Introduction of a novel Methodology for Inter-branch Flexibility Measurement of Production Systems ecoflex

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1 Introducton of a novel Methodology for Inter-branch Flexblty Measurement of Producton Systems ecoflex Sven Rogalsk ISPE/PDE, FZI Forschungszentrum Informatk Karlsruhe, Germany and Prof. Jvka Ovtcharova IMI, Unversty Karlsruhe (H) Karlsruhe, Germany ABSRAC Demands on producton systems are changng constantly as a result of changng compettve condtons and are lnked to the performance goals of tme, qualty, cost and nnovaton ablty. he ncreased uncertanty of plannng, regardng knds and volume of producble products, s an especally complcated challenge for producton companes, whch therefore leads to a growng demand of flexblty. In ths context, methods for estmate the flexblty of producton systems wll be more mportant. he followng artcle presents the constructon and the methodology of an nnovatve evaluaton technque called ecoflex, whch allows producton planners and manager to create relable statements about ther producton systems. hs paper detals the general concept for estmatng the flexblty of volume, mx and expanson, and the mathematcal approach to calculate concrete ratos for these flexbltes on dfferent levels of the producton system -- from the workplace level to the factory level. Keywords: Flexblty Measurement, Producton Systems 1. Motvaton he basc condtons of economc producton have changed greatly n the last years and have enormously ncreased the mportance of the flexblty of producton systems. In partcular, the handlng of the contnuously growng uncertanty of plannng, regardng knds (product/varant mx) and volume (output) of producble products, s a pvotal success factor for protecton of compettveness [1] [2]. As a reacton to ths, producton companes are forced to adapt ther systems, strateges and concepts to permt enough range of freedom to handle these uncertantes [2] [3] [4]. Presently, ntensvely followed strateges, lke Agle Manufacturng, Mutablty and Holstc Producton Systems, consder the flexblty as well as further assocated propertes of adaptaton and modfcaton as an mportant goal. hey nfluence the dfferent concepts about producton system desgn and organzaton, whch drectly depend on producton strateges. [3] [2]. In today s turbulent operaton envronment, there exst many methods to realze flexble producton: Outsour cng, acquston of hgh automated manufacturng systems, Insourcng, ncreasng of stocks or transton to flexble workng hours [5] [6] [7] [8] [2]. Practce shows that these methods can contrbute to more flexble producton wthn a planned range [9] [6] [10]. But the problem s that there does not exst satsfyng technque to estmate the flexblty to allow evaluaton of the lack of flexblty n producton systems [9] [11] [4] [8]. he absence of such bases of estmaton, especally n product mx and necessary volume, s a tough challenge for producton companes to fnd the optmal degree of flexblty n the applcaton of such methods and guarantee an economcal producton n ths way [8] [11] [1]. For example, out of fear of mage and turnover losses, a company bulds a hgh potental of flexblty to prevent havng demands whch cannot be met. But the potental of flexblty wll not be used, leadng to needlessly hgh addtonal costs that can be dangerous for a proftable producton. Vceversa s also true when the potental of flexblty s lackng. hs wll lead to adverse effects caused by contnuous, quck, unplanned and uncoordnated system adaptatons. As a result, an economcally worthwhle balance should be found between the uncertantes and the necessary degree of flexblty, as shown n the followng fgure. Uncertanty Internal and external nfluences Flexblty of Producton Systems Potenzal actons Stocks,, Insourcng, Outsourcng, hgh automated systems, flexble workng hours Levels of System Factory, Segment, Lne, Workplace Optmal Degree of Flexblty Fgure 1: Economcally worthwhle balance between uncertantes and necessary degree of flexblty based on [8]

