SUPPLY CHAIN DESIGN BASED ON THE COST OF QUALITY ANALYSIS

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1 SUPPLY CHAIN DESIGN BASED ON THE COST OF QUALITY ANALYSIS 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 Recent studes have revealed that managng the cost of qualty (COQ) s more economcally mportant than prevously perceved. Whereas prevous wors have shown nterest n COQ appled as an nternal performance measure wthn companes, the purpose of ths paper s to explore the relatonshp between the COQ externally wthn a capactated supply chan (SC). The proposed COQ model ntegrates the opportunty cost (OC) and analyzes ts effect on the qualty level (QL). In addton, t also examnes the effect of allocatng an nvestment at each SC level to ensure the best overall QL. Our model mnmzes a seres of COQ and operaton costs as an ntegrated SC networ to ensure the lowest overall cost whle provdng the best QL. Therefore, the model can be used to desgn a COQ based model that acheves a mnmum total cost whle consderng an overall QL and to evaluate the nfluence of nvestment n COQ to ncrease overall qualty. A numercal example s presented to llustrate the behavor of the model and the results showed how the QL and COQ functons change dependng on the cost type (.e. conformance or nonconformance) and locaton. Keywords Supply Chan, Cost of Qualty, Investment Allocaton, Qualty Level. I. INTRODUCTION The supply chan has recently become the trend of the global maret, as t s not anymore a sngle frm show whch can effcently compete. Despte all of the complcatons, such as development nconsstences and dssmlartes of obectves wthn supply chan, the emergence of allance and cooperaton among supply chan enttes plays a sgnfcant role n today s maret. All levels of supply chan from upstream to downstream could drastcally affect the supply chan productvty. Thus there should be adacent collaboraton between all enttes to strengthen the chan value. Even though qualty s a dffcult term to defne, as t s understood from a dfferent perspectve by manufacturer and enduser, delverng a satsfactory qualty product s an ultmate goal of all supply chans enttes. Cost of qualty (COQ) could be used as a measurng tool to evaluate any servce/producton system performance. In the supply chan perspectve, COQ could be utlzed as a ey performance measurement and evaluaton tool. It provdes an opportunty to express supply chan performance n monetary terms n order to facltate 165

2 understandng of all the supply chan shareholders. In the lterature we fnd numerous studes concerned wth COQ measurement and analyss, however, only a few studes attempted to ntegrate COQ and supply chan performance measurements together. Even dough COQ has been consdered wthn manufacturng supply chan by several authors, such as Ramudhn et al. [1] and Castllo-Vllar et al. [2], no a comprehensve COQ model for the supply chan has been proposed so far. Therefore, ths research ams at modellng COQ n a manufacturng SC wth consderaton of the qualty level n all SC facltes. In addton, the model wll be used as an evaluaton tool to examne the mpact of COQ nvestment at each SC level. The rest of the paper s organzed as follows: In secton two we present a lterature revew pertanng to COQ, and then to COQ n supply chan. In the thrd secton, an optmzaton model that represents a capactated SC, four-level system (.e. supplers, manufacturers, retalers, and customers) amng at the mnmzaton of the overall operaton and qualty costs s formulated. Next, the results are presented. The fnal secton presents the conclusons and the future wor. II. OVERVIEW OF COQ The mportance of qualty arses from the fact that t greatly affects customer s decson about the purchase of any