A MODEL TO ANALYZE COST OF QUALITY FOR SUPPLY CHAIN DESIGN CONSIDERING MATERIAL FLOW

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1 A MODEL TO ANALYZE COST OF QUALITY FOR SUPPLY CHAIN DESIGN CONSIDERING MATERIAL FLOW Asama Alglawe Department of Mechancal & Industral Engneerng (MIE), Concorda Unversty, 1515 Ste-Catherne O,Montreal, QC, H3G 2W1, Canada Onur Kuzgunaya Department of Mechancal & Industral Engneerng (MIE), Concorda Unversty, 1515 Ste-Catherne O, Montreal, QC, H3G 2W1, Canada Andrea Schffauerova Concorda Insttute for Informaton Systems Engneerng (CIISE), Concorda Unversty, 1515 Ste-Catherne O, Montreal, QC, H3G 2W1, Canada Abstract Consderng cost of qualty (COQ) n supply chan networ desgn s of great mportance as consderng operaton related costs. Its purpose s to mprove qualty level of goods n a manner for a company to obtan the overall lowest possble costs. In a centralzed supply chan networ t s crucal to determne the optmal allocaton of qualty system related expendtures. Optmzaton s a tool that can be effectve n these nds of problems, because t can provde a dependable decson based on COQ allocaton, ts accompaned qualty level, and materal dstrbuton. In ths research we develop an optmzaton model to better allocate COQ n uncapactated supply chan. Sx dfferent COQ scenaros were desgned and nvestgated n order to fnd the mnmum cost scenaro that allocates the COQ expendtures among the (SC) enttes. Preventon & apprasal (PA), falure (F), and opportunty costs (OC) were used as functons n the model. The results showed that the hghest porton of the COQ should be allocated downstream whle the lowest porton should be ept upstream. In addton, we found that the hghest qualty level s n most cases assocated wth the hghest porton of COQ. Even though our study was nspred by Juran s cost model, our model consders general PA, F, and OC as functons and may reflect accurate evaluaton for many proects. Keywords Supply Chan, Cost of Qualty, Materal Flow, Cost of Qualty Allocaton, Qualty Level. I. INTRODUCTION Qualty has been long recognzed as an mportant factor n the decson mang of consumers when selectng among the varety of products on the maret. Cost of qualty (COQ) elements depend on tangble costs, whch are emboded n the accountng system as expenses because they are consdered as actual transactons that are used n the producton process. The purpose of consderng COQ n ndustry practces s to demonstrate and hghlght the benefts of mprovng qualty and to relate t to customer satsfacton, as well as to ln them wth a matchng cost n order to be able to reduce total costs and ncrease profts. Therefore, the cost of qualty can be consdered as a tradeoff between the cost of conformance and the cost of non-conformance [2]. These costs consttute the wdely used tradtonal, preventon, apprasal, and falure (PAF) model, whch 157

2 was proposed by Fegenbaum [3]. PAF model has obtaned general acceptance amongst dfferent researchers and organzatons, such as ASQ. Preventon and apprasal costs are expendtures to ensure conformance to the specfcatons (.e. costs of conformance). Falure costs are costs resultng from nonconformance to the specfcatons. Campanella [4] stated that qualty costs are categorzed and defned, as follows: Preventon costs. The costs of all actvtes that occurred to reduce or prevent poor qualty n products or servces, such as, qualty plannng, process control costs, and tranng and general management costs. Apprasal costs. The costs related to measurng, evaluatng, and/or audtng products or servces to ensure conformance to qualty standards and performance requrement, for example, test and nspecton costs, and nstrument mantenance costs. tradtonal costng systems, whch represent qualty costs as those costs are easly seen and montored. Hdden costs, such as opportunty cost (OC) do not characterze true money, thus they are excluded from the company boos. OC s conventonally defned as the dfference between an nvestment one maes and another one whch he/she chose not