Research Article A Hybrid Support Vector Machines and Two-dimensional Risk Matrix Model for Supply Chain Risk Assessment

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1 Research Journal of Appled Scences, Engneerng and Technology 7(11): , 2014 DOI: /rjaset ISSN: ; e-issn: Maxwell Scentfc Publcaton Corp. Submtted: February 15, 2013 Accepted: March 21, 2013 Publshed: March 20, 2014 Research Artcle A Hybrd Support Vector Machnes and Two-dmensonal Rsk Matrx Model for Supply Chan Rsk Assessment Fan Jang and Junfe Chen State Key Laboratory of Hydrology-water Resources and Hydraulc Engneerng, Busness School, Hoha Unversty, Nanjng , Chna Abstract: In recent years, the supply chan managements have been pad more and more attenton. The supply chan rsk management s an mportant content for enterprses mplementng supply chan management. Therefore, how to measure the rsk of supply chan s qute mportant. In ths study, a supply chan rsk evaluaton model based on support vector machnes and two-dmensonal rsk matrx s proposed. The ndex system of supply chan rsk assessment whch ncludes 14 ndces s establshed. The case study shows that the proposed model s reasonable, effectve and t can provde an mportant reference for supply chan rsk management. Keywords: Rsk assessment, Supply Chan (SC), Support Vector Machnes (SVMs), two-dmensonal rsk matrx INTRODUCTION As an ntegrated management mode under the globalzaton background, supply chan management has been wdely adopted n varous felds. Supply chans are consdered as co-operatve and dynamc networks, whch lnk supplers, manufacturers, thrdparty logstcs, dstrbutors, retalers and customers together. They merge enterprse producton, materal procurement, logstc, merchandse sales and other sectors nto an organc whole, whch benefts the related busnesses. Due to the unpredctablty of the operatng envronment and the complexty of the supply chan system tself, rsks exst almost everywhere and can be spread through the supply chan network, whch wll eventually gve rse to the supply chan rsk. Even lttle rsk occurred n a small corner n a supply chan can brng about catastrophe and badly damage the supply chan. Hence, t has a great sgnfcance to study supply chan rsk management. The practces of supply chan management around the world have proved that the ablty to effectvely dentfy and control the rsk of supply chan operaton s a major ssue related to whether we can obtan the desred results from supply chan management. So the supply chan rsk assessment s of great sgnfcance. The research on supply chan rsk assessment has become an mportant research drecton. Zhou (2008a) establshed a Dffuson Model (DM) of a supply chan rsk whch conssted of rsk networks and a dffuson calculaton process. The rsk of the entre supply chan was assessed from three angles ncludng rsk factors, node enterprse and supply chan network. Neger et al. (2009) proposed the Value-Focused Process Engneerng (VFPE) methodology that combned process-based and objectves-based busness modelng approaches nto a model that enabled holstc representaton of the busness. It can be used for dentfyng the supply chan rsk resulted from the ntegraton of exstng goal modelng and process modelng approaches and was therefore easly extended to nclude a mult-dscplnary vew of rsk that was flexble enough to accommodate varances arsng from specfc requrements of a supply chan structure beng modeled. Tuncel and Alpan (2010) presented a hghlevel Petr Net (PN) based modelng methodology and a rule based approach for rsk management n supply chans. Ths methodology could be appled for desgnng, analyzng, specfcaton and evaluaton of SC as well as for solvng uncertanty and rsk related problems usng a real-tme decson-makng tool. Wu and Davd (2008) consdered three types of rsk evaluaton models for supply chans: Chance Constraned Programmng (CCP), Data Envelopment Analyss (DEA) and Mult-Objectve Programmng (MOP) models. Varous rsks are modeled and smulated accordng to specfc probablty dstrbuton n rsk-embedded attrbutes by these three types of rsk evaluaton models. The results showed that the proposed approach allowed decson makers to perform trade-off analyss among expected costs, qualty acceptance levels and on-tme delvery dstrbutons. Amanda and Sngh (2012) presented a numercal analyss usng a smulaton model motvated by an actual consumer packaged goods supply chan. The results demonstrated the mportance of consderng rsk quanttatvely and t s helpful for rsk-nformed decsons makng. They also demonstrated that a Correspondng Author: Junfe Chen, Busness School, Hoha Unversty, Nanjng , Chna, Tel.: Ths work s lcensed under a Creatve Commons Attrbuton 4.0 Internatonal Lcense (URL:

2 systematc approach was necessary for control the downsde of a dsrupton. Reducng rsk at a sngle locaton n the network may not be helpful f the rest of the network was too vulnerable. Improvng the strength of the weakest lnks n a chan would ncrease a chan s strength overall. Mary and Norbs (2011) developed a two-part assessment methodology, whch ncludes a scorng system for assessng each partcpant of the supply chan n turn and an aggregaton mechansm based on graphc modelng that results n a sngle supply chan rsk ndex value for a specfc supply chan of nterest. Adhtya et al. (2009) thought that supply chan networks were n many ways smlar to chemcal plants, therefore well-establshed methods and concepts from chemcal process rsk management can be adapted for supply chans. Followng the Hazard and Operablty (HAZOP) analyss method n process safety, rsk dentfcaton could be performed by systematcally generatng devatons n dfferent supply chan parameters and dentfyng ther possble causes, consequences, safeguards and mtgatng actons. However, some of the studes above are not vsual for us to see the degree of rsk and ths does not help us to recognze the supply chan rsk. Although some others of them can solve ths problem by conductng a comprehensve rsk evaluaton model on the foundaton of the sub-rsks "rsk value". That s to say, the frst s to determne the scorng methods and then the result s obtaned based on the scorng methods and the subrsks. Unfortunately, ths may lead to a devaton and the magntude of the devaton whch can hardly be known because of human s subjectvty. Besdes, as for the rsk degree and the rsk s lkelhood, the so-called "rsk value" only takes one nto consderaton whle the other s gnored. Support Vector Machnes (SVMs) proposed by Vapnk n the mddle of 1990s are a novel machne learnng technology based on Statstcal Learnng Theory (SLT) and can solve a seres of practcal problems lke classfcaton and multvarate regresson and have been wdely used n many felds. Comparng wth the tradtonal neural network learnng methods, SVM can effectvely solve the model selecton and over learnng problems, non-lnear and dmenson dsaster, as well as ssues such as local mnma by solvng a quadratc optmzaton problem to be the global optmal soluton. In ths study, the SVMs method s proposed and utlzed to evaluate the supply chan s rsk and the accuracy of the rsk assessment can be mproved. In addton, the supply chan s rsk by the degree of harm and the lkelhood of rsk based on the two-dmensonal matrx s analyzed, whch enables the assessment system to adapt to the operatng envronment (e.g., tme and space) and makes the result more relable. Res. J. Appl. Sc. Eng. Technol., 7(11): , Fg. 1: The optmal hyper plane splt of SVM METHODOLOGY Support vector machnes: The SMVs s a novel machne learnng theory that frst developed by Cortes and Vapnk (1995) on the bass of Statstcal Learnng Theory (SLT). The SVMs adopt the Structure Rsk Mnmzaton (SRM) prncple and have been shown to outperform the tradtonal Emprcal Rsk Mnmzaton (ERM) prncple used by conventonal artfcal neural networks. The SVMs have been wdely used because of ther excellent generalzaton performance, robustness n hgher dmensons and effcency n computaton. SVMs are orgnally developed for bnary classfcaton ntendng to fnd out the optmal hyper-plane that makes the margn of separaton between two dfferent data sets maxmzed. The basc dea of SVMs s: when the lnearly nseparable data sets map nonlnearly to a hgh dmensonal feature space through the nner product kernel functon, t becomes lnearly separable data sets; and n the hgh dmensonal feature space, we can establsh the optmal classfcaton hyper plane.e., the so-called optmal hyper plane whch can not only make the two types separate correctly but also maxmze the margn (L et al., 2009; Karm and Mahmoud, 2008). The basc dea of SVMs can be expressed n Fg. 1. In Fg. 1, and respectvely represents a dfferent class. H s the so-called optmal separatng hyper plane. and respectvely represents a straght lne through the pont closest to H and they parallels to H (the dstances from and to H are the same). Gven the sample set {(, ), (, ),, (, )}, [+1, -1], for both stuatons.e., lnearly separable or lnearly nseparable, these data can be separated by a hyper plane. The hyper plane satsfes: 1 T mn ( w ) w 2 s. t. y [( w x ) + b] 1+ ξ 0, ξ 0, = 1,2, L, n (1)