product. The dfferences among varous products can thus be recognzed by the qualty and ts cost. Over the past thrty years there has been a hostle battle among busnesses tryng to mprove qualty whle mantanng t at lowest possble cost, and, consequently, only those who managed t survved. In today s maret, the qualty preferences became a crtcal element n competton Bowbrc [3]. Therefore, a clear defnton of the COQ for any product s necessary n order to compete effectvely and to contnue n the maret Ben- Areh and Qan [4]. Even though the defnton of qualty costs s crucal for measurng the qualty tself, there s no sngle and generally accepted defnton, as dfferent authors tend to defne qualty costs n dssmlar ways (Chadamrong [5]; Denns [6]; Evans & Lndsay [7]). Several authors, such as Plunett and Dale [8], Kumar et al. [9], and Schffauerova and Thomson [10] provded a revew of generc models and approaches to measure COQ; these models nclude Preventon, Apprasal, and Falure (PAF) models, Crosby s model, opportunty or ntangble cost models, process cost models, and actvty-based costng (ABC) models. Juran s [11] model s the most common model n the lterature, whch s also wdely used n manufacturng ndustry due to ts easy nterpretaton Jau et al. [12]. Juran clams that n order to obtan the lowest rate of COQ, falure costs should be equal to preventon and apprasal costs [11]. Ths can be observed n the trend graph n Fg. 1. However wth the ncrease n the organzaton complexty these costs are ncreasng as well, and ther cost elements may become unclear and more dffcult to be captured. Cheah et al. [13], Campanella [14], Krshnan [15] and Wood [16] supported the vew that most qualty costs are n fact hdden and are not easy to be measured. Accordng to Srvastava [17], COQ or qualty costs can be defned as a measurement system that translates qualty related actvtes nto a monetary language for managers,.e. t s the aggregate of costs occurred to mae sure that the qualty requrements are beng met. There are dfferent estmatons of total costs of qualty n the lterature, for example, Kent [18] apprased them between 5-15% of ncome for companes n Great Brtan. Crosby [19] estmated them between 20-35% of sales for manufacturng and servce companes n the USA, and Fegenbaum [20] at 10% of revenues. Schffauerova & Thomson [10] have hghlghted the savngs acheved through the COQ employment n varous companes. As examples of publshed success stores, ITT Europe headquartered n Belgum has saved over $150 mllon durng fve years of copng wth qualty cost control Groococ [21]. Hagan [22] and Morse et al. [23] descrbed huge savngs related to reducng COQ for ITT New Yor, Unted Technologes Corporaton. Essex Telecommuncaton Products Dvson establshed COQ measurement and reported that after fve years of mplementaton the productvty ncreased by 26%. Thompson & Naamura [24] have collected and reported COQ data from several development proects at AT&T Bell Laboratores, Transmsson System Dvson and confrmed that managng COQ n the R&D process s a feasble way to 166

3 mprove product development. In general, t s expected that the total cost of qualty wll decrease f the organzatons mplement a strong qualty cost system, and the external falure costs wll decrease too as a percentage of total COQ. Fg. 1 Juran s model for COQ [11] A. COQ n Supply Chan COQ ntegrates the qualty mprovement efforts, mplcatons of poor qualty, and hdden qualty costs. It translates them to understandable monetary terms to all staeholders of the organzaton Castllo-Vllar et al. [2]. Although there are numerous cases that measure COQ and ts mplementatons n organzatons ndvdually, only few studes attempt to measure COQ n the whole supply chan networs. Srvastava [17] was