to mae,.e. benefts that are not earned as a result of pursung another alternatve [7]. So far OC dd not gan much nterest n the lterature on COQ, and most emprcal studes have faled to fnd a way to express opportunty cost. Sandoval-Chavez and Beruvdes [8] suggested that the COQ concept should be mproved to consder ntangble and OC as well. Lu et al. [9] argued that ntangble costs, such as loss of customer goodwll, are n fact the most mportant costs that need to be managed properly. Falure costs. The cost occurred due to products or servces not conformng to requrements of customer/user needs. Falure costs are subdvded nto nternal and external falure cost categores: o Internal falure costs. Falure costs arse before fnalzng and pror to delvery of the product, or provdng of a servce, to the customer/user, such as, costs of scrap, rewor, retest, re-nspecton and redesgn. o External falure costs. Falure costs occur after the product and durng or after a servce reaches to the customer/user, such as, cost of repars, returns, dealng wth complants, and compensatons. Juran [5] provded a graphcal representaton of how costs of conformance affect the overall qualty level of a gven system. Juran s model s consdered as the most common model n the lterature, whch s used n manufacturng ndustry because t s easy to understand [6]. Juran [1] states that the lowest level of COQ can be obtaned when falure costs are equal to preventon and apprasal costs. Ths can be understood from most of Fg. 1 Juran s model for COQ [1] Some studes dd attempt to capture the opportunty costs n ther COQ calculatons. For example, Snesa et al. [10] used a plot study to nvestgate the external falure cots whle consderng the hdden costs at a medcal supply servce company n Lthuana. They used qualty functon deployment modfed plannng matrx, whch was developed by Moen [11], and loss calculaton method due to unsatsfed customers lost, whch was mplemented by Jones and Wllams [12]. Snesa et al. [10] found the hdden external falure qualty costs equal may reach up to 30% of the analyzed perod sales. COQ studes have so far focused on nternal qualty costs of ndvdual frms but not on the costs of an entre supply chan [13]. COQ ntegrates the mplcatons of poor qualty, qualty mprovement efforts and hdden qualty costs, and translates them to 158

3 understandable monetary terms for all staeholders of the organzaton [14]. Thus, t s mportant to extend COQ to the SC measures and to ntegrate the nclusve costs nto supply chan modellng. However, the concept of dentfyng COQ elements and mplementng COQ model s not very straghtforward and there have been some dfferences about what these costs comprse [15]. Srvastava [13] was the frst author who combned and estmated COQ n supply chan performance measurement. Srvastava estmated COQ n a supply chan n monetary terms at selected thrd-party contract manufacturng stes of a pharmaceutcal company located n Inda. He defned COQ n SC as: the sum of the costs ncurred across a SC n preventng poor qualty of product and/or servce to the fnal consumer, the costs ncurred to evaluate and ensure that the qualty requrements are beng met, and any other costs ncurred as a result of poor qualty [13, p.194]. Another wor drected towards ntegratng COQ n the supply chan was ntroduced by Ramudhn et al. [16]. Ths nsprng study presents three echelon system (supplers, manufacturng plants, and customer groups) that ntegrates COQ nto the modellng of a supply chan networ. The model ntended to mnmze the overall operatonal and qualty costs. Ramudhn et al. [16] fnd that the soluton changes completely by addng a COQ functon only for supplers nto the obectve functon. The soluton ncreases by approxmately 16% n costs when COQ s consdered, n addton, the fnal optmal networ wll choose ey supplers who mplement the lowest operatonal costs, whch ensures the lowest overall cost. More recently, Alzaman et al. [17] establshed a mathematcal model to ncorporate a nown COQ quadratc functon ntegratng a defect rato at all