Modeling of a Three-Echelon Supply Chain: Stability Analysis and Synchronization Issues

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1 Modelng of a Three-Echelon Supply Chan: Stablty Analyss and Synchronzaton Issues K.R. Anne, J.C. Chedjou, S.K. Bhagavatula, K.Kyamakya Insttute for Smart Systems-Technologes Unversty of Klagenfurt Klagenfurt, Austra Abstract Ths paper ntroduces the supply chan networks ntegraton and dscusses the nterest of synchronzaton wthn them. The evaluaton of the causes of uncertantes wthn the supply chan networks s consdered. The structure of a threeechelon supply chan s envsaged and the modelng of ths structure s carred out. It s shown that the supply chan network can be exposed to both external and nternal perturbatons. The orgn of these perturbatons s dscussed and t s shown that the stablty of the supply chan network s very senstve to these perturbatons. The effects of the external perturbatons on the supply chan network are consdered. It s shown that these perturbatons can saturate the supply chan network and also create bullwhp effects and chaotc phenomena wthn the network. A method s developed whch s based on an adaptve algorthm for the automatc cancellaton of the effects of external perturbatons by re-adjustng the nternal thresholds of the supply chan network n order to acheve synchronzaton. Some addtonal nsghts nto theory and practce n supply chan managements are provded. Keywords Synchronzaton; Supply chan networks; Supply chan network control; Supply chan optmzaton; Bullwhp effect; Chaos n supply chans I. INTRODUCTION Supply chan management (SCM) s the combnaton of management and scence. SCM helps n mprovng/managng the way a company fnds sources for the raw components t needs to make a product and the way t dstrbutes the product to customers. The modern supply chan networks are global n nature and have many nterconnectons.e. dependency or couplng between each. The supply chan network comprses of geographcally dspersed facltes, lke sources of raw materals, manufacturng plants, warehouses and transportaton facltes. The facltes may be operated by sngle entty, many enttes wthn a company, thrd-party provders or other companes. The prmary objectve of the supply chan network, or the ndvdual enttes n the network, s to delver the product n the correct quanttes at correct tme by meetng all the qualty measures wth compettve prce. In addton to ths, the threshold of stocked products, quanttes must be contnuously sustaned and uncertantes (that can occur wthn the supply chan) must be well controlled n order to avod breakng n stocks and also the well known bullwhp effect at a gven level of the supply chan. Ths can be acheved through a good coordnaton or synchronzaton between the varous levels of supply chan. In order to acheve the stated objectve, all the stakeholders n the supply chan network are ntegrated/coupled. The frst part of couplng s concerned wth functonal ntegraton of purchasng, manufacturng, transportaton, and warehousng actvtes. Besdes functonal ntegraton ntertemporal couplng, also called herarchcal ntegraton, of these actvtes over strategc, tactcal, and operatonal levels s also mportant [, 2]. Ths ntertemporal couplng requres consstency among overlappng supply chan decsons at varous levels of plannng. However the major role of the ntertemporal ntegraton s n product lfe cycle desgn. Improved couplng of actvtes across multple companes/enttes n a supply chan s a concern of ncreasng mportance. Informaton technology s the key enabler for the couplng n supply chan. The nformaton systems provde the necessary nformaton needed for the ntegraton. Each entty works wth ther own objectve, there by showng a tendency only for loose couplng. The structure of the paper s as follows, secton II s concerned wth a bref descrpton of few factors that are contrbutng for the uncertantes and need to synchronze the uncertantes. Secton III deals wth supply chan modelng. We present the structure of the supply chan under consderaton whch s made-up of three levels. The communcaton between these levels and also the data traffc wthn them s explaned /dscussed and t s shown that the scenaro/dynamcs of the complete supply chan can be modeled by the Lorenz system. In secton IV, we wll descrbe what type of synchronzaton s appled n supply chan networks. Secton V descrbes the effects of the external perturbaton on the system and the controllng method. Transtons from regular effects to bullwhp effects or chaotc effects are shown through the stablty analyss. Secton VI deals wth the concluson and proposals for future works. II. UNCERTAINITIES IN SUPPLY CHAIN NETWORKS Even though ntegraton of the stakeholders should provde the deal soluton for the optmzaton of the supply chan networks, n many cases t s not [-3]. Busness s not usual always; there are many thngs that happen wth tme. The major source for uncertantes n supply chan networks orgnates from the fact that operatons are performed over