the frst author who combned COQ n supply chan performance measurement. He defned COQ n supply chan based on hs chan as: the sum of the costs ncurred across a supply chan n preventng poor qualty of product and/or servce to the fnal consumer, the costs ncurred to ensure and evaluate that the qualty requrements are beng met, and any other costs ncurred as a result of poor qualty Srvastava [17, p.139]. The lterature presents dfferent approaches and methodologes, whch ncorporate COQ nto SC. Srvastava measured COQ at selected thrd party manufacturng stes for a pharmaceutcal company. He suggests that mappng COQ can reveal where qualty mprovement efforts are needed most and where to exert more effort n order to reduce the COQ. Ramudhn et al. [1] argue that ncorporatng COQ n supply chan declnes the overall processes costs. Conversely, there s a hgh rs of low qualty supplers selecton when supply chan networ does not consder COQ. Ramudhn et al. [1] studed sngle product three echelon supply chan. Ther model mnmzes total operatonal and qualty costs at the same tme. They clam that addng suppler qualty costs to the obectve functon mnmzes percentage of defectves at the suppler, whle ths also mnmzes the overall obectve functon. They argue that addng COQ to the obectve functon ncreases the obectve value by 16% and changes the soluton consderably. The ustfcaton s due to the nfluence of COQ Ramudhn et al. [1]. Alzaman et al. [25] later proposed a heurstc approach to solve a mathematcal model contanng a quadratc COQ functon. They state that a quadratc COQ functon can be ncorporated n supply chan networ desgn wth bnary varables and solved profcently. Castllo-Vllar et al. [2] studed the mpact of COQ on supply chan networ desgn and used Genetc Algorthm (GA) and Smulated Annealng (SA) to solve ther nonlnear model. Ther proposed model was able to fnd the best combnaton of nteger varables that maxmzes the proft and mnmzes the total COQ. Recently Lm et al. [26] proposed a mathematcal programmng model to optmze COQ. The model consders PAF framewor and was recommended to be lnearzed n order to provde nsghts nto the effects of changes n COQ parameters. Studyng the QL n the SC whle analyzng COQ have not been proposed yet. Accordngly, our model wll ncorporate QL analyss n the SC, whch wll consder the synchronzaton of the COQ (wthout and wth OC) n the SC. Ths research model and fndngs are presented n the next secton. III. MODEL AND FINDINGS Methodology The model represents a capactated supply chan, whch conssts of four-level system as shown n Fg. 2. The model ams at mnmzng the overall operaton and qualty costs. Here, the standpont wll be that of the supply chan as a whole, meanng the supplers, manufacturers, retalers, and customers are subsdary of the supply chan and are ntegral parts of t. 167

4 Fg. 2 Capactated supply chan For example the operaton cost and COQ at the suppler s level would also be cost attrbutes for the supply chan and would be accounted for n the model. The costs wll be calculated n the same manner at the manufacturers and retalers level wth the consderaton to the opened and closed facltes costs. The model s mxed nteger nonlnear n nature, as t has nonlneartes n the obectve functon and also n the constrants. The obectve functon of the model wll mnmze the total operaton and qualty costs at the supplers level, total operaton and qualty costs at the manufacturers levels, and total operaton and qualty costs at the retaler, and total transportaton costs between SC levels. The nput parameters, decson varables, and constrant parameters are explaned n general forms as follows: I: Set of supplers, J: Set of manufacturers, K: Set of retalers, and C: Set of customers. 