3 where, w = The coeffcent of the optmal hyper plane b = The threshold value ξ = The non-negatve slack varable when, ξ = 0, t s lnearly separable whle ξ >0 s nseparable. Accordng to the theory of SVMs, the nput vector X can be mapped to a hgh dmensonal feature space by a gven nonlnear mappng. And then the optmal separatng hyper plane can be found n ths hghdmensonal space, the problem to seek the optmal classfcaton s transformed: 1 mn x yαα K( x x ) α 2 n = 1 j j j j = 1 = 1 j= 1 s. t. yα = 0 n n n 0 α C, = 1,2,, n where, K (u, v) = The kernel functon C = The penalty coeffcent C>0 and the larger C means the greater penalty for msclassfcaton. Accordng to the Eq. (2), we can get the optmal soluton = (,, ) and = - (, ), so the decson-makng functon s f (x) = sgn (, + ). SVMs are well appled to classfcaton problems. It s crtcal to pre-determned kernel functon and set the approprate parameters for n order to fnd out the optmal hyper plane. In ths study, Radal Bass kernel Functon (RBF) s used: 2 ( γ ) Res. J. Appl. Sc. Eng. Technol., 7(11): , 2014 α (2) K( x, x ) = exp x x (3) j j Due to the robustness and the global optmzaton ablty of the Genetc Algorthm (GA), t s partcularly suted to deal wth the complex and nonlnear problems. So, the GA s used to optmze the SVM s parameters (Huang and Wang, 2006; Avc, 2009). The man feature of the genetc algorthm s the exchange of nformaton between the group search strategy and the ndvduals of populatons. Due to the robustness of the genetc algorthm, t s partcularly suted to deal wth the complex and nonlnear problems. The manly steps are as follows: Step 1: Generate an ntal random populaton, a set of groups randomly and encoded n the parameter space 2195 Table 1: Index system of supply chan rsk assessment Target layer Crteron layer Index layer Overall rsk (U) System rsk (U 1) Natural dsasters (U 11) Instablty of laws and polces (U 12) Economc crss (U 13) Changes n market demand (U 14) Cooperaton rsk (U 2) Structure of the supply chan rsk (U 21) Requrement forecast accuracy rate rsk (U 22) Rsks of benefts dstrbuton (U 23) Partners trust rsk (U 24) Coordnated control rsk of the focal company (U 25) Self-rsk (U 3) Qualty safety rsk (U 31) Innovaton capablty rsk (U 32) Fnancal rsk (U 33) Rsk of producton and processng securty (U 34) Logstcs rsk (U 35) Step 2: Calculate the ftness value of ndvduals Step 3: Judge whether t meets the pre-set stop crteron and f t meets the crteron, goes to Step 6; else, go to Step 4-5 Step 4: Determne the number that should be coped based on the ftness value of ndvduals and then do crossover and mutaton operatons to generate a new populaton Step 5: Calculate the ftness value of ndvduals of the new generated populaton and then return to Step 3 Step 6: Get a new GA optmzed parameters and establsh GA-SVM model Step 7: Judge whether the accuracy of GA-SVM model meets the pre-set stop crtera, f t meets the crteron, go to Step 8; else, return to Step1-6 Step 8: Determne the SVM optmal penalty factor C and the kernel functon parameter G Index system of supply chan rsk assessment: In ths study, the supply chans n whch the manufacturng enterprses are as the core enterprses are studed. Accordng to lteratures (Wang et al., 2012; You et al., 2009; Zhou, 2008b; Oehmen et al., 2009; Moenzadeh and Hajfathalha, 2009; Tang et al., 2012) and experts nqures, the rsk factors related to the supply chan manly ncludng the sectors of producton, management and consumpton etc. The man rsk sources n the supply chan system nclude three aspects,.e., System Rsk, Cooperaton Rsk and Self-Rsk. Accordng to the prncple of systemc, mportance, as well as unversalty, we establsh the ndex system combnng the expert s nvestgaton. The ndex system of supply chan rsk evaluaton n ths study s as shown n Table 1.