supply chan nodes. Ther COQ functon s based on Juran s orgnal model [1]. They argued that, although the COQ functons are quadratc, they can be ncorporated n supply chan networ desgn and can be solved successfully. Castllo-Vllar et al. [14] developed a formal framewor for computng the qualty cost across a sngle-product three-echelon seral supply chan model, whch can be used to desgn a supply chan logstc route. The model presented a mnmum total cost whle t mantans an overall qualty level. Ther model ntended to evaluate the mpact of nvestment n qualty and showed how t can be used to ncrease overall profts. In prevous studes, the total qualty cost was mplemented as a quadratc functon based on percentage of defectve unts, and the functon s assumed to be gven. Ths paper mproves the cost model to compute and analyze the allocaton of qualty cost for a supply chan based on three cost sources, whch are: PA, F, and opportunty cost (OC) n each level of an un-capactated supply chan to provde decsons wthn the supply chan, such as qualty level and materal flow at each supply chan entty. No prevous wor has addressed how the three COQ components nteract together or how to better allocate them n the supply chan. II. MODEL AND FINDINGS Methodology The model represents un-capactated sngle product supply chan, three-echelon system (.e. supplers, manufacturer, retaler, and customers) as shown n Fg. 2. The model ams at mnmzng the overall fxed and qualty costs. Here, the standpont wll be that of the supply chan as a whole, meanng the suppler, manufacturer, retaler, and customers are subsdary of the supply chan and are ntegral parts of t. For example, the fxed cost and COQ at the suppler would also be cost attrbutes for the supply chan and would be accounted for n the model. The manufacturer and retaler are represented n the same manner. The obectve functon of the model mnmzes the total fxed and qualty costs. Fg. 2 Un-capactated supply chan model consders cost of qualty and materal flow The nput parameters, decson varables, and constrant parameters are explaned n general forms as follows: 159

4 : Refers to suppler, : Refers to manufacturer, : Refers to retaler, and c: Refers to customer. 1) Decson Varables Z, Z, & Z = Number of components to enter suppler (), manufacturer, and retaler () respectvely. Os,, Pm,, and Qr,c = Number of components to ext from suppler (), manufacturer (), and retaler () respectvely. x, y, & u = Qualty level at suppler, manufacturer () & retaler () respectvely. 2) Parameters (Input Data): Fx, Fx, & Fx = Fxed costs at suppler (), manufacturer (), and retaler () respectvely. fpa(x ), fpa(y ), & fpa(u ) = Preventon and apprasal cost functons at suppler (), manufacturer () & retaler (); respectvely. ff(x ), ff(y ), & ff(u ) = Falure cost functons at suppler (), manufacturer () & retaler () respectvely. foc(x ), foc(y ), & foc(u ) = Opportunty cost functons at suppler (), manufacturer () & retaler () respectvely. 3) Constrants Input Parameters: Dc = The producton demand for customer c. The proposed non-lnear model wll consst of the followng sets: Mn Qr J I Fx Z I fpa( y ) ff( y ) * Z foc( y ) S.t., c * Z * u Pm Z,, 0 < x 1, 0 < y Os Dc Z Z y Z * x Z 0, Z Qr Os, c Pm,, 0, Z fpa( x ) ff( x ) * Z foc( x ) K 1, 0 < u 0,Os, Fx Z 1 0,pm J K, Fx Z fpa( u ) ff( u ) * Z foc( u ) 0, Qr, c (1) The obectve functon mnmzes the followng costs: (1) Fxed cost (Fx ) (.e. handlng cost) at suppler (); (2) COQ at suppler (), whch conssts of preventon and apprasal cost functons (fpa(x )) together, falure cost functon (ff(x )), and opportunty cost functon (foc(x )); (3) Fxed cost (Fx ) (.e. handlng cost) at manufacturer (); (4) COQ at manufacturer (), whch comprses preventon and apprasal cost functons (fpa(y )) together, falure cost functon (ff(y )), and opportunty cost functon (foc(y )); (5) Fxed cost (Fx ) (.e. handlng cost) at retaler (); and (6) COQ at retaler (), whch comprses preventon and apprasal costs (fpa(u )) together, falure cost (ff(u )), and opportunty