1) Decson Varables Z, Z, and Z = Suppled components to suppler, manufacturer, and retaler respectvely; I, J, K. = Number of good components to ext from suppler, manufacturer, and retaler respectvely; I, J, K. x, y, and u = Qualty level at suppler (), manufacturer () & retaler (); I, J, K. q 2 = Bnary varable; 1 f manufacturer s open; 0 f manufacturer s shut; J. q 3 = Bnary varable; 1 f retaler s open; 0 f retaler s shut; K. 2) Parameters (Input Data): Opc = Operaton cost at suppler ; I. Fc and Fc = Faclty fxed cost at manufacturer, and retaler respectvely; J, K. fpa(x ), fpa(y ), and fpa(u ) = Preventon and apprasal cost functons at suppler (), manufacturer () & retaler (); respectvely; I, J, K. ff(x ), ff(y ), and ff(u ) = Falure cost functons at suppler (), manufacturer () and retaler () respectvely; I, J, K. foc(x ), foc(y ), and foc(u ) = Opportunty cost functons at suppler (), manufacturer () and retaler () respectvely; I, J, K. PA nv = PA cost nvestment value. = Transportaton cost of products from suppler to manufacturer ; I, J. = Transportaton cost of the products from manufacturer to retaler ; J, K. = Transportaton cost of the products from retaler to customer c; K, c C. 3) Constrants Input Parameters: Dc = The producton demand for customer c; c C. Cap = Total capacty of suppler ; I. Cap = Total capacty of manufacturer ; J. Cap = Total capacty of retaler ; K. The obectve functon for a synchronzed SC COQ cost model, whch mnmzes the operaton costs, fxed costs, and COQ n the SC and t s constrants are presented as follows: Mn Mn K I J K S.t. Opc Z Pm Fc q 3, Tr, I fpa(x) ff(x) * Z OC(x) f J Fc q 2 K I J Os, Tr, fpa(u) ff(u ) * Z OC(u ) f J K cc fpa(y ) ff(y ) * Z OC(y ) f Qr, c Tr, c (1) 168

5 K Z J Z Z I 0 x 2 Cap Cap, q 1, 0 y {0,1} c 1, and 0 u 1 Z 0, Z 0, Z 0, Os 0, pm,, 3 Dc cc 3, c Z K 2 Z Cap q Z x Qr Z u Pm y Os,c,, Z J q Qr q Os Pm,, 0, Qr,c 0 The constrants from (2) to (13) perform the followng: Constrant (2) ensures the customer demand s satsfed. Constrant (3) puts an upper lmt for the retaler s capacty demand. Constrant (4) ensures that the retaler s good products equal to the customer demand at the customer level. Constrant (5) s the manufacturer s good products, whch satsfy a retaler demand. Constrant (6) s the manufacturer s capacty constrant whle constrant (7) s the manufacturer s suppled good products constrant. Constrant (8) s the equalty constrant for the good products from the suppler to satsfy a manufacturer s demand. Constrant (9) s the suppler capacty constrant. Constrant (10) s the constrant for the suppled good products from the suppler. Constrants (11) s the qualty level constrant for suppler, manufacturer, and retaler consecutvely. Constrant (12) s the ntegralty constrant for the manufacturers and retalers. Constrant (13) mposes the non-negatvty restrcton on the decson varables. To solve the model, few assumptons were appled n order to smplfy the model and ts constrants, so that t could be solved by common ndustral software, such as Solver. We assume that all the products are of the same type, sngle components, and necesstate the same manufacturng actvty at each level. The retalers are part of the the supply chan and they add qualty to the manufactured products (.e. perform tests and fnal nspectons). Transportaton costs were substtuted by zeroes because they can affect faclty choces and have no value to add to products qualty. 