4 Res. J. Appl. Sc. Eng. Technol., 7(11): , 2014 Fg. 2: Two-dmensonal rsk matrx Table 2: Scores and descrptons Scores Dmensons Rsk harm degree Catastrophc Serous Moderate Acceptable Mld Rsk lkelhood Almost certan Probable Uncertan Doubtful Not lkely Table 3: Rsk levels and output vectors Comprehensve rsk levels Descrpton Levels (α, β) Hgh C (4, 4) B - (4, 3), (3, 4) B (4, 2), (3, 3), (2, 4) B + (4, 1), (3, 2), (2, 3), (1, 4) Low A (3, 1), (2, 2), (1, 3) A + (2, 1), (1, 2) A ++ (1, 1) Table 4: Experts scorng card Scores Index DG LR Natural dsasters (U 11) Instablty of laws and polces (U 12) Economc crss (U 13) Changes n market demand (U 14) Structure of the supply chan rsk (U 21) Requrement forecast accuracy rate rsk (U 22) Problems of dstrbuton of benefts (U 23) Partners trust rsk (U 24) Coordnated control of the core enterprse rsk (U 25) Qualty safety rsk (U 31) Innovaton capablty rsk (U 32) Fnancal rsk (U 33) Rsk of producton and processng securty (U 34) Logstcs rsk (U 35) Levels 3 2 Two-dmensonal rsk matrx: In ths study, we use the Delph method to obtan the rsk evaluaton data of the supply chan n a varety of crcumstances by consultng experts (James and John, 2001). Referrng to the study of Hallkas et al. (2002, 2004), we use fvelevel gradng method and respectvely measure Lkelhood of Rsk (LR) and Degree of Harm (DG). Ths gradng method s as shown n Table 2. After processng each sample data by SVMs, We can get a two-dmensonal output vector, represented by (α, β). And α represents the DG level, β represents the LR level. We use 1, 2, 3, 4 four levels to measure them and the comprehensve rsk levels that conssts of the DG levels and the LR levels can be obtaned. Ths approach to measure rsk levels s shown n Table 3 and a two-dmensonal rsk matrx Fg. 2. We mark varous knds of supply chan rsk n ths matrx accordng to the lkelhood of rsk and the degree of harm. Accordng to the results, decson makers can come up wth correspondng strateges and control the rsk. CASE STUDY In ths study, 30 supply chan samples n whch manufacturng enterprses are core enterprses are 2196 chosen. The samples are dvded nto two parts, 25 samples as tranng data and the others are as test samples. Varous experts n the supply chan feld are nvted to assess each ndex of supply chans for 30 samples. Index values were determned by related experts accordng to the gradng method shown n Table 2. Besdes, experts should also use the Delph method to gve the 25 scores of the DG level and LR level of each supply chan by consderng the overall operatonal status and trends (Ma et al., 2004; Saleh et al., 2011; Member and Swarup, 2011; Chen and L, 2010). The scorng card s shown as Table 4. The tranng samples and test samples are selected and the data are normalzed accordng to Eq. (4): X X X mn = (4) X -X max mn The LbSVM, whch s a toolkt developed by Ln and can be used for classfcaton and regresson quckly and effcently accordng to the prncple of SVM, s used to tran the SVMs wth the tranng samples (Chang and Ln, 2011). In ths study, the Radal Bass Functon (RBF) as kernel functon s used

5 Res. J. Appl. Sc. Eng. Technol., 7(11): , Ftness Curve (GA Method) best c=9.903, best g=0.422, tranng accuracy=84.00% Ftness Fg. 3: Parameter-optmzaton result (DG) 45 best ftness average ftness Generatons 80 Ftness Curve (GA Method) best c=16.319, best g=0.288, tranng accuracy=80.00% Ftness Fg. 4: Parameter-optmzaton result (LR) best ftness average ftness Generatons and the Genetc Algorthms (GA) whch has the global optmzaton ablty s used to fnd the best penalty factor C and kernel functon parameter γ. Accordng to the calculaton steps n above secton, we can establsh a contact between the ftness functon and the objectve functon. And wth the ncrease of generatons, the ftness value of ndvduals shows a rsng trend (Fg. 3 and 4). The larger the ftness value s, the stronger the vablty of populaton wll become. That means the parameters wll be more sutable. Durng the process, 2197 we can grasp at the bggest ftness value among all we have calculated and can determne the optmum parameters. Here, for DG, the best C = and the best γ = 0.422, whle the accuracy of classfcaton (ftness value) s 84%. For LR the best C = , the best γ = and the accuracy of classfcaton (ftness value) s 80%. The test samples are predcted by the traned SVMs and the levels of DG and LR can be obtaned, as shown n Table 5.