cost (foc(u )). The constrants from: (2) to (9) can be explaned as follows: Constrant (2) s to satsfy the customer demand. Constrant (3) s to provde good unts from the retaler. Constrant (4) s equalty constrant to satsfy retaler s nput unts. Constrant (5) provdes good unts from manufacturers. Constrant (6) s the equalty constrant for a suppler good unts and a manufacturer nput unts. Constrant (7) s to provde good qualty unts from supplers. Constrant (8) puts an upper and lower bound on qualty level of suppler, manufacturer, and retaler respectvely. Constrant (9) mposes the nonnegatvty restrcton on the decson varables. 4) Model Inputs And Assumptons Fg. 3 Shows the shape of the COQ functons, n whch fpa(x ), fpa(y ), & fpa(u ) are represented by exponental equatons, fpa(x ), fpa(y ), & fpa(u ) are represented by polynomal equatons, and fpa(x ), fpa(y ), & fpa(u )are represented by polynomal equatons. The shape of the COQ n each level s shown n Fg. 4. In ths study we consder the OC n our model as a separate cost functon at each SC level n order to present a soluton that ntegrates dfferent COQ functons. The nput COQ functons are presented n Table I. Three COQ levels can be observed n ths table, whch are: frst, low spendng on COQ, whch was denoted by a dollar sgn ($), second, medum COQ, whch was symbolzed by a two dollar 160

5 sgn ($$) and last, the hghest amount of the COQ was characterzed by a three dollar sgn ($$$). Fg. 3 Shape of the COQ functons at the suppler, manufacturers and retalers The COQ functons were nspred by [1] COQ model. The three quadratc COQ ($, $$, and $$$) functons n the Table I are shown n Fg. 4 (fcoq(x ) - - ($$), fcoq(y ) -- ($$), & fcoq(u ) -- ($)). Gong bac to the vewpont of ntroducng the SC as an ntegrated networ, meanng that supplers should satsfy the manufacturers demand, manufacturers should provde the retalers wth ther requred products, and fnally the retalers fulfll the customers demand. In ths model COQ s hghly affected by the qualty level at each echelon. In addton, the qualty level drectly affects the number of unts that s suppled to each echelon (.e. Z, Z, & Z ) and the output unts from each echelon (OS,, Pm,, and Qr,c ). In our model, the retaler s consdered one of the producton system and t has ts own producton and qualty costs. For example, fnal tests and nspectons, whch are ust before pacagng. At each level, we set fxed costs to be equal to $10. The total customer demand (Dc) s 4500 unts. We assume that the OC s equally dvded among the SC enttes. Sx dfferent scenaros were desgned to fnd out the best scenaro whch allocates the COQ among the the SC enttes. All scenaros are expected to satsfy the model constrants. The best scenaro wll provde the mnmum obectve value. These sx scenaros are provded n Table II, n whch the frst scenaro s shown n Fg. 4. TABLE I COST OF QUALITY FUNCTIONS COQ = ($) COQ = ($$$) COQ ($$) fpa(x ) = 0.085e^6.41x fpa(y ) = 0.27e^5.69y fpa(u ) = 0.18e^6.01u ff(x ) = 8x^-2 5x 2 ff(y ) = 21y^-2 7y 14 ff(u ) = 11u^-2 8u 3 foc(x ) = 5x^-2 5x foc(y ) = 5y^-2 5y foc(u ) = 5u^-2 5u fcoq(x ) = fpa(x ) + ff(x ) + foc(x ) fcoq(y ) = fpa(y ) + ff(y ) + foc(y ) fcoq(u ) = fpa(u ) + ff(u ) + foc(u ) Fgure 4 Three dfferent COQ ($, $$, $$$) functons demonstraton TABLE II COQ SCENARIOS AMONG SC ENTITIES Scenaro No. COQ Dstrbuton among SC Echelons 1 S = $$ M = $$$ R = $ 2 S = $ M = $$$ R = $$ 3 S = $$ M = $ R = $$$ 4 S = $ M = $$ R = $$$ 5 S = $$$ M = $$ R = $ 6 S = $$$ M = $ R = $$ (S = Suppler, M = Manufacturer, & R = Retaler) 161