2 The customer demand s 4,500 unts. Qualty functons are tabulated n Appendx I, and the other 3 nput parameters are as follows: operaton cost for each 4 faclty () s $10.0 per unt, fxed cost for each open 5faclty for the manufacturers () and retalers () s $ Cap and Cap s 2000 unts each. Cap s unts. 7 We present the SC as an ntegrated networ, meanng that supplers should satsfy the manufacturers 8 demand, the manufacturers should provde the retalers 9wth the needed products, and fnally the retalers have 10to fulfll the customer demand. Cost of qualty s hghly affected by products' QL at each SC level. The COQ 11 equatons n our optmzaton model were nspred by 12 Juran s (1951) COQ model. Our model optmzes the 13COQ at each open faclty n the SC, as well as the operaton costs, whch are located at each open suppler faclty (). Fxed costs, whch are the costs of each open faclty at the manufacturers and retalers levels. The presented solutons are obtaned from sx-supplers, sxmanufacturers, and sx-retalers. The model represents the COQ nputs parameter wth dfferent cost equatons for each SC entty. When the OC was not consdered n the model, two equatons were used at each faclty to represent PA and F costs, and n total thrty sx equatons for the whole SC. When the OC was consdered n the model, three equatons were used at each faclty to represent PA, F and OC costs, and n total ffty four equatons for the whole SC (see Appendx I). Fg. 3 roughly shows the shape of costs of conformance and the costs of nonconformance (COQ functon) at each faclty,, and. The COQ equatons were generated by Excel. Costs of conformance functons, PA, were represented by exponental equatons and costs of nonconformance functons, F and OC, were represented by polynomal equatons. Ths valdated our model, because when the QL approaches zero we can see that COQ s hgh, then the QL decreases as PA ncrease tll certan pont after whch the QL starts to ncrease because of the costs of nonconformance approachng ther lowest values. Constrant 12 was annulled as the model s expected to freely fetch the optmum QL values, x, y, and u ; therefore an optmal x, y, and u are fetched between zero and one. The data sets for our model are generated n an attempt to create a wde range of applcable stuatons. Our data sets examned dfferent practcal scenaros n respect to the 169

6 COQ functons and were used to represent COQ model when all SC enttes are synchronzed to satsfy customer demand. Fg. 3 COQ for the SC ncorporatng OC Based on the prevous assumptons, the model was constructed and optmzed to obtan the solutons usng Excel Solver (GRG nonlnear). The solutons were fetched n less than a mnute tme after we provded the model wth ntal values. more facltes were opened, especally at the supplers and manufacturers level. Ths s due to the nature of the COQ functons, whch are quadratc functons. In order to overcome the burden of the added OC n the model, the model has ncreased the values of PA and QL n Fg. 5. Conversely, the suppled nput materals Z, Z, and Z have decreased when the OC s consdered n the model (Fg. 5). The decrease n the nput materals occurred due the ncrease n QL, n whch the materals are n nverse proporton wth QL. Ths means f the QL ncreases at any faclty, waste (falure) of the output materals wll decrease. In general, to mnmze the consequence of the the added costs of nonconformance (OC), the model leaned towards ncreasng the QL and reducng the flow of the nput materals to the opened facltes. IV. RESULTS In ths paper, as an example, we present the best soluton of our nput data set, to show frst the effect of ncorporatng the nonconformance costs (OC) to the model, and second, to demonstrate the effect of PA nv allocatng n each SC level separately. A. Optmzed model (wth & wthout OC) Fg. 4 SC COQ model wthout OC The results of the optmzed model are presented n Fg. 4 and 5, whch show the results wthout and wth OC (wthout consderng PA nv n the model). In Fg. 4, the results obtaned wthout ntegratng the OC nto the obectve (.e. OC = 0). The obectve value n ths stuaton s $719, After we added the OC to the obectve functon, the results of whch are provded n Fg. 5, we have notced that the obectve value has ncreased to reach $784, Ths s equal to an ncrease of about 9.1%, whch s hgher than the obectve value wthout OC. It s mportant to notce that n Fg. 5 the QL has ncreased n each open faclty and consequently the overall average QL has ncreased n each level by approxmately 2.0%, and, n addton, Fg. 5 SC COQ model wth OC Table 1 provdes the decson varables results, whch 170

