SENSITIVITY ANALYSIS AND OPTIMIZATION OF DIFFERENT INVENTORY CONTROL POLICIES ALONG THE SUPPLY CHAIN

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1 SENSITIVITY ANALYSIS AND OPTIMIZATION OF DIFFERENT INVENTORY CONTROL POLICIES ALONG THE SUPPLY CHAIN Dulo Curco (a), Francesco Longo (b) (a) (b) Modelng & Smulaton Center - Laboratory of Enterprse Solutons (MSC LES) M&S Net Center at Department of Mechancal Engneerng Unversty of Calabra Va Petro Bucc, Rende, 87036, ITALY (a) (b) {dcurco, f.longo}@uncal.t ABSTRACT Ths paper focuses on the nventory management problem along the supply chan. A three three-echelons supply chan made up of supplers, dstrbuton centers and retal stores s consdered. The analyss of multple nventory control polces montored by usng multple performance measures s proposed. To ths end a smulaton model, capable of recreatng the complex supply chan envronment, has been developed. Keywords: senstvty analyss, nventory control, supply chan 1. INTRODUCTION Accordng to Lee and Bllngton (1993), a Supply Chan (SC) s a network of dfferent enttes or nodes (plants, dstrbuton centers, warehouses and retalers) whch provdes materal, transform them n ntermedate or fnshed products and delver them to customers n order to satsfy market requests. Each SC node s dentfed by two dfferent parameters: the demand; the productve capacty. In order to defne each parameter a great amount of data have to be collected. Moreover, nformaton and materal flow management among SC nodes becomes a very complex task characterzed by a number of crtcal ssues related, for example, to demand (volume and producton range), processes (machnes downtmes, transportaton modes), and supply (parts qualty, delvery schedules). The Supply Chan Management (SCM) takes care of the above mentoned ssues, studyng and optmzng the flow of materals, nformaton and fnances along the entre supply chan. The man goal of a supply chan manager s to guarantee the correct flows of goods and nformaton throughout the SC nodes for assurng the rght goods be delvered n the rght place and quantty at the rght tme. Among the others, the nventory management problem along the supply chan plays a crtcal role n terms of supply chan performances. Lee and Bllngton (1993) consder the nventory control as the only tool to protect SC stablty and robustness. In effect, the objectve of the Supply Chan Inventory Management (SCIM) s to satsfy the ultmate customer demand ncreasng the qualty and servce level and decreasng at the same tme total costs; nventores affect SC costs and performance n terms of: values ted up, e.g. raw materals have a lower value than fnshed products; degrees of flexblty, e.g. raw materals have hgher flexblty than the fnshed products because they can be easly adopted for dfferent producton process; levels of responsveness, e.g. products delvery could be made wthout strct lead tmes whereas raw materals transformaton usually requres strngent lead tmes. Durng the last years a number of research studes on SCIM have been proposed. Mnner (2003) proposes a revew on Inventory Models (IMs) and addresses ther contrbuton to SC performance analyss. In partcular, models analyzed concern to: dfferent SC confguratons (sngle/multechelon systems): Dellaert and De Kok (2004) present an ntegrated approach for resource and producton management of an assembly system; Chen and Lee (2004) mplement an analytcal model for demand varablty, delvery modes, nventory level and total costs n a mult-echelon SC network; parameters varablty,.e. demand dsruptons: see Q et al. (2004) who analyze devaton costs of a one suppler one retaler after demand dsrupton; order quantty as reported n Zhou et al. (2007) who ntroduce an algorthm to compute the parameters of a sngle tem-perodc revew nventory polcy; 824

2 neural network approaches. Long et al. (2004) propose a revsted Economc Order Quantty (EOQ) model characterzed by the ntroducton of fuzzy lead tmes. Dfferent commercal software and programmng languages have been used for developng the smulaton models. Lee and Wu (2006) model the reorder pont order-quantty and the perodc revew order-up polcy of a dstrbuton system by usng the commercal package em-plant ; Al-Rfa and Rossett (2007) adopt Arena for testng a new analytcal model for a two-echelon nventory system, whereas Bertazz et al. (2005) mplement n C++ a vendor-managed nventory polcy n order to mnmze purchasng, replenshment and delvery total costs. constrants,.e. De Sens et al. (2007) propose the analyss of