2 long perod of tme and stakeholders are dspersed globally. Supply chan management s a complex set of processes and flows (nformaton flow, product flow, monetary flow) that can ether add a great deal of effcency and proft or can cause serous problems for a company. SCM s technology ntensve n some aspects, n some ways t can be compared to a smple game gossp game. In the game, one passes the secret to hs frend, whch s then passed around a crcle of frends. The secret can be true ether because the captal nvested s small or they can arrange fnancng and storage at advantageous rates, also those whose setup costs are hgh, wll prefer large lot szes and correspondng large nventory. Retalers wth hgh value of goods but no setup costs wll prefer to hold the mnmum stock they deem necessary to ensure good customer servce. These ndvdual varyng factors create demand varablty n order to make maxmum profts. There are also the problems of msunderstandng the market promotons, socal mstrust, forecastng problems. All these leads to more nventory at or false, but what s usually the case wth the secret s that t becomes exaggerated f the secret starts out as there s an nsect outsde, t ends as a monster s n the school. The supply chan can often be seen as the same crcle. Today s supply chans pass nformaton relatng to tem nformaton, forecastng and replenshment upstream and downstream among manufacturers, brokers, dstrbutors, retalers and warehouse, transportaton, management and global trade systems. The fnal result s a flow of nformaton from the creaton of a product to the pont where that product s sold to the end consumer. As n the gossp game, the accuracy of nformaton often depends on the qualty of the data at the begnnng of the cycle, and mantanng same nformaton throughout the supply chan. If the nformaton s wrong n the begnnng, t never has a chance of beng correct when t fnally gets up or down the supply chan. In fact, f nconsstences reman, there are chances for errors to propagate through the whole supply chan. The defnton of a truly effcent supply chan s when all companes nvolved are communcatng correct or relable data a manufacturer s communcatng the relable product nformaton and recevng accurate purchase orders; a retaler s recevng the specfc products that were ordered; and the product s avalable to the end consumer at the rght tme and at the rght prce. However communcatng the relable data s always not possble n supply chans as each stake holder has dfferent objectves and constrans. In well-managed supply chans, the nventory flows between members of the chan wth lttle delay. The goal of supply chan management s to optmze the whole system [-3]. Total chan-wde transportaton, holdng, and setup costs should be mnmzed. However, ths ntegraton may be dffcult to acheve because dfferent members of the chan have conflctng objectves. Supply chan members whose nventory holdng cost s small, dfferent levels and can cause the well known bullwhp effect or forester effect. In ths paper, the occurrence of ths effect and also the chaotc effect n the supply chan due to external perturbaton of the system s shown. III. SUPPLY CHAIN MODELING The theoretcal framework for the supply chan management underles the settng, optmzaton and control of the system model. Here, In ths work we use the structure of a three-level supply chan as llustrated n Fg.. Tme perod m Rato of customer demand satsfed k Safety stock coeffcent x y z The quantty demanded for products n current perod The quantty dstrbutors can supply n current perod The quantty produced n current perod depend on the order A three echelon model s envsaged n Fg. to descrbe a smple scenaro n a very complex supply chan. Fg. also llustrates the relatonshp between the three layers. The orders they make may not be equal to orders they receve. The order out quantty depends not only on how much nventory you have already, and how much you want to supply out. Order out quantty at retaler depends on the rato m at whch the demand s satsfed durng the prevous order. Dstrbutor needs to take nto consderaton among other thngs, the dstorton rate r that can occur n the nventores. The producer needs to take care about the safety stock k n order to avod the small producton batches. These phenomena are explaned below wth mathematcal modelng.