2 2. Current Challenges for Command of Flexblty he prevous fgure leads producton companes to the queston: how can we calculate the degrees of freedom and varety n producton n reacton to fluctuatons n volume demands? hese knds of uncertantes are not only relevant from an operatonal pont of vew, but also from a strategc perspectve. herefore, understandng the possbltes for capactve expansons s also key ssue. Moreover t s mportant to know how changes of the product mx affect the economcal producton. In ths context t should be possble to analyze the flexblty on dfferent levels of vew, because drver of producton changes can nfluence dfferent levels of a system. Hence an approved methodology for estmatng the flexblty has to allow a unform and obectve evaluaton for the followng three knds of flexblty: volume flexblty product/varant mx flexblty expanson flexblty. he volume flexblty s a measure for the degree of capablty to react to changes n demands, especally to ncreasng demands. he mx flexblty s the grade of stablty and freedom concernng the product/varant mx of producton systems. Changes n demand and offer have not only operatonal mportance, but also strategcally relevance. In ths context the expanson flexblty plays a promnent role for estmate opportuntes to modfy systems for permanent ncreasng of capacty [12] [11]. In spte of the hgh mportance and exstng varous soluton methods, such methods are rarely used n the ndustral practce. In the lterature there s a huge amount of approaches. hs shows there s great nterest on ths topc, but also the lack of a generally accepted method. Intensve nqures for selectve approaches showed there are many methods for estmatng volume, mx or expanson flexblty. But, comparson of those methods shows that they follow dfferent termnologes and are usually developed for a specfc problem; the applcatons of the methods are restrcted to ther specfc problems. Hence comprehensve and obectve estmatons regardng volume, mx and expanson flexblty on dfferent levels n producton systems are not possble, whch shows the necessty for novel soluton approaches. 3. Desgn and Functonalty of ecoflex ecoflex s an nnovatve evaluaton methodology, whch allows obectve and nter-branch evaluatons about volume, mx or expanson flexblty, based on concrete calculatons. It ntegrates dfferent calculaton methods, called flexblty metrcs. hese consder n addton to aspects of tmes and costs also dfferent levels of vews, the workplace-, lne-, segmentand factory vew. Furthermore ecoflex ensures practcable usage of flexblty metrcs for the producton and change management. hs s acheved usng a producton system model, a scheme of producton nfrastructure obects to be evaluated as well as ther relatons and dependences. he connecton of the flexblty metrcs wth ths model s the precondton to analyze the adaptablty of producton facltes, furthermoret allows to estmate possble alternatve confguratons (cp. Fgure 2). Fgure 2: Graphcal User Interface of ecoflex ecoflex supports producton planers and managers n makng relable evaluatons about the flexblty of ther producton systems, and makes t possble to react to the ncreasng complexty and dynamc as well as decrease reacton tme to servce the market. So ecoflex s an nstrument for decson support, whch can analyze and compare both real exstng producton nfrastructures and nfrastructures that are stll to be planned. In ths context analyzes between producton system from varous branches are possble and lead to remarkable synergetc effects. 4. Concept of Evaluaton of Flexbltes n ecoflex Volume flexblty he key rato of the volume flexblty shall evaluate the possblty of a short-term, proftable capacty adustment wthout a change of the amount of elements and the structure of the examned producton-system. he evaluaton of ths knd of flexblty s conducted by lookng at the margnal, quanttatve output wthn a predefned perod of tme (e.g. a week or a month). In ths perod, a proftable producton s feasble. Hereby the relevant key ratos applyng to the defned observaton perod are the break-even-pont and the Capacty Maxmum of the producton-system. Whle the break-evenpont s ndcatng the output whose earnngs exactly cover the relevant expenses, the Capacty Maxmum s markng the greatest, stll proftable (quanttatve) output of the producton system. he capacty maxmum s determned by the techncal effcency and organsatonal steps (e.g. overtme or changes of the shft work). Both ratos fx the lmts of a range called Flexblty Space. Wthn ths Flexblty Space the producton s economcally flexble (cp. fgure 3).