dfferent nventory control polces under demand patterns and lead tme constrants n a real supply chan; Longo and Mrabell (2008) analyze the effects of nventory control polces, lead tmes, customers demand ntensty and varablty n three dfferent supply chan performance measures. Chen and Krass (2001) propose a new nventory approach, based on the mnmal servce level constrant whch conssts n achevng a mnmum defned servce level n each perod; Huang et al. (2005) study the mpact of the delvery mode on a onewarehouse mult-retaler system, n order to evaluate the optmal nventory orderng tme and the economc lot sze for reducng total nventory costs. Inderfurth and Mnner (1998) nvestgate an analytcal model to determne safety stocks consderng as constrant dfferent servce levels. 2. THE SUPPLY CHAIN CONCEPTUAL MODEL The SC consdered n ths research work s made up by three stages as shown n Fgure 1: Analytcal models for nventory management take nto account all the parameters whch affect the nventory level. Allen and D Esopo (1968) n ther research work propose a revew of the re-order pont order-quantty polcy ntroducng a new tme parameter, the expedted leadtme, lower than the normal procurement leadtme. Ramasesh et al. (1991) propose a varant of the same polcy wth parameters related to demand varablty and lead tmes n order to mnmze total purchasng, delvery and nventory costs. Durng the years one of the most mportant tool for studyng nventory management along the supply chan has been the Modelng & Smulaton based approach. In effect, the evaluaton of the performance of dfferent enttes nvolved n the SC, from supplers to fnal customers passng through dstrbuton centers, consderng a number of stochastc varable and parameters s a qute complex task n whch analytcal models often fall short of results applcablty. Bhaskaran (1998) carres out a smulaton analyss of SC nstablty and nventory related to a manufacturng plant: n ths case, smulaton s used to better understand the effects of dfferent nventory strateges on the SC structure. In ths context, artfcal ntellgence technques (.e. fuzzy theory and genetc algorthms) combned wth the smulaton models support the decson makng process. Gupta et al. (2007) apply the genetc algorthm theory for nvestgatng an nventory model of a system characterzed by a sngle tem wth undefned nventory costs under the effect of dfferent marketng strateges. Gannoccaro and Pontrandolfo (2002) propose an artfcal ntellgence algorthm n order to manage nventory decsons at all SC stages (optmzng the performance of the global SC). Huang et al.(2005) solve the orderng and postonng retaler nventores problem at the warehouse and stores, satsfyng specfc customer demand and mnmzng total costs by usng M manufacturng plants (MPs); N dstrbuton centers (DCs); J stores or retals (STs). Product demand s defned by the fnal customer. Fgure 1: The Conceptual Model of the Supply Chan 2.1. The manufacturng plants As above mentoned the SC beng analyzed has M manufacturng plants. Each manufacturng plant has K dentcal processes and t s equpped n order to manufacture I dfferent types of products. Varables characterzng the manufacturng plants are: the setup tme due to plant swtchng from one product to another; the processng tme dependent on order sze; the producton capacty The dstrbuton centers The second SC level s made up by N Dstrbuton Centers (DC) whch store all the I products. The nventory control wthn each DC s as follows. When an order arrves to a DC, the current nventory poston 825

3 (on-hand nventory plus the quantty already on order mnus the quantty to be shpped) s checked. If the order s fully satsfed, ts status s consdered completed and, as a consequence, the nventory level of the DC s decreased of the order quantty, otherwse a lost quantty s recorded. The most mportant performance measures wthn a DC are the number of fully satsfed and partally satsfed store orders per perod the total lost sales quantty per perod to defne the servce level and the fll rate 2.3. The stores The thrd SC level s represented by stores. Each ST works on an eght-hours shft. At the begnnng of the day an nventory revew s made at each store n order to decde about an order emsson at one of the N dstrbuton centers. It s necessary to underlne that, accordng to ths polcy, store orders are delayed untl the begnnng of the next day so order replenshment s guaranteed by the DC the followng day. Each store chooses the DC capable of replenshng the maxmum order quantty requested. The quantty to order for each product s defned after by checkng the current on-hand nventory at the store. At each ST, number of fully or partally satsfed orders, lost sales quantty and total quantty ordered for each product s recorded. These data are then used for performance measure evaluaton (e.g. the servce level, fll rate, etc.). 