3 We consder that the demand nformaton s transmtted wthn the layers of the supply chan wth a delay of one unt tme. As llustrated n Fg., the orderng quantty s not same as the requested order quantty at any level. The order quantty at current perod of tme at retaler s lnearly coupled wth the dstrbutor and t s nfluenced by how much of demand s satsfed n prevous perod of tme. Ths phenomenon can be represented as shown n Eq.. x = ( ) m y x () m s the rato at whch the demand s satsfed. As t appears from Fg., the dependency or couplng of dstrbutor on producer and retaler s no more lnear. Indeed the dstrbutor needs to take the combned effect of retaler and producer nto consderaton before makng hs order,.e., quadratc couplng. Apart from ths, the dstrbutor also needs to take nto consderaton the expected loss rate or dstorton that can take place on the producer s supples. Ths can be expressed mathematcally as shown n Eq. 2. y ( ) = x r z.(2) r s the dstorton coeffcent. The producton quantty from the producer unt typcally depends on the dstrbutor s orders and the safety stock. However the dstrbutors orders agan depend on the retaler s orders,.e., the producer needs to take the combned effect of retaler and dstrbutor nto account before makng producton decsons. Ths can be represented as z = x y + kz (3) Eqs. -3 represent the quantty demanded by customers (Eq. ), the nventory level of dstrbutors (Eq. 2) and the quantty produced by producers (Eq. 3). Where x < 0 denotes that the supply s less than customers demand n the prevous perod y <0 denotes that nformaton s severely dstorted and no adjustment s necessary to nventory level z <0 denotes the cases of overstock or return and hence no new productons. Evdently the contnuous forms of Eqs -3 can be rewrtten as Lorenz equatons of state: x& = σ ( y x) (4) y& = rx y xz (5) z& = xy bz (6) Dependng upon the parameter values, ths model produces a wde varety of nonlnear features. In Fg. 2, we showed the reference model wth the parameter values σ = 5 r = 29, and b = 2/ 3 to llustrate the regular state of the reference supply chan model. IV. SYNCHRONIZATION ISSUES IN SUPPLY CHAIN NETWORKS In ths secton we brefly ntroduce the mportance of synchronzaton and present the modern methods to deal wth t. When organzatons synchronze supply chans and have real-tme access to data, they enjoy several compettve advantages: Anomales and exceptons are dentfed early and the data for ntellgent response s mmedately avalable. Ths greatly mnmzes the bullwhp effect and saves downstream partners and customers from needless actvty Back-end processng of change orders, modfed nvoces, and updates to nventory systems can happen as decsons are beng made Vsblty nto partner systems makes plannng easer and enables managers to see opportuntes that were not apparent before. Ths vsblty also enables supply chan partners to collaborate more effectvely. Ths cooperaton s essental when problem resoluton requres the coordnaton of several supply chan partners Easer ntegraton and expanson. Because the synchronzaton and data passng mechansms are not based on packages from supply chan software vendors or ERP frms, the software s optmzed for all players. Packages can be changed wthout dsruptng the nfrastructure and new partners can be added easly Fgure 2: Reference System wth gven coeffcents Is supply chan synchronzaton the ultmate concept? In realty, t s only one of the steps towards the ntegraton of all components of the supply chan. To date, the majorty of supply chan effcences has come from mprovements wthn the four walls of each ndvdual company. Certanly, there has been collaboraton between tradng partners n terms of mproved communcaton (EDI and current nternet based web nformaton exchanges), better nformaton (pont of sale data and the CPFR ntatves), and a general wllngness to work more closely together. But the effcences have been ganed through mprovements that any executve can effect at hs or her own workplace by puttng n place the approprate company-wde ntatves amed at mprovng the nternal busness process. Now comes the most dffcult part: True coordnaton between and among all tradng partners, whch s most dffcult. To take the next step, t s crtcal that companes not only agree to communcate and work together, they must also begn to functon as a sngle entty.

4 Apart from all these data dscrepances, there may be other dsturbances whch occur due to external perturbatons. There are dfferent methodologes appled to study these dscrepances and to quantfy ther effects. In ths paper we study the two major synchronzaton types appled n supply chan networks based on the supply chan model [4]. Complete Synchronzaton: the cycle tme at an upstream stage equal to cycle tme of the next downstream stage Partal synchronzaton: the cycle tme at an upstream stage s an nteger multple of the cycle tme of the next downstream stage In ths paper, we present methodology to control the effects caused by external perturbatons through nternal measures. A. Complete synchronzaton Complete synchronzaton enables the supply chan to react quckly to changes n demand and n product desgn. Ths type of synchronzaton s partcularly sutable n