more effectve to control the system snce the baclog controller only acts when the planned utlzaton of the system s reached, otherwse, baclog does not arse. In ths case, the WIP controller assumes the control tas. The authors of the aforementoned wor compare the two controllers to the conventonal producton control methods: capacty s usually ncreased when baclog ncreases n a producton system; f the range eeps growng, the queue n front of the wor system can be reduced by reducng the nput rate of the system. The functonng of the combned system s outlned as follows. Frst, n order to run the model, t s necessary to decde to whch operatng state on the characterstc curve the system should be drven. For ths purpose, a value of utlzaton of the system must be set. Then, the necessary capacty s derved from the planned output and the planned utlzaton. In the other branch of the system shown n Fg. 6, the relatve planned WIP (mwp rel,plan ) s multpled by the mean WIP mnmum resultng n the planned mean WIP. The baclog of the system s calculated by means of the ntegraton of the devatons between the planned and realzed performance over a tme nterval. The baclog controller then calculates the planned performance for the next perod, whch wll lead to the corrected capacty of the system. The actual mean WIP of the system s also compared to the planned mean WIP. Based on the devatons, the WIP controller corrects the nput rate of the system [1], [17]. Fgure 4. Concept of the automatc baclog controller [1], [17]. Fgure 6. Concept of the combned WIP and baclog controller [1], [17]. 41

6 In order to evaluate the proposed system, the aforementoned authors carred out smulatons where an urgent order s ntroduced when the system s balanced. They compared the performance of the system wthout control and wth control, observng the behavor of the mean WIP and the baclog over tme n both cases. As expected, n the controlled system, wor-n-process and baclog were reduced to the ntal level much faster than n the uncontrolled system. D. A dynamc sngle-product manufacturng system modeled wth bond-graphs (Model 4) The dynamcs of the manufacturng systems s modeled usng the bond-graph methodology n [20]. The bond graphs express general class physcal systems through power nteractons between the components. The methodology s based upon an analogy wth the deal propertes of basc electronc components, such as resstors, capactors and transformers. Each of these components have a correspondent graphcal representaton. From the graphcal model, the mathematcal structure of the system,.e., the state representaton, can be deducted. Four types of generalzed varables are consdered n ths technque, as nown: stress (e), flow (f), moment (q) and dsplacement (p). In the model developed by [20], the flow varable f represents the evoluton of the materal flow over a gven secton of the manufacturng system, whle the moment q s the producton volume, whch corresponds to the ntegral of the producton flow. The varable stress e s used to represent the couplng phenomenon between a machne and ts precedent stoc, n the case when ts producton capacty s mpeded by the entty located upstream for mssng avalable materal. The dsplacement varable s not used. The producton enttes used are: sources, stocs, machnes, convergent and dvergent junctons and wells. The sources provde the materal flow to the system, whle the wells are smlar to stocs wth nfnte capacty, used to represent the system outputs. The machnes are represented by resstors, whle the stocs are modeled, by analogy, as capactors. Each machne s preceded by a correspondent stoc; they are connected by means of a couplng structure, formng a producton staton. The convergent and dvergent junctons enable the representaton of the topology of the manufacturng system,.e., they aggregate the dfferent paths of flow that must go through an specfc staton or they dstrbute the materal flow nto the dfferent statons of the system. The bond-graph representaton of a staton, that s, a stoc-machne entty s shown n Fg. 7. In order to llustrate the bond graph applcaton to manufacturng systems, [20] modeled the sngle-product manufacturng system presented n Fg. 8. The state representaton of the manufacturng system s derved from the consttutve equatons of each element,.e., resstor, capactor, juncton, etc., whch are well nown among the bond graph users. U 02 S 02 U 01 S 01 nput e e f e C : C 0 1 R : T = 1/ U 1 S e : mn(1, q ) output e s Fgure 7. Bond graph model of a staton [20]. Staton 2 U 2 Staton 1 U 1 Staton 3 U 3 f s Staton 4 U 4 P 4 Fgure 8. Elementary sngle-product manufacturng system modeled and smulated n [20]. The control objectve s to adjust the level of the output flow of the system to attend the demand of the consdered product, whle, at the same tme, eepng the wor n process (WIP) at the desred levels. Ths objectve must be acheved by controllng the producton frequences of the machnes and the flow sources, represented by the varable U n Fg. 8. In [20], the control of the system was smulated for the followng condtons: null ntal stoc levels for all the ntermedate stocs; reference levels of 15, 10, 20 and 22 materal unts for the stocs 1 to 4, respectvely; reference producton frequency of the machnes derved from the soluton of the state model of the system for the permanent regme. Ths presented system s dynamc n the sense that t can respond to some unexpected events, such as machne breadowns. In order to test ths feature of the system, the breadown of machne 3 at the tme t = 45s was smulated. The machne remaned broen for 3s. After machne 3 stops, the producton frequences of the machnes 1 and 2 are temporally reduced to avod an excessve WIP accumulaton at staton 3. Also, the supply flow of the sources 01 and 02 s reduced. The quantty of materal accumulated n the stoc of staton 4 enables t to contnue producton normally. After approxmately 120s, all the reference levels for the stocs are acheved and the system becomes stable, operatng at ts permanent regme. Therefore, the results showed that the system was able to dynamcally respond to the machne breadown. III. COMPARATIVE AND CRITICAL ANALYSIS A comparatve analyss among the three dscussed models s summarzed n Table 1. As t can be seen, models 1 and 2 are smlar regardng ther applcaton and tme doman. These models wor wth detaled and dscrete 42