7 are PA, F, and OC wthout and wth OC. We can summarze ths table as follows: when OC was added to the obectve functon, the average PA costs ncreased from $13.1 to $18.6 by around 42.0% at the supplers, from $24.3 to $28.3 by around 16% at the manufacturer, and from $36.9 to $50.1 by around 36% at the retaler. On the other hand, the average F costs decreased by nearly 9.0%, 15.0%, and 17.0% at the supplers, manufacturers, and retalers respectvely. Here, one can see that to reduce the effect of the nonconformance costs a hgh porton of nvestment n PA s necessary to be allocated at the retalers echelon. It s worth to notce that the relatonshps between PA and F costs are dfferent from one faclty to another, therefore, an ncrease n PA costs n one faclty mght have dfferent effect on F costs at another faclty. Ths explans why there s no drect relatonshp between the ncreased average of PA costs and the decreased average of F costs after we consder OC n the obectve value. TABLE I. COQ WITHOUT AND WITH OC IN THE COQ Wthout OC ($) COQ Wth OC ($) Cost ($) S M R S M R PA(faclty 1) = N/A N/A N/A 55.5 F( faclty 1) = N/A N/A N/A 7.5 OC( faclty 1) = N/A 1.7 PA( faclty 2) = F( faclty 2) = OC( faclty 2) = PA( faclty 3) = N/A N/A F( faclty 3) = N/A N/A OC( faclty 3) = N/A PA( faclty 4) = N/A N/A F( faclty 4) = N/A N/A OC( faclty 4) = N/A PA( faclty 5) = 10.5 N/A F( faclty 5) = 9.1 N/A OC( faclty 5) = PA( faclty 6) = N/A N/A N/A 59.1 F( faclty 6) = N/A N/A N/A 11.8 OC( faclty 6) = N/A 4.9 Aver. PA Aver. F Aver. OC B. consderng PAnv n each echelon In ths secton we have consdered the PA nv values at each echelon separately n the obectve functon (.e. three tmes) n order to fnd the best average QL. In order to acheve our goal, we added one constrant for each echelon to the prevous constrants as follows: fpa(x ) + PA nv = G nv (x ) : when the nvestment s allocated at the supplers level fpa(y ) + PA nv = G nv (y ) : when the nvestment s allocated at the manufacturers level fpa(u ) + PA nv = G nv (u ) : when the nvestment s allocated at the retalers level Where: G nv (x ), G nv (y), and G nv (y) are the upper lmt for each faclty whch s equal to the summaton of the optmum value (best value obtaned n the prevous secton) plus to the PA nv value. The model s expect to present n whch level t s better to allocate the nvestment PA nv that ncreases the overall SC QL. Each PA nv = $4.0 n the constrants and fpa(x ), fpa(y ), fpa(u ) provded the best PA costs obtaned n the prevous secton A (.e. the soluton shown n Fgure 5 and Table I). Ths s to provde the best opton that allocates the COQ, whch can mprove the overall SC QL. Fgures 6-8 show the results for the PA nv allocaton at each level of the SC separately. In Case I, whch s shown n Fgure 6, PA nv was allocated and constraned to each suppler faclty. The results for the average QL at each level are as follows: 0.80, 0.92, and 0.89 for the supplers, manufacturers, and retalers levels, respectvely. For Case II, whose results are shown n Fgure 7, PA nv was allocated at each manufacturer faclty and the average obtaned QL at each level s as follows: 0.78, 0.92, and 0.91 for the supplers, manufacturers, and retalers correspondngly. In Case III, whch s shown n Fgure 8, PA nv was allocated at each retaler faclty and the average values obtaned QL at each level are as follows: 0.79, 0.89, and 0.90 for the supplers, manufacturers, and retalers, respectvely. (S = Suppler, M = Manufacturer, R = Retaler, And N/A = Not Applcable) 171