just-ntme supply chan networks. To acheve the complete synchronzaton the complete chan should be ntegrated. Many retalers and manufacturers have looked to the Internet to provde a cost-effectve avenue for mprovng the data defcences present n today s supply chans. One of the man ways to decrease the amount of nconsstent tem nformaton beng passed among companes s to automate many of the tem mantenance functons, such as data changes and new tem ntroductons, performed by manufacturers. Synchronzaton tools automate processes that are tradtonally conducted through excessve paperwork, such as nformng tradng partners of changes to product nformaton. Ths synchronzaton method affects the regstry and lfecycle management of synchronzed products, locatons and tradng capabltes. Data synchronzaton nvolves a strategc combnaton of technologes, busness strateges and mplementaton of ndustry standard n messagng that tes together the nformaton management systems of all partes partcpatng n a gven supply chan [4, 5]. The modern synchronzaton tools provde automaton of the paper work but not concentrate on what happen f the gven data s slghtly changed accdentally. Effectve data synchronzaton frst nvolves makng nformaton vsble wthn a secured envronment, whch s agan a case that we are dscussng throughout ths paper. B. Partal synchronzaton Partal synchronzaton s acheved through the controller tem. Apart from the data synchronzaton as explaned n complete synchronzaton, a controller tem s developed to mtgate the effect caused due to tme lag. In these synchronzaton major efforts s placed n modelng the effect and quantfyng t. The modelng and quantfcaton of the effect caused by the tme lag, nformaton dscrepancy, and ndvdual objectves helps n desgnng the controller/synchronzer element. Ths controller tem can be unque for each entty or supply chan as a whole. Partal synchronzaton s also acheved ndrectly by quantfyng the regon where uncertantes exsts. After dentfcaton of uncertan regons they try to avod or extra careful n that regon [, 3-7]. In practce, as we dscussed n secton II and secton III, management of commercal supply chans s a challengng ssue as dverse pre-defned data thresholds or requrements wthn them should be currently stablzed wth regard to the exstence of some uncontrollable effects due to both nternal and external perturbatons to whch the supply chans may be subject. The dynamc character of the nformaton flows wthn the commercal supply chans s another factor whch makes t very dffcult to stablze the overall behavor of the whole supply chan. Therefore, the nstablty of the supply chan may be drectly perceved as the modfcaton of data thresholds or pre-defned requrements based on the uncertantes dscussed n secton II. In secton V, we wll descrbe the effects that can be caused by the external perturbaton to the stablty of the system and how t can be controlled nternally. V. SYSTEM ANALASYS AND SYNCHRONIZATION. The causes of supply chan nstablty can be broadly classfed nto two categores. The frst cause s the dynamcal and nonlnear character of the motons (.e. materal/products flow, nformaton exchanges, etc ) between dfferent enttes n supply chans. The second cause orgnates from the effects of both external and nternal perturbatons to whch the supply chan s subjected. An optmal management of the nformaton flows wthn the supply chans may be of hgh mportance n order to allevate the effects resultng n negatve consequences on the flows wthn the supply chans. Ths could be acheved through an adaptve control mechansm whch s based on a current comparson of the dynamcal data wthn the supply chans wth the pre-defned data fxed by the requrements of the supply chans. Here, an automatc or adaptve control of the flows wthn the supply chans should be able to detect changes n the flows wthn the supply chans and act accordngly/consequently (by undertakng a gven acton wthn the supply chans) n order to allevate the undesrable effects and therefore stablze the system behavor that has been perturbed. The achevement of synchronzaton s observed when the acton undertaken has allowed the recovery of the orgnal behavor (eventually thresholds or reference requrements) of the supply chan. Ths paper develops an adaptve method (algorthms and/or tools) for the systematc and automatc control of the flows wthn the supply chans. The external perturbatons can be a consequence of the dynamcal behavor of the market demand, forecastng methods, hgh lead tmes, etc. In fact, due to the dynamc changes as dscussed (n tme doman), some pre-defned data or requrements wthn the supply chans (thresholds lke safety stocks) may be varyng accordngly as consequence of these perturbatons. The nternal perturbatons wthn the supply chans are random (or undesrable) effects whch can orgnate from the malfunctonng of a gven echelon of the supply chan (e.g. Machne breakdowns, transportaton delays etc.,). It should be worth mentonng that a combnaton of the smultaneous effects of both nternal and external perturbatons may be responsble of the dynamc moton varatons (e.g. flow of materals, nformaton

5 exchange, etc.) wthn the supply chan. Ths s a concrete and/or realstc scenaro as the supply chans of many companes are currently exposed to the both types of perturbatons. Ths later scenaro s however out of scope of ths paper, whch does concentrate solely on external perturbatons and related nternal adjustment of parameters to acheve synchronzaton. Thus, for the sake of smplcty, we consder the case where there s no nternal perturbaton of the motons wthn the supply chans. In essence, ths work looks at the possblty of re-establshng approprate data thresholds fxed by the pre-defned behavor requrements. We restrct our analyss to the case where the external perturbatons are perodc. It s well-known that perodc waves/sgnals are characterzed by ther ampltude and frequency. Consderng ths restrcton, the ampltudes of perturbatons can gve/show the rate of varaton of the products quanttes. The frequency of perturbatons determnes the rhythm or the sequence of the process related to the varatons n the products quanttes. The development of methods (algorthms) to automatcally control and allevate the effects of external perturbatons s of hgh mportance as n practce the overall system behavor may be very senstve to external perturbatons. Ths may lead to nstablty. We develop a method based on an adaptve algorthm for the automatc cancellaton of the effects of the external perturbatons by re-adjustng the nternal thresholds. Indeed, ths method s an adaptve numercal code whch performs a regulaton by currently comparng the perturbed data wthn a gven supply chan wth the reference data (whch are fxed and pre-defned data) accordng to the requrements of the three echelon supply chan. Dependng upon the key characterstc parameters of the external perturbatons, the state of the flows wthn the reference scheme of the supply chan can even be saturated due to external perturbatons as shown n Fg. 3. Here, the saturaton manfests tself by a sudden exhbton of fxed or constant values/data along each echelon of the globally perturbed three echelon supply chan. Indeed, the states of the reference supply chan are represented by the attractors (Xref., Yref., Zref.) as shown n Fg. 2. The state of the externally perturbed system s represented by the attractors (Xext., Yext., Zext.) n Fg. 3. Fg. 3 clearly shows the saturaton of the reference system due to external perturbatons. To allevate the effects due to external perturbatons, we develop a numercal code based on a regulaton feedback. In fact, the numercal code consders the effects of external perturbaton and adjust the values of the nternal parameters of the three echelon supply chan by ncrementng all of them smultaneously whereby the ncrementng of each nternal parameter s performed n a well defned wndows or nterval of varaton. The numercal code always compares the results from the supply chan submtted to both external perturbaton and the nternal adjustment of the system parameters wth the results of the reference (or orgnal) supply chan behavor. A threshold error was fxed (whch s less than approxmately 0.) under whch full allevaton of the effects due to external perturbaton s supposed to be effectve, leadng to the achevement of synchronzaton, whch results n the recovery of the reference system behavor. Ths s clearly llustrated n Fg. 4 where the attractors obtaned are almost smlar to those of the reference model shown n Fg.2. Fgure 4: Allevaton of the saturaton effect caused by Fgure 3: Saturaton of the supply chan due to external perturbatons external perturbaton wth adaptve numercal code In a further study, we consdered the same reference model of the three echelon supply and show that a partcular change of the key parameters of the external perturbatons can lead to well- known bullwhp and chaotc phenomena. Ths s clearly llustrated n Fg. 5 whch shows chaotc attractors representng the perturbed state of the supply chan.

6 Fgure 5: chaotc state of the supply chan due to external perturbatons For these specfc states of the perturbed supply chan we obtaned that the value of the Largest D numercal Lyapunov exponent s equal to The same feedback/regulaton process (see the descrpton above) has been performed and we obtaned the achevement of the complete synchronzaton as shown n Fg.6. The adjustment of some nternal parameters could reestablsh the reference supply chan system behavor as shown n Fg. 6. Ths last case shows the achevement of synchronzaton wth very small values of synchronzaton errors as llustrated by the attractors n Fg. 6 whch are smlar to those n Fg. 2. forecastng methods are prone to dynamcs, servce contracts are well fxed n advance and many other constrans create uncertantes as dscussed throughout ths paper. Ths paper sets up a three-level supply chan, smlar to the well known Lorenz model, and probes nto the causes and presence of the saturaton and chaos when the system receves external perturbatons. Ths work llustrates how a supply chan can go nto saturaton mode under external perturbatons. It also detals how the same system can go to chaotc mode causng forester effect, f the parameters of the external perturbatons are changed. The states llustrated n ths work can occur to dfferent parameter values.e., they are not specfc to only a set of values. Ths paper also proposes an adaptve algorthm for the automatc cancellaton of the effects of the external perturbatons by re-adjustng the nternal thresholds. Ths method s partcularly appealng as t s possble to control or adjust the nternal thresholds of the supply chan network. The achevement of synchronzaton was shown for dfferent sets of the threshold parameters. The smulaton results show that the proposed methods are ndeed effectve. The solutons proposed n ths paper offer a new range of possbltes for rsk managers and provde a future research drecton. The future research s also proposed n arrvng at the adaptve synchronzaton wth the help of analog smulaton based on CNN (Cellular Neural Network) technology. An nterestng and challengng problem of practcal nterest may be the development of adaptve numercal codes to acheve synchronzaton wthn a supply chan network under the cumulatve effects of both nternal and external perturbatons. Ths s a realstc scenaro whch currently manfests tself n commercal supply chan networks. It would also be of great nterest the analyss the couplng between dfferent structures of supply chans and the achevement of synchronzaton wthn them. It s well known that n practce, many commercal supply chans are coupled. Fgure 6: Allevaton of the chaotc effect caused by external perturbaton wth adaptve numercal code VI. CONCLUSION The management of supply chan networks s a complex ssue whch nvolves numerous dynamc stuatons varyng wth tme. In addton to the couplng between the enttes, the entre supply chan s customer orented. In ths modern era of globalzed supply chans, market demand s short lved, REFERENCES [] L. d. Gacomo and G. Patrz, "Dynamc nonlnear modelzaton of operatonal supply chan," Journal of Global Optmzaton, vol. 34, pp , [2] H. B. Hwarng and N. Xe, "Understandng supply chan dynamcs: A chaos perspectve," European journal of operatons research, pp , [3] R. Wldng, "The supply chan complexty trangle: Uncertanty generaton n the supply chan " Internatonal Journal of Physcal Dstrbuton & Logstcs Management vol. 28, pp [4] M. Khouja, "Synchronzaton n supply chans: mplcatons for desgn and management," journal of the operatons research socety, pp , [5] Y. Narahar, N. Vshwanadham, and R. Bhattacharya, "Desgn of synchronzed supply chans: A sx sgma tolerancng approch," presented at Internatonal conference on robotcs & automaton, Sanfranscso, 2000.

7 [6] F. Chen, Z. Drezner, J. K. Ryan, and D. Smch-Lev, "Quantfyng the Bullwhp Effect n a Smple Supply Chan: The Impact of Forecastng, Lead Tmes, and Informaton," Management Scence vol. 46, pp [7] Z. Le, L. Y-jun, and X. Yao-qun, "Chaos Synchronzaton of Bullwhp Effect n a Supply Chan," presented at Management Scence and Engneerng, ICMSE ' Internatonal Conference on, Llle, Date: 5-7 Oct [8] J. D. Sterman, "Modelng manageral behavor: msperceptons of feedback n a dynamc decson makng experment," Management Scence vol. 35 pp Kyandoghere Kyamakya obtaned the M.S. n Electrcal Engneerng n 990 at the Unversty of Knshasa. In 999 he receved hs Doctorate n Electrcal Engneerng at the Unversty of Hagen n Germany. He then worked three years as postdoctorate researcher at the Lebnz Unversty of Hannover n the feld of Moblty Management n Wreless Networks. From 2002 to 2005 he was junor professor for Postonng Locaton Based Servces at Lebnz Unversty of Hannover. Snce 2005 he s full Professor for Transportaton Informatcs and Drector of the Insttute for Smart Systems Technologes at the Unversty of Klagenfurt n Austra. Koteswara Rao Anne receved hs BE n Electroncs and Communcaton and MSc n Electrcal engneerng and Informaton Technology from Bharathyar Unversty, Combatore, Inda and Lebnz Unversty of Hanover, Germany, n 200 and 2006, respectvely. He s now a Ph.D. student at the Unversty of Klagenfurt n Austra. Hs research nterests nclude advanced plannng and schedulng n producton systems, Intellgent supply chans, systems dynamcs, mult-agent systems, chaos and ts applcatons. Jean Chamberlan Chedjou receved n 2004 hs doctorate n Electrcal Engneerng at the Lebnz Unversty of Hanover, Germany. He has been a DAAD (Germany) scholar and also an AUF research Fellow (Postdoc.). From 2000 to date he has been a Junor Assocate researcher n the Condensed Matter secton of the ICTP (Abdus Salam Internatonal Centre for Theoretcal Physcs) Treste, Italy. Currently, he s a senor researcher at the Insttute for Smart Systems Technologes of the Alpen-Adra Unversty of Klagenfurt n Austra. Hs research nterests nclude Electroncs Crcuts Engneerng, Chaos Theory, Analog Systems Smulaton, Cellular Neural Networks, Nonlnear Dynamcs, Synchronzaton and related Applcatons n Engneerng. He has authored and co-authored 2 books and more than 22 journals and conference papers. Sreeram Kumar Bhagavatula receved hs BSc n Comper Scence and MSc n Computer Scence from Andhra Unversty, Inda, n 2002 and 2005, respectvely. He worked as programmer operatons n Indan ralways from He s now a Ph.D. student at the Unversty of Klagenfurt n Austra. Hs research nterests nclude mltary supply chans, cty logstcs, mult-agent systems, chaos and ts applcatons.

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