3 Fxed Costs Revenue/ Costs Pont Flexblty Space Capacty Maxmum otal Costs Revenues (varable + fxed Costs) Output Fgure 3: Evaluaton of the Flexblty Space n a producton system Mx flexblty he concept of the Mx flexblty ntends to assess the freedom n composte of the product/varant mx of producton producton-programme. he freedom s the ablty to renounce certan products or to substtute them wthout an mpact on the hghest reachable proft. Startng wth an optmal productonprogramme, t makes sense to determne the Mx flexblty by usng the average devaton of the producton-proft. hs devaton s derved from the quanttatve change of the products that need to be manufactured. he necessary ratos for that are the system-optmal producton-proft and the productspecfc proft-devaton. he system-optmal producton-proft s the greatest possble proft for a certan perod of tme that can be reached when the producton-programme s composed optmally. hs s concernng the type of products as well as the amount of products to be manufactured. On the contrary, the productspecfc proft-devaton s nvestgatng how a quanttatve change of a sngle product nfluences the system-optmal producton-proft whle all other crcumstances reman unchanged. Consequently the hghest possble proft of the examned producton-system needs to be calculated, where as a sngle product out of the manufacturng portfolo s not beng manufactured. hs calculaton needs to be conducted for every sngle product of the manufacturng portfolo he productspecfc proft-devaton s derved from the dfference to the system-optmal producton-proft. In order to be comparable, heterogeneous producton-systems are to be descrbed n the form of a rato. By computng the arthmetc mean for out of all product-specfc proft-devatons contaned n the productonsystem, t s possble to determne the average proft-devaton of the producton. Accordng to ths concept a productonsystem s completely mx-flexble, f the proft always remans constant, no matter what product out of the manufacturng portfolo s beng manufactured. Mx flexblty he expanson flexblty shall show the ablty of a productonsystem to ncrease ts capactes permanently by changng ts amount of elements and/or ts structure. Due to the fact that t descrbes a system-specfc Cost-Beneft Rato wth regard to the capacty ncrease, the economcal expendture for a capacty ncrease s the crucal evaluaton parameter. he dffculty hereby s the quantfcaton of ths rato. In addton to that, often there are varous alternatves of ncreasng capactes. hose alternatves exhbt dfferent ntensty of tmes and costs and can lead to dfferental ncreases of the capactes. herefore, a so-called target-capacty must be fxed. he targetcapacty states by how many percentages the current Capacty Maxmum has to be ncreased. hrough that the alternatves of expansons whch do not reach the new border of capacty can already be elmnated. All other alternatves that reach the target-capacty respectvely surpass t, are quantfed on the bass of a homogeneous evaluaton method by usng the quanttatve Flexblty Space explaned n secton Hereby the prevously defned target-capacty s assumed to be a fx value: the new Capacty Maxmum of the system. Notwthstandng whether there s one or more potental alternatves surpassng the target-capacty. So the sze of the Flexblty Space of each permssble alternatve of expanson depends on ts break-even-pont. he earler an alternatve reaches ths pont, the greater s ts Flexblty Space and consequently has a more postve effect on the Cost-Beneft Rato of the examned system. Fnally, n order to determne the Cost-Beneft Rato n a quantfable way respectvely the economc expendture resultng from t, the best alternatve of expanson (the one wth the bggest Flexblty Space) s beng compared wth the orgnal Flexblty Space of the system. he proportonal devaton of the two Flexblty Spaces from each other gves nformaton about the expanson flexblty of the system (cp. fgure 4). Fxed Costs Revenues/ Costs Fxed Costs Legend: current system alternatve of expanson Pont Flexblty Space Punkt Flexblty Space Capacty Maxmum arget Capacty ( +30% ) Revenues otal Costs otal Costs Fgure 2: Valuaton of the Cost-Beneft Rato of an expanson alternatve 5. Basc Calculatons used n ecoflex Output Based on the conceptual consderatons of the assessment methodology the flexblty relevant parameters that determne the volume, mx and tmng to expand flexblty are dependant from cost- and product-dependent restrctons. hereby they can, because of the common exstence of varous manufacturng facltes of one or more products, for example, because of a number of exstng dentcal or smlar resources and manufacturng flows, whch could ultmately lead to nconsstent or even contradctory assessments of flexblty. herefore, t s absolutely necessary, to determne the relevant parameters on the bass of ther lmts (mnmum or maxmum), based on a vald producton plan and the current restrctons, that are thus optmal. Such a producton plan, often called producton program, descrbes the system resources n terms of ther nature and extent of ther use for a specfed perod, leadng to a certan number of manufactured products. he common challenge n the calculaton of the varous flexbltes wthn the valuaton methodology s thus the determnaton of restrcton conform, optmum producton programs, to dentfy economc producton lmts. hs leads to so-called optmzaton problems, whch can be adopted as lnear. her soluton s usually usng the smplex algorthm, whch should be used as the man method of lnear optmzaton