8 suppled materal to SC facltes Z, Z, and Z. However, allocatng PA nv at the manufacturers presented a slghtly better mprovement n the overall QL than n the other two echelons. Fg. 6 Case I, PA nv allocated at the supplers Fg. 7 Case II, PA nv allocated at the manufacturers Fg. 8 Case III, PA nv allocated at the retalers In general, the three cases have presented almost the same results, whch s may be due to the small value of PA nv. However, we can observe that n Case II, the results, n whch PA nv was allocated at the manufacturer, the QL are slghtly better (ths s regardless to the obectve values), and, furthermore, Case II presented lower suppled materals Z, Z, and Z than the other two cases. To summarze ths secton, the three nvestments presented a slght mprovement n the overall SC QL, whch consequently decreased the V. CONCLUSIONS AND FUTURE WORK In ths paper the cost of qualty was measured wthn a capactated supply chan, where ndvdual COQ parameters were studed as COQ functons. We have modeled preventon and apprasal costs, falure costs, and opportunty cost n each SC faclty. Our model was bult based on the PAF model approach usng a nonlnear mathematcal programng model. The SC has consdered four levels, whch are: sx capactated supplers, sx capactated manufacturers, sx capactated retalers, and N customers. The unque feature of our model s the consderaton of OC and ts ntegraton nto the model. Wth the exstence of the nonlnearty n the obectve functon and n the constrants we stll could reach nsghtful solutons, whch could provde the best qualty level, COQ parameters, and materal needed n each open faclty to satsfy the customer demand. In general, the model has found a soluton whch taes nto consderatons day to day COQ tradeoffs n SC operatons. By ntegratng the OC to the model and mnmzng the overall cost of the SC we have obtaned a reasonable soluton, whch caused an ncrease n the obectve value by around 9.1%. Ths occurred to compromse the effect of the nonconformance cost (OC). In addton, snce QL s drectly proportonal to PA costs the ncrease n the PA costs caused the QL to rse as well. Our model had not only sought to examne the effect of ntegratng the OC to PAF n the SC but also consdered the allocaton of an nvestment (PA nv ) n each SC level separately. We were able to demonstrate the dfferences among consderng the the PA nv n each SC and how t can affect the QL. Our soluton showed that by allocatng PA nv at the manufacturers the average SC QL mproves slghtly, and t also presented better QL at the retaler (ths was done regardless of the obectve value). Just le COQ was modeled based on PAF and OC at each faclty, further research could model dfferent cost functons whch can be dsntegrated from the SC and whch can form a system of cost functons and optmze the total costs n order to provde more n depth cost 172