6 We mplemented each scenaro separately n the obectve functon. In each scenaro we determned the optmum value n the model. Constrant 8 was annulled for the purpose of optmzng qualty level x, y, and u freely and as they expected to be between zero and one: so optmal QL of x, y, and u and ther COQ s fetched. III. RESULTS Excel Solver was used to solve the model for the sx scenaros. The accuracy of the results for our model was compared wth results obtaned n the lterature to valdate our model. The accuracy we acheved greatly surpassed our expectatons. Here the accuracy s the accuracy of repeatng the optmzaton for the same condtons, whch provded the same results although the nonlnearty s exst n the obectve functon and constrants. In addton, as our model uses Juran s COQ prncples, we confrmed that the behavor of the model presented a smlar tendency. Juran [1] clamed that when any nvestment s made n the costs of conformance, costs of non-conformance wll decrease, as well as total COQ, whch wll reach ts mnmum value at a certan qualty level after whch - wth more nvestment n costs of conformance - t wll start to rse agan (see Fg. 1). Ths behavor was clearly observed n our model as well. The results of the sx scenaros are presented n Table III and IV. Table III, whch shows dfferent results for the sx proposed scenaros, ncludes the followng parameters: total SC PA cost, total SC F cost, and total SC OC, and ther subsequent total SC COQ and obectve values for each scenaro. The best scenaro among the sx scenaros s scenaro no. 3 wth the mnmum SC obectve value n whch the COQ s allocated as follows: the manufacturer spends the lower level of COQ ($),the suppler the medum COQ level ($$), whle the hghest porton of COQ ($$$) s allocated at retaler. For ths scenaro, the mnmum obtaned obectve value s $847, In Table IV, the QLs and the suppled materals to each echelon are provded, In general, n whatever scenaro we observe: 0.85 x 0.80, 0.91 y 0.85, and 0.94 u Therefore, the most nterestng fndng n these sx scenaros s that the hghest QL was assgned to the retaler except n scenaro no. 6 n whch the manufacturer was assgned the hghest QL at around It s worth notcng that the range between the hghest and lowest COQ n Table III s around $4.2/unt, whch s the dfference between COQ n scenaros 1 and 5 (COQ = $121.2), and COQ n scenaro 3 (COQ = $117.0). TABLE III OPTIMUM RESULTS FOR EACH SCENARIO IN THE SC Scenar o No. However, one can notce that the hghest COQ scenaros do not necessarly lead to hgh obectve values. Ths can be ustfed because the qualty level also affects the suppled unts to each SC echelon, whch are Z, Z, and Z. Ths means n case of hgh QL the COQ wll be hgh and conversely the suppled unts wll decrease leadng to an overall decrease n the obectve value, whch s a recprocal effect between both QL and COQ together and the suppled unts to each echelon. TABLE IV Scenaro No. SC SC SC SC SC Sum PAs ($)/un t DECISION VARIABLES FOR THE SIX SCENARIOS Z (Unt) Sum Fs ($)/un t QL (x) Z (Unt) Sum OCs ($)/un t QL (y) COQ ($)/un t Z QL Ob. Val. ($) Dc (Unt) (u) (Unt) 162

7 Table V provdes detals about the obectve functon of scenaro no. 3. In ths table, n order to satsfy the customer demand of 4,500 unt, the suppler has to start wth Z = 7075 unts and he has to wor at a QL of x = 0.80 to provde Z = 5439 unts. The manufacturer should wor at a hgher QL of y = 0.86 n order to provde Z = 4705 unts, and fnally the retaler should wor at the hghest QL of u = 0.92 to satsfy the fnal demand, 4500 unts. The retaler should also spend hgher conformance costs, PA, than what suppler and retaler together spend, whch equal to $50.6 at retaler and around $22.0 for each of suppler and manufacturer. However, wth ths QL the manufacturer and retaler wll ncur less falure and opportunty costs, whle the suppler wll end up wth hgher nonconformance costs. TABLE V DECISION VARIABLES FOR SCENARIO NO. 3 S M R QL = x = 0.80 y = 0.86 u = 0.92 PA = F = OC = COQ = Z = 7075 unt--z = 5439 unt--- Z = 4705 unt-- -D c = 4500 unt Obectve value = $847,149.5 (S = Suppler, M = Manufacturer, & R = Retaler) IV. CONCLUSIONS AND FUTURE WORK Cost of qualty (COQ) analyss s an mportant subect whch attracts the attenton of many researchers. However, whle few researchers mplement COQ n the supply chan (SC), no research has been done so far to analyze the concept of allocatng COQ and ts qualty level (QL) n SC. Therefore, the novelty of ths wor s n ts attempts of analyzng COQ and ts QL n SC. We have modeled