4 problems. Before the smplex algorthm can be appled, however, t s frst necessary to standardze the optmzaton problem. hs s acheved through the Ecoflex-specfc bass algorthm, whch s descrbed by the followng three successve steps. Formulaton of the obectve functon (Step 1) Wth the formulaton of the obectve functon, result varables R wll be defned n the form of a vector x, whch descrbes a producton plan. It defnes to each product EZG and workplace the manufactured producton quantty x EZG,. hereby R ndcates the amount of all product-workplace combnatons, E the set of all products and W the amount of workplaces. An obectve functon s requred for the calculaton of the result varables, n order to resolve the respectve optmzaton problem n terms of dentfyng an optmal R producton plan. It s represented by a vector c, where R s the set of all possble product-workplaces combnatons. he target value of ths functon c for a determned producton plan, s the scalar product of and c c x : ( x) = c x = c1 x1 + c2 x2 + K+ c x R R c Each vector component represents the target value, whch stands for the manufacture of the products EZG at workplace. By the calculaton of the ndvdual characterstcs of amounts-, mx- or extenson- flexblty ths obectve functon may vary. hs depends on the crtera whch dentfyng the partcular characterstc. Formulaton of the constran (Step 2) he constrants, expressed by the mathematcal and logcal relatons of the respectve optmzaton problem, as well as the target functon are dependng on the flexblty relevant ndcator, whch has to be determned. herefore they can vary. However, wthn the basc algorthm two types of secondary condtons can be provded. hey are vald for all n the valuaton methodology feasble and flexblty relevant calculatons. he tme condtons are the frst type of constrants. hey represent the man lmtng factors for the relevant optmzaton problems. hey result from the fact that for the producton of one unt of the product EZG at workplace a certan process tme t s needed. Moreover, the maxmum PZ, EZG, workng tme for each workplace t max, per perod P s constraned by the used workng tme model AZM and the addtonal workplace-specfc dle perods t zl,. As a consequence an nequalty constrant reveals for each producton system contaned n the workplace, whch can be summarzed as a matrx nequalty: stands for a matrx of sze matrx x max, W R. Each value of the represents the process tme, whch workplace requres to produce the product from r,. If r, doesn t apply to the workplace, then the respectve matrx entry assgns the value 0 as a process tme. On the other hand, descrbes max a vector, whch ndcates the maxmum operatng tme t max, mnus the extra dle costs t for every workplace. zl, he rato condtons are the second fundamental type of constrants of the basc algorthm. hey result from the product mx, whch has to be specfed for the flexblty calculatons and from the component dependences of the ndvdual products. he latter can be descrbed usng a so-called n n component matrx C, whch specfes how many unts of a product are drectly used to manfacture a unt of another product. he product mx, whch represents the rato of fnshed products n terms of ther sale, s descrbed wth the vector P v. For not saleable products EZG ZP apples v = 0. he smplex algorthm provdes the manfactured product amounts to be sold, whch followng ths vector, have to be a multple of v. hat means the saleable output x' and x' of two products ( EZG, EZG ) E must meet the restrcton n n C x' : x ' = v : v. Snce accordng to the matrx selfmanufactured products can be used n other products and because of the ncluson of defectve products, t s qute possble that the total output quanttes dffer from ths proporton. In order to descrbe the rato condtons resultng from the product mx n a smple mathematcal form, a rato matrx E R V has to be defned, summarzng all product mx relatons. In addton, t has to detach any unts from the relaton, whch are no longer avalable because of defecton or further processng. hs requres a pror knowledge of the respectve total producton x EZG for each product EZG on all workplaces. On the other hand, an a pror knowledge of the overall needs for every product EZG ZP used for the manufacture of downstream products n producton process s also necessary. he resultng calculatons are summarzed n the base algorthm represented n the followng matrx equaton: V x = 0 hs matrx equaton leads to an optmal producton plan. However t doesn t have to explot all producton capacty, as the product mx has to be taken nto account. he lmtng factor s thus the product, whch reaches ts capacty lmts frst. Formulaton of the lnear optmzaton problem (Step 3) In order to formulate the basc optmzaton problem for calculaton of varous flexbltes n ecoflex, t s necessary to convert the matrx equaton, whch ndcates the rato condtons. hs necessty arses from the fact, that the standard procedure for solvng lnear optmzaton problems doesn t allow lnear equatons as a constrant. A possblty s to transform each of the equatons nto two nequaltes, as an equaton a = b s equvalent to a b ( a) ( b). he resultng nequaltes led durng the development of