9 analyss. In addton, further research could address a mult-product sourcng wth the consderaton to the transportaton networ. REFERENCES [1] 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 , [2] 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 , [3] P. Bowbrc, The Economcs of Qualty, Grades and Brands. Routledge, London, [4] D. Ben-Areh and L. Qan, Actvty-based cost management for desgn and development stage, Int. J. Prod. Econ., vol. 83, no. 2, pp , [5] N. Chadamrong, The development of an economc qualty cost model, Total Qual. Manag. Bus. Excell., vol. 14, no. 9, pp , [6] G. Denns Beecroft, The role of qualty n strategc management, Manag. Decs., vol. 37, no. 6, pp , [7] J. R. Evans and W. M. Lndsay, The management and control of qualty, [8] J. J. Plunett and B. G. Dale, Qualty costs: a crtque of some economc cost of qualty models, Int. J. Prod. Res., vol. 26, no. 11, pp , [9] K. Kumar, R. Shah, and P. T. Ftzroy, A revew of qualty cost surveys, Total Qual. Manag., vol. 9, no. 6, pp , [10] 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 , [11] J. M. Juran, Qualty Control Handboo, 1st ed. McGraw-Hll). New Yor., [12] S. B. Jau, R. P. Mohanty, and R. R. Lahe, Towards managng qualty cost: A case study, Total Qual. Manag., vol. 20, no. 10, pp , [13] S.-J. Cheah, A. Shah, M. Shahbudn, Fauzah, and M. Tab, Tracng hdden qualty costs n a manufacturng company: an acton research, Int. J. Qual. Relab. Manag., vol. 28, no. 4, pp , [14] J. Campanella, Prncples of Qualty Costs. Prncples, Implementaton and Use, 3rd ed. ASQC, Mlwauee, [15] S. K. Krshnan, Increasng the vsblty of hdden falure costs, Meas. Bus. Excell., vol. 10, no. 4, pp , [16] D. C. Wood, The executve gude to understandng and mplementng qualty cost programs: reduce operatng expenses and ncrease revenue. ASQ Qualty Press, [17] S. K. Srvastava, Towards estmatng cost of qualty n supply chans, Total Qual. Manag., vol. 19, no. 3, pp , [18] R. Kent, Manufacturng strategy for wndow fabrcators 14 the cost of qualty, Tanagram Technology [19] B. Crosby Phlp, Qualty Wthout Tears: The Art of Hassle-Free Management. McGraw-Hll, New Yor, [20] A. V. Fegenbaum, Total qualty control: McGraw-Hll New Yor, [21] J. M. Groococ, Qualty cost control n ITT Europe, Qual. Assur., vol. 6, no. 3, p. 37, [22] J. Hagan, Qualty costs at wor. ASQC Techncal Conference Transactons, 1973, p [23] W. J. Morse, H. P. Roth, and K. M. Poston, Measurng, plannng, and controllng qualty costs. Inst of Management Accountants, [24] W. G. Thompson Jr and S. Naamura, Measurng costs of qualty n the development process, n IEEE Internatonal Conference on Communcatons, 1987, vol. 87, p [25] 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 [26] C. Lm, H. D. Sheral, and T. S. Glcman, Costof-qualty optmzaton va zero-one polynomal 173

10 programmng, IIE Trans., vol. 47, no. 3, pp , APENDIX I COQ Input functons to the model PA, F, and OC Model Functon Cost functon ($) Supplers Manufacturers Retalers PA(faclty 1) = = *e^(7.807*x 1 ) = 0.15* e^(5.907*y 1 ) = 0.25*e^ (5.907*u1) F( faclty 1) = = 18*x 1^-2-8*x 1-10 = 10*y 1^-2-5*y 1-2 = 30*u1^- 2-7*u1-22 OC( faclty 1) = = 8*x 1^-2-3*x 1-5 = 5*y 1^-2-5*y 1 = 10*u1^- 2 +3*u1-13 PA( faclty 2) = = *e^ (9.207*x 2 ) = 0.059*e^ (6.97*y 2 ) = e^ (7.17*u2) F( faclty 2) = = 12*x 2^-2-7*x 2-5 = 10*y 2^-2-10*y 2 = 20*u2^-2-7*u2-13 OC( faclty 2) = = 4*x 2^-2-1* x 2-3 = 3*y 2^-2-4*y = 9* u2^-2-5* u2-4 PA( faclty 3) = = *e^ (6.95*x 3 ) = e^(5.17*y 3 ) = 0.34*e^ (6.37*u3) F( faclty 3) = = 9*x 3^-2-11* x = 11*y 3^-2-9*y 3-2 = 26*u3^-2-11 u3-10 OC( faclty 3) = = 8*x 3^-2-3*x 3-5 = 2*y 3^-2-3*y =7*u3^-2-12*u3 +5 PA( faclty 4) = = *e^ (8.4*x 4 ) = *e^(4.87*y 4 ) = 0.49* e^ (6.27*u4) F( faclty 4) = = 12*x 4^-2-13*x = 7*y 4^-2-3*y 4-3 = 17*u4^-2-18*u4 +1 OC( faclty 4) = = 6*x 4^-2-5*x 4-1 = 3*y 4^-2-2*y 4-1 =8*u4^-2-2*u4-6 PA( faclty 5) = = *e^ (9.27*x 5 ) = 0.395*e^(4.81*y 5 ) = * e^ (7.81*u5) F( faclty 5) = = 14*x 5^ *x 5-30 = 9*y 5^-2-1*y 5-6 = 24*u5^-2-10*u5-14 OC( faclty 5) = = 11*x 5^-2 + 7*x 5-18 = 7*y 5^-2 1*y 5-6 = 5*u5^-2-12*u5 + 7 PA( faclty 6) = = 0.095*e^ (6.88*x 6 ) = 0.97*e^(3.958*y 6 ) = 0.47* e^ (5.75*u6) F( faclty 6) = = 17*x 6^-2+12*x 6-26 = 16*y 6^-2-1*y 6-16 = 21*u6^-2-13*u6-7 OC( faclty 6) = = 9*x 6^-2+5*x 6-14 = 5*y 6^-2-4*y 6-1 = 8*u6^-2 10*u