COQ n the SC usng a nonlnear mathematcal programmng model. The non-lnearty s present n our obectve functon through the convex qualty functons, where dfferent equatons were used at each level of the SC to represent preventon and apprasal, falure, and opportunty cost. The nonlnearty s present n the constrants as well. By mplementng the model and analyzng the results we were able to acheve nsghtful results. COQ functons that were used were nspred by Juran s model [1]. They can represent mathematcally the qualty system of gven un-capactated SC,.e. suppler, manufacturer, and retaler. Whle COQ vares among dfferent companes, one can certanly analyze the COQ based on QL wth respect to x, y, and u, and buld a mathematcal functon to represent them. Hence, by usng COQ functons and QL we can bypass the complcatons of accountng systems because we can use more than one cost functon to represent dfferent cost attrbutes and better understand SC costs that correspond to QL, whch can be connected to number of producton unts and costs. Ultmately, we can allocate our COQ n a way that can mnmze our total SC costs. Just le COQ and QL were modeled n uncapactated SC, further research could focus on modellng COQ and QL n a capactated SC,.e. number of capactated supplers, manufacturers, and retalers. Moreover, further research could address dfferent COQ products n SC. Ths wll be nterestng and wll expand the model to have more decson varables and extra constrants, and wll add more 163

8 complexty to the SC model. Ths s due to the nterrelatons between parameters and decson varables n the model. The complexty of such a problem would perhaps be too hgh for standard solver and t would therefore requre the formulaton of a soluton methodology that uses some stochastc search procedures, such as genetc algorthms. REFERENCES [1] J. M. Juran, Qualty Control Handboo, 1st ed. McGraw-Hll). New Yor., [2] A. Schffauerova and V. Thomson, A revew of research on cost of qualty models and best practces, Int. J. Qual. Relab. Manag., vol. 23, no. 6, pp , [3] A. V. Fegenbaum, Total qualty-control, Harv. Bus. Rev., vol. 34, no. 6, pp , [4] J. Campanella, Prncples of Qualty Costs: Prncples. Implementaton, and Use, 2nd ed. ASQC Qualty Press, Mlwauee, [5] M. Juran Joseph, Qualty control handboo, McGraw Hll, [6] S. B. Jau and R. R. Lahe, Qualty costs n a manufacturng ndustry: a gateway for mprovement, Int. J. Appl. Eng. Res., vol. 4, no. 6, pp , [7] Y. K. Son, A cost estmaton model for advanced manufacturng systems, Int. J. Prod. Res., vol. 29, no. 3, pp , [8] D. A. Sandoval-Chavez and M. G. Beruvdes, Usng opportunty costs to determne the cost of qualty: A case study n a contnuous-process ndustry, Eng. Econ., vol. 43, no. 2, pp , [9] X. Lu, F. Cu, Q. Meng, and R. Pan, Research on the model of qualty cost n CIMS envronment, n Busness and Informaton Management, ISBIM 08. Internatonal Semnar on, 2008, vol. 1, pp [10] V. Snesa, A. Daunorene, and A. Zeevcene, Hdden Costs n the Evaluaton of Qualty Falure Costs, Eng. Econ., vol. 24, no. 3, pp , [11] R. M. Moen, New qualty cost model used as a top management tool, TQM Mag., vol. 10, no. 5, pp , [12] P. Jones and T. Wllams, Busness Improvement Made Smple., Informaton Press, [13] S. K. Srvastava, Towards estmatng cost of qualty n supply chans, Total Qual. Manag., vol. 19, no. 3, pp , [14] K. K. Castllo-Vllar, N. R. Smth, and J. L. Smonton, A model for supply chan desgn consderng the cost of qualty, Appl. Math. Model., vol. 36, no. 12, pp , [15] F. Machows and B. G. Dale, Qualty costng: An examnaton of nowledge, atttudes, and perceptons, Qual. Manag. J., vol. 5, no. 3, [16] A. Ramudhn, A. Artba, P. Castaglola, C. Alzaman, and A. A. Bulga, Incorporatng the cost of qualty n supply chan desgn, J. Qual. Mant. Eng., vol. 14, no. 1, pp , [17] C. Alzaman, A. Ramudhn, and A. Bulga, Heurstc procedures to solve a bnary nonlnear supply chan model: A case study from the aerospace ndustry, n Computers & Industral Engneerng, CIE Internatonal Conference on, 2009, pp