7 producton orders, whlst model 3 uses weghted averages calculated from dscrete orders data. Also, model 3 s sutable for a more complex producton confguraton. Thus, the use of average values may be advantageous to smplfy the soluton of the problem, snce job shop schedulng problems are NP-complete. TABLE I. COMPARISON BETWEEN THE PRESENTED MODELS Modelo 1 Modelo 2 Modelo 3 Modelo 4 Doman dscrete dscrete contnuous contnuous Applcaton schedulng schedulng shop floor control shop floor control Nature of the dynamc, not statc dynamc, automatc dynamc, automatc problems automatc Producton not applcable (sngle flow shop sngle machne job shop confguraton product) Number of multple multple multple sngle products/ jobs Man varables and parameters Theoretcal bacground for modelng processng tmes, maespan extenson of Johnson s algorthm processng tmes, due dates, controller gans, lateness expressons of PI and PID controllers (not used n the dynamc sense) wor content, WIP, range, baclog, utlzaton, performance analogy wth flud systems, funnel model, logstc curves WIP, nventory reference levels, frequency of operaton of the machnes analogy wth electrcal systems, bond graph technque It s worth mentonng that model 2 s, n fact, an teratve method to obtan a near optmal schedule, replacng conventonal heurstcs. Therefore, t s not a dynamc model n the strct perspectve of System Dynamcs and Control Theory. The feedbac loop present n ths model s an nternal element that s part of the algorthm for schedulng optmzaton; t does not wor as a controller tself. The dscrete varable t that appears n ths model represents the teratons executed to reach the soluton. There s no drect relaton between ths varable and the real tme of shop floor events. Although some dsturbances may be presented to the model, such as the ncluson of an extra job to be scheduled, t deals n essence wth a statc problem, where there s a fxed number of parts to be scheduled and, after a gven number of teratons, the best schedule s found. The model 1, on ts turn, has a vald feedbac system. From the desgn perspectve, however, t does not ft nto the conventonal parameters of control theory, snce the compensaton acton of the system s not automatc and t s not mathematcally represented. The compensaton, n ths case, s done by an acton of the user, whch reapples the proposed heurstcs to a dfferent set of ntal condtons. On the other hand, ths practcal feedbac of the schedulng executon status s of much nterest for managers, even f t s not automatc. Thus, ths feature s an advantage of model 1. In the sense of automatc feedbac, the models 3 and 4 are the most algned to control theory prncples. The controllers of these models automatcally respond to an nput dsturbance, amng to mnmze the effect of ths dsturbance and brng the system bac to a stable pont. The dsturbance corresponds to the arrval of an urgent job, n the case of model 3 and a machne breadown, n the case of model 4. The varable tme (t) consdered n model 3 corresponds to real shop calendar days. Thus, t s possble to obtan an accurate estmatve of how much tme the system would need to stablze and how much capacty ncrement would be necessary. On the other hand, model 3 s much more complex than the others not only regardng mathematcs, but also n terms of practcal applcaton. It requres the contnuous measurement of several varables related to the schedule executon n the shop floor and the estmaton of varous parameters of the system. In summary, ths model encompasses more varables and requres hgher data acquston and pre-processng efforts. The common element of the models are the applcaton for whch they are desgned. As prevously sad, all the models are developed for producton schedulng or producton control n the short term. On the other hand, t can be seen that the methodologes employed for modelng and the varables used are pretty dverse. The producton confguraton for whch the models are applcable also dffers. IV. CONCLUSIONS AND DIRECTIONS FOR FUTURE WORKS Ths paper presented and dscussed three recent models for Schedulng and Shop Floor Control based on control theory elements. The presented comparatve analyss hghlghted some advantages and dsadvantages of each model, beng also useful to help practtoners when choosng the most sutable model for specfc contexts. Ths short revew showed that there s a lot of room for the development of dynamc models for Schedulng and Shop Floor Control. In comparson to the other applcatons of control n producton and nventory systems, ths body of nowledge s stll ncpent. One relevant branch would be usng control theory n the development of models for dynamc schedulng, snce the vast majorty of wors approaches statc problems, usng a varety of heurstcs. Other drecton could be the extenson of some models, whch were appled to a sngle machne confguraton, for nstance, to more complex confguratons such as flow shop or job shop systems. An addtonal contrbuton would be the applcaton of the presented models n real systems, n order 43

8 to defne more realstc parameters and evaluate system performance. Many dynamc and control models rely on several parameters,.e. tme constants, and values for the controller gans. Usually, for electrcal or mechancal applcatons, there s a systematc procedure for determnng these parameters, whch does not exst for most of the manufacturng applcatons. A methodology that focuses on ths pont can be also a subject for future research. The Artfcal Intellgence tools could be appled n the System Identfcaton feld, n order to help to defne the parameters of the modeled manufacturng systems. The pattern recognton capabltes of the Artfcal Neural Networs are often appled to that am, such as n [21-25]. In some of these wors, fuzzy logc s also appled [21] [25]. Once agan, most of the exstng applcatons are devoted to mechancal, electrcal or chemcal systems. The lterature lacs applcatons of AI tools to System Identfcaton of manufacturng systems. 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