A fuzzy MADM approach for project selection: a six sigma case study

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1 Decson Scence Letters 5 (2016) Contents lsts avalable at GrowngScence Decson Scence Letters homepage: A fuzzy MADM approach for proect selecton: a s sgma case study Raeev Rath a*, Dnesh Khandua b and S.K.Sharma c a Research Scholar, Department of Mechancal Engneerng, Natonal Insttute of Technology, Kurukshetra, Haryana, Inda, b Professor, Department of Mechancal Engneerng, Natonal Insttute of Technology, Kurukshetra, Haryana, Inda, c Former Professor, Department of Mechancal Engneerng, Natonal Insttute of Technology, Kurukshetra, Haryana, Inda, C H R O N I C L E A B S T R A C T Artcle hstory: Receved June 25, 2015 