6 Table 5: Levels of DG and LR No Levels of DG Levels of LR Table 6: Comprehensve rsk levels No Comprehensve rsk (2, 3) (3, 4) (1, 1) (2, 2) (4, 2) Levels B + B - A ++ A B Fnally, accordng to Table 3 and Fg. 2, we ntegrated the predcted results of DG and LR above and obtaned the comprehensve rsk level, as shown n Table 6. As we know, DG represents the degree of harm and the levels of DG largely reflect the characterstcs of ndustres n supply chans and the reasonableness of supply chan structures. Lkewse, LR represents the lkelhood of rsk and the levels of LR are reflectons of the external condtons of supply chans and can be regarded as descrptons of management level and operaton status of supply chans. So, we can obtan a lot of nformaton from DG level and LR level and we can take targeted measures to control DG level and LR level so as to control comprehensve rsk levels. Based on the above understandng, we can obtan some results as followng accordng to the result of Table 6. Frstly, Supply Chan No. 28 s at a lowest level n terms of both DG and LR, ts comprehensve rsk level s A ++, whch ndcates that No. 28 s n good and safe condton. Secondly, the rsk levels of No. 26 and No. 29 are B + and A respectvely, whch can be regard as a moderate level. But t s stll necessary to strengthen the supply chan management and cooperaton n order to further reduce the lkelhood of rsk. Thrdly, for Supply Chan No. 30, whose rsk level s B, t s mportant to reconsder the ratonalty of ts supply chan structure because of ts hgh DG level. Before that, should fgure out where the defects are and whether they orgnate from characterstcs of the ndustry. Ths rsk may be dffcult to be elmnated completely because the rsk s accompaned by the brth of the ndustry. If possble, the development of the technology and theory wll be the best way to solve the problem. But managers should frstly take steps to adjust the structure of the supply chan to make t approprate and reasonable as far as possble. And t s stll necessary to make the supply chan management and cooperaton more effectvely and effcently. Fourthly, the comprehensve rsk level of Supply Chan No. 27 s hgh, reachng B - level, whch mples that ths supply chan means enormous rsk. It s urgent to take measures to control the overall rsk level of the supply chan; otherwse t wll cause great harm to all Res. J. Appl. Sc. Eng. Technol., 7(11): , enterprses of the supply chan. And managers must choose a holstc way to thnk about t. However, to supplers, manufacturers, retalers, consumers, etc., once they realze the rsk, they may choose other cooperators nstead of lookng for change. In other words, to qut from the orgnal supply chan s the most drect way to solve the problem f the cost of the change can be accepted. So, t s of great sgnfcance to asses the overall rsk n tme. CONCLUSION Along wth the quckly development of theory and applcaton about supply chan management, the supply chan rsk management become an mportant content for enterprses. In ths study, SVMs are used to the feld of supply chan rsk assessment. Usng the multclassfcaton functon of SVMs, the problem of supply chan rsk assessment s transformed nto rsk ratng problem. Besdes, a two-dmensonal rsk matrx consstng of the degree of harm and the lkelhood of rsk s establshed, whch can be more vsually to demonstrate the rsk levels of the supply chan and enable decson makers to take more targeted measures to control the supply chan rsk. Fnally, a case s studed and the results show the feasblty of ths method. However, there are stll some specal attentons whch we wll pay attenton to when we apply ths method. The ndex system may be dfferent for dfferent supply chans. In addton, the supply chan rsk evaluaton s a complex system evaluaton problem and the further studes are certanly desrable on rsk assessment and control. ACKNOWLEDGMENT Ths study was supported partally by the Specal Fund of State Key Laboratory of Hydrology-Water Resources and Hydraulc Engneerng, Chna (No ) and Project of Excellent talents support plan of Hoha Unversty. REFERENCES Adhtya, A., R. Srnvasan and I.A. Karm, Supply chan rsk dentfcaton usng a HAZOP- Based approach. AIChE J., 55(6): Amanda, J.S. and M. Sngh, A quanttatve analyss of dsrupton rsk n a mult-echelon supply chan. Int. J. Prod. Econ., 139(4): Avc, E., Selectng of the optmal feature subset and kernel parameters n dgtal modulaton classfcaton by usng hybrd genetc algorthmsupport vector machnes: HGASVM. Expert Syst. Appl., 26(2):

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