5 ecoflex to numercal dffcultes, so that often an unvald soluton n the usual data types was dsplayed. For ths reason, a personal nnovatve extenson of the lnear optmzaton problem was made. It provdes an effcent reformulaton of the rato condtons. he basc dea s that each of the equatons n the summarzed rato matrx allows to calculate a soluton varable of the other matrces. hus, t s not absolutely necessary to determne all varables n the course of solvng of the optmzaton problem. It s better to use the smple weghted sum that results from the gven equatons. hs wll prevent the mentoned numercal problems and smplfy the soluton, because the algorthm must consder less varables than prevously. he appled calculaton rule s explaned as follows: he equat on system gven by the equaton V x = 0 should be solved n accordance to the approprate varables. hs results n a form n whch these varables can be easly calculated by nsertng the values of all other varables. he coverage of these other varables usng the vector y, allows the formulaton of a transformaton matrx E, so that x = E y. All calculated quantty vectors fulfl the ancllary condton equaton, and vce versa, all the quantty vectors, whch fulfll the ancllary condton, can be represented n ths form. As a consequence of ths reformulaton t s necessary to transform the obectve functon and the remanng constrants too, so that only a lnear optmzaton problem y has to be solved. Summarzed results thereof: Requrements Obectve Functon Constrants Search for producton plan x = E y, whch lead to a maxmum obectve functon c ( y) = c Ey = ( c E) y Ey = ( E) y max x = Ey 0 Fgure 3: Formulaton of optmzaton problem for basc algorthm Usng ths clever transformaton of the constrant condtons n the form of lnear nequaltes s the appled mathematcal model for the basc algorthm, consstng of calculaton parameters, outcome varables and constrants, transformed n a form from whch wth the help of standard soluton procedures an optmal producton plan can be determned. 5. CONCLUSIONS hs artcle provded a detalled nsght nto the procedure of flexblty-measurement of producton-systems usng the ecoflex method. hs approach, that ncludes an extensve examnaton, allows a novel, comprehensve manner of examnng and evaluatng flexblty. hereby varous levels of the system are consdered, from the workstaton-level untl the factory level. Smultaneously t creates a fundament for the comparableness of producton-systems of dfferent ndustry sectors. hat facltates companes to unerrngly ncorporate the flexblty as a decson crteron when selectng and formng the producton-system sutably. Currently the evaluaton-method EcoFlex s expermentally appled by a reputable, globally operatng automoble suppler. One of ts producton areas s analysng defcts n flexblty and evaluatng alternatves of extensons on the bass of actual producton-data. Furthermore, the evaluaton-method s assmlatng addtonal requrements regardng possble analyses. By dong so, t s pushng the expanson and temsaton of the functonalty and of the applcablty of ecoflex. 6. REFERENCES [1] Nemann, J.: Ene Methodk zum dynamschen Lfe Cycle Controllng von Produktonssystemen, Dssertaton Unverstät Stuttgart, 2007 [2] Kaluza, B.; Blecker,.: Erfolgsfaktor Flexbltät. Strategen und Konzepte für wandlungsfähge Unternehmen, Erch Schmdt Verlag, Berln, 2005 [3] Barth, H.: Produktonssysteme m Fokus, In: wt Werkstattstechnk onlne, Jahrgang 95, Heft 4, Sprnger- VDI-Verlag, Düsseldorf, 2005 [4] Krappe, H..; Rogalsk, S.; Sander, M.: Challenges for Handlng Flexblty n the Change Management Process of Manufacturng Systems, IEEE Conference on Automaton Scence and Engneerng (IEEE-CASE), Shangha, 2006 [5] Horst Wldemann, H.: Betrebermodelle: En Betrag zur Stegerung der Flexbltät von Unternehmen?, In: Kaluza, B.; Blecker,. (Hrsg.): Erfolgsfaktor Flexbltät. Erch Schmdt Verlag, Berln, 2005 [6] Bellmann, K.: Flexblserung der Produkton durch Denstlestungen, In: Kaluza, B.; Blecker,. (Hrsg.): Erfolgsfaktor Flexbltät. Erch Schmdt Verlag, Berln, 2005 [7] Beyer, H-.: Optmales Leferantenmanagement, Onlne Lehrbuch Marktprozesse, Unverstät Erlangen-Nürnberg, 2004, lefmgt.pdf [8] Zäh, M. F.; von Bredow, M.; Möller, N.: Methoden zur Bewertung von Flexbltät n der Produkton, In: Industre Management, GIO-Verlage, 4/2006 [9] Kaluza, B.; Blecker,.: Flexbltät - State of the Art und Entwcklungstrends, In: Kaluza, B.; Blecker,. (Hrsg.): Erfolgsfaktor Flexbltät. Erch Schmdt Verlag, Berln, 2005 [10] Wurst, K.-H.; Hesel, U.; Krcher, C.: (Re)konfgurerbare Werkzeugmaschnen notwendge Grundlage für ene flexble Produkton, In: wt Werkstatttechnk, Band 96, H. 5, 2006 [11] Rogalsk, S.; Krahtov K.: Änderungsmanagement für zukunftsorenterte Produkton (el 1), edm-report Nr. 2, Dressler Verlag, 2006 [12] Rogalsk, S.; Krahtov K.: Änderungsmanagement für zukunftsorenterte Produkton (el 2), edm-report Nr. 3, Dressler Verlag, 2006