3. THE SIMULATION MODEL The goal of ths research work s to analyze the supply chan performance mplementng three dfferent Inventory polces n order to estmate the nventory level at each SC stage and, as a consequence, nventory costs. The smulaton model s mplemented usng the commercal smulaton software em-plant by Tecnomatx Technologes. The smulaton model development makes use of an advance modelng approach. The classcal modelng approach based on lbrary objects to reproduce statc and dynamc enttes (materals flow, machnes, producton lne, etc.) s replaced wth a new one that substtutes flows of enttes wth a flow of nformaton stored n tables. To access, update and record such nformaton stored n tables, ad-hoc programmed routnes have been mplemented. The modelng approach proposed has the advantage to allow hgh flexblty levels n terms f smulaton model modfcaton n order to reproduce several system behavors under dfferent operatve envronments (further nformaton can be found n Longo & Mrabell, 2008). Note that the man dsadvantage of the modelng approach beng used s the anmaton: generally anmaton reproduces the enttes flow wthn the smulaton model; n ths case, the anmaton s not consdered a prorty aspect of the smulaton study although model structure allows anmaton mplementaton The Manufacturng Plants Model Implementaton The part of the smulaton model representng the manufacturng plants, recreates the tems producton process. If all the machnes of a plant are busy when an order arrves, ths order s queued watng for another avalable resource. The swtch from an product type to another requres a set up tme. No warehouses are avalable at each plant (make-to-order system). DCs select plants to send the order on the bass of lead tme and quantty that the plant can refurbsh. Fgure 2 shows the block dagram of the MP selecton process. Fgure 2: Block dagram for the manufacturng plant selecton The smulaton model, accordng to the DCs orders, evaluates total process tmes and set up tmes, then selects the best machne n each plant (capable of processng the order) and fnally the best machne among all the plants. The selecton of the best machne s made accordng to the tme requred to complete watng orders and to start the new order The Dstrbuton Centers Model Implementaton At the begnnng of the day the purchase orders from stores arrve at the DCs. The model checks the nventory levels to verfy f ncomng orders can be satsfed. In each DC, Items number of ncomng orders s compared wth the on-hand nventory level. If there s enough on hand nventory, STs demand s totally satsfed and the on-hand nventory level s updated; f demand s partally satsfed or unsatsfed, lost sales are recorded. Each DC emts purchase orders toward the manufacturng plant on the bass of demand forecast. The man actvtes that take place wthn each DC are summarzed by the block dagram n Fgure The Stores Model Implementaton The actvtes performed by the part of the smulaton model representng the stores are qute smlar to the actvtes performed n the DCs. In effect at the end of the day the nventory level s checked n order to evaluate whether or not a purchase order has to be emtted. 826

4 the reorder tme-order quantty polcy; the (s, S) polcy; Before startng to descrbe each polcy, t s necessary to defne notaton to whch authors wll refer: Fgure 3: The Dstrbuton Centers Block Dagram The block dagram n Fgure 4 descrbes the actvtes performed by the smulaton model wthn each store. s (t), the re-order level at tme t for the tem ; S(t), the target level at tme t for the tem ; SS(t), the safety stock level at tme t for the tem ; DF(t), the demand forecast at tme t for the tem ; OHI(t), the on-hand nventory at tme t for the tem ; OQ(t), the quantty already on order at tme t for the tem ; SQ(t), the quantty to be shpped at tme t for the tem ; Q(t), the quantty to be ordered at tme t for the tem ; L(t), the lead tme of the tem ; DFL(t), the demand forecast over the lead tme for the tem ; IP(t), the nventory poston at tme t for the tem ; The nventory poston IP(t) s the on-hand nventory plus the quantty already on order mnus the quantty to be shpped. In partcular, t s defned as: IP (t ) = OH (t ) + OQ (t ) SQ (t ) (1) 4.1. The mathematcal model In ths secton authors derve the mathematcal model for each polcy presented makng reference to a sngle product The reorder pont-order quantty polcy (RPOQ) In ths control polcy the nventory level s contnuously checked accordng to producton/demand requrements. Accordng to ths polcy, f IP(t) falls below the s (t), the purchase order has to be emtted. The quantty to be ordered can be defned usng the Economc Order Quantty (EOQ) approach. Fgure 4: The Stores Block Dagram 4. THE INVENTORY CONTROL POLICIES In ths research work, authors nvestgate an nventory stockng problem. In detal, the focus conssts n comparng fve dfferent Inventory Management Polces (IMPs) by usng a Modelng & Smulaton approach n order to test the performance of the SC analyzed. Accordng to the SCIM prncples, the objectve of the nventory control polces s twofold: evaluaton of the tme for purchasng order emsson; evaluaton of the quantty to be ordered. (2) Q (t ) = EOQ (t ) (3) Such polcy should be adopted when nventory level at each SC node s automatcally montored; there are no advantages n usng scale economes; purchase orders can be regularly emtted. The nventory control polces mplemented n the smulaton model wthn each store and each dstrbuton center are: s (t ) = DFL (t ) + SS (t ) the reorder pont-order quantty polcy; 827

5 The reorder tme-order quantty polcy (RTOQ) Unlke the prevous control polcy, the reorder tmeorder quantty polcy s based on a perodc check. If T (t) s the revew perod of the tem, the quantty to order s defned by S (t) mnus IP (t). The value of T (t) can be defned usng the nverse formula usually used for evaluatng the EOQ. In ths polcy, S (t) represents the target level. Ths polcy should be used when: nventory level s not automatcally montored; there are advantages related to scale economy; orders are not regular The (s (t),s (t)) polcy Ths polcy can be derved from the prevous polces above mentoned. Accordng to lterature, there are two parameters whch characterze ths polcy: s (t), the re-order level at tme t for the tem ; S (t), the target level at tme t for the tem. Authors ntroduce a new parameter, K (t), a constant parameter whch represents the average demand of the tem over a certan perod of tme. The equatons expressng s (t) and S (t) are as follows. s ( t) = DFL ( t) + SS ( t) (4) S ( t ) = s ( t ) K ( t ) (5) + Equatons 6 and 7 respectvely express the re-order condton and the quantty to be ordered. IP ( t) < s ( t) (6) Q ( t) = S ( t) IP ( t) = s ( t) + K ( t) IP ( t) (7) 5. INVENTORY POLICIES COMPARISON Consder for each supply chan node the nventory control polces before descrbed, dfferent values of lead tmes, dfferent level of demand ntensty and demand varablty as summarzed n Table 1. The values of the lead tmes, demand ntensty and demand varablty are expressed as percentage of the actual values. Table 1: Factors and Levels Factors L1 L2 L3 Lead Tme 90% 100% 110% Demand Intensty 90% 100% 110% Demand Varablty 90% 100% 110% Smulaton results, for each factors levels combnaton, are expressed n terms of average fll rate and on-hand nventory (.e. the fll rate at store, for each tem, s evaluated as rato between the fully satsfed orders and the total quantty of orders). Smulaton results are avalable for each store and for each dstrbuton center. Let us consder the smulaton results regardng one of the dstrbuton center, smlar results have been obtaned for the remanng dstrbuton center and stores. The followng scenaros have been analyzed: () comparson of the 90%, 100% and 110% scenaros n terms of demand ntensty; () comparson of the 90%, 100% and 110% scenaros n terms of demand varablty; () comparson of the 90%, 100% and 110% scenaros n terms of lead tmes. For each scenaro we nvestgated the behavor of the nventory control polces mplemented n the smulaton model. Table 2 reports the smulaton results n terms of fll rate for the frst scenaro. Table 2: Smulaton results comparson of the nventory control polces under dfferent demand ntensty fll rate Scenaros RPOQ RTOQ ss 90% Demand Intensty % Demand Intensty % Demand Intensty The best results n terms of fll rate are provded by the s (t),s (t) nventory control polcy. The lowest value by the RTOQ nventory control polcy. Note that the hgher s the demand ntensty the lower s the fll rate (for each nventory control polcy). In addton for hgh demand ntensty the RPOQ and s (t),s (t) nventory control polcy show smlar behavors n terms of fll rate values. Table 3 reports the smulaton results n terms of onhand nventory for the frst scenaro. Table 3: Smulaton results comparson of the nventory control polces under dfferent demand ntensty on hand nventory Scenaros RPOQ RTOQ ss 90% Demand Intensty % Demand Intensty % Demand Intensty Concernng the on-hand nventory the s (t),s (t) performs better than the other polces. Table 4 reports the smulaton results n terms of fll rate for the second scenaro. Table 4: Smulaton results: comparson of the nventory control polces under dfferent demand varablty fll rate Scenaros RPOQ RTOQ ss 90% Demand Varablty % Demand Varablty % Demand Varablty

6 The RTOQ nventory control polcy gves the worst performance. Note the smlar behavor of the RPOQ and s (t),s (t) polces. The polcy based on the revew perod shows a better behavor n correspondence of low demand varablty. In effect the hgher s the demand varablty the hgher s the demand forecast error. The best polcy wth low demand varablty s the s (t),s (t), wth the actual demand varablty RPOQ and s (t),s (t) show smlar behavor, fnally wth hgh demand varablty s (t),s (t) allows to obtan the hghest fll rate values. Table 5 reports the smulaton results n terms of onhand nventory for the second scenaro. Table 5: Smulaton results: comparson of the nventory control polces under dfferent demand varablty on hand nventory Scenaros RPOQ RTOQ ss 90% Demand Varablty % Demand Varablty % Demand Varablty Concernng the on-hand nventory, once agan, the s (t),s (t) performs better than the other polces. Table 6 reports the smulaton results n terms of fll rate for the thrd scenaro. Table 6: Smulaton results comparson of the nventory control polces under dfferent lead tme values fll rate Scenaros RPOQ RTOQ ss 90% Lead Tme % Lead Tme % Lead Tme Such scenaro nvestgates the effect of dfferent lead tmes on the fll rate. Note that the hgher s the lead tme the lower s the fll rate (for each nventory control polcy). The fll rate reducton passng from 90% to 100% lead tme and from 100% to 110% are as follows: () 1.1% and 3.9% for the RPOQ control polcy; () 3.3% and 4.2% for the RTOQ control polcy; () 0.9% and 0.5% for the ss control polcy. Consequently the s (t),s (t) polcy performs better than RPOQ and RTOQ. Table 7 reports the smulaton results n terms of on-hand nventory for the thrd scenaro. Table 7: Smulaton results comparson of the nventory control polces under dfferent lead tme values on hand nventory Scenaros RPOQ RTOQ ss 90% Lead Tme % Lead Tme % Lead Tme The smulaton results analyzed n ths secton regard one of the dstrbuton center. The varaton of the demand ntensty, of the demand varablty and of the lead tme allows to compare the dfferent behavors of the nventory control polcy n order to fnd out the best polcy n each stuaton both n terms of fll rate and n terms of on-hand nventory. Smlar results have been obtaned for each supply chan node, both retalers and dstrbuton centers, analyzng the nventory systems along the supply chan. 6. CONCLUSIONS The authors mplemented a smulaton model of a three echelons supply chan for studyng the nventory management problem along the supply chan. Three dfferent nventory control polces have been mplemented n each node of the supply chan (on each store and dstrbuton center excludng the manufacturng plant that work as make to order system wthout warehouse). The nventory control polces have been compared under dfferent condtons n terms of demand ntensty, demand varablty and lead tmes, observng the varaton of the fll rate and of the onhand nventory. In partcular three dfferent values have been consdered for the demand ntensty, three for the demand varablty and three for the lead tme (n each case the mddle value s the actual value). The smulaton results analyss shows that the varaton of the factors consdered strongly affect the behavor of the nventory control polces, for each scenaro the most sutable nventory control polcy should be used. Further researches are stll on gong applyng the genetc algorthms for evaluatng optmal values for the parameters of both the demand forecast models and of the nventory control polces. REFERENCES Al-Rfa, M.H., Rossett, M.D., An effcent heurstc optmzaton algorthm for a two-echelon (R, Q) nventory system. Producton Economcs, 109, Bhaskaran, S., Smulaton analyss of a manufacturng supply chan. Decson Scences, 29 (3), Bruzzone A.G., Mosca R., Brano C., Brandoln M Models for Supportng Customer Satsfacton n Retal Chans. Proceedngs of HMS, Portofno, October 5-7. Bruzzone A.G., Masse M., Brandoln M., Smulaton Based Analyss on Dfferent Logstcs Solutons for Fresh Food Supply Chan. Proceedngs of SCSC2006, Calgary, Canada. Bruzzone A.G., Bocca E Logstcs and Process Solutons for Supply Chan of Fresh Food In Retal. Proceedngs of HMS2006, Barcelona. Bruzzone, A.G., Longo, F., Brandoln, M., Enhancement Process Based on Smulaton Supportng Effcency & Organzaton, Proceedngs of Summer Computer Smulaton 829

7 Conference, July 30 th August 03 rd, Calgary Canada. Bruzzone, A.G., Longo, F., Vazzo, S., Mrabell, G., Papoff, E., Masse, M., Brano, C., Dscrete event smulaton appled to modellng and analyss of a supply chan. Proceedngs of Modelng and Appled Smulaton Conference, Bergegg (SV) (Italy). Chen, C., Lee, W., Mult-objectve optmzaton of mult-echelon supply chan networks wth uncertan product demands and prces. Computers and Chemcal Engneerng, 28, Chen, F., Krass, D., Inventory models wth mnmal servce level constrants. Operatonal Research, 134, Curco, D., Longo, F., Mrabell, G., Inventory polces comparson n a manufacturng process usng modelng & smulaton. Proceedngs of the Internatonal Medterranean Modellng Multconference, October 04 06, Bergegg (Italy). Dellaert, N., De Kok, T., Integratng resource and producton decsons n a smple mult-stage assembly system. Producton Economcs, 90, De Sens, G., Longo, F., Mrabell, G., Inventory polces analyss under demand patterns and lead tmes constrants n a real supply chan. Producton Research. D Esopo, A., An orderng polcy for stock tems when delvery can be expedted. Operatons Research, 16 (4), Gannoccaro, I., Pontrandolfo, P., Inventory management n supply chans: a renforcement learnng approach. Producton Economcs, 78, Hau, L.L., Bllngton, C., Materal Management n Decentralzed Supply Chans. Operatons Research, 41(5), Hsu, V., Lee,C., So, K., Optmal Component Stockng Polcy for Assemble-to-Order Systems wth Lead-Tme-Dependent Component and Product Prcng. Management Scence, 52 (3), Huang, H.C., Chew, E.P., Goh, K.H., A twoechelon nventory system wth transportaton capacty constrant. Operatonal Research, 167, Inderfurth, K., Mnner, S., Safety stocks n multstage nventory systems under dfferent servce measures. Operatonal Research, 106, Lee, H.T., Wu, J.C., A study on nventory replenshment polces n a two-echelon supply chan system. Computers & Industral Engneerng, 51, Longo, F., Mrabell, G., Papoff, E., Materal Flow Analyss and Plant Lay-Out Optmzaton of a Manufacturng System. Internatonal Journal of Computng, 5(1), Longo, F., Mrabell, G., An Advanced Supply Chan Management Tool Based on Modelng & Smulaton, Computer and Industral Engneerng, 54 (3), Longo, F., Mrabell, G., Papoff, E. Modelng Analyss and Smulaton of a supply chan devoted to support pharmaceutcal busness retal, Proceedngs of the 18 th Internatonal Conference on Producton Research, July 31 August 4, Salerno, Italy. Mnner, S., Multple-suppler nventory models n supply chan management: A revew. Producton Economcs, 81, Monzadeh, K., An mproved orderng polcy for contnuous revew nventory systems wth arbtrary nter-demand tme dstrbutons, IIE Transactons, 33, Q, X., Bard, J., Yu, G., Supply chan coordnaton wth demand dsruptons. Omega, 32, Ramasesh, R., Keth, O., Hayya, J., Sole versus Dual Sourcng n Stochastc Lead-Tme (s, Q) Inventory Model. Management Scence, 37 (4), Zhou, B., Zhao, Y., Katehaks, M., Effectve control polces for stochastc nventory systems wth a mnmum order quantty and lnear costs. Producton Economcs, 106, AUTHORS BIOGRAPHIES DUILIO CURCIO was born n Vbo Valenta (Italy), on December the 15 th, He took the degree n Mechancal Engneerng from Unversty of Calabra (2006). He s currently PhD student at the Mechancal Department of Unversty of Calabra. Hs research actvtes nclude Modelng & Smulaton and Inventory Management theory for producton systems and Supply Chan desgn and management. He collaborates wth the Industral Engneerng Secton of the Unversty of Calabra to research projects for supportng Research and Development n SMEs. FRANCESCO LONGO was born n Crotone (Italy), on February the 08 th, He took the degree n Mechancal Engneerng from Unversty of Calabra (2002). He receved the PhD n Industral Engneerng (2005). He s currently researcher at the Mechancal Department (Industral Engneerng Secton) of Unversty of Calabra and scentfc responsble of the Modelng & Smulaton Center Laboratory of Enterprse Solutons (MSC-LES) n the same department. Hs research nterests regard modelng & smulaton of manufacturng systems and supply chan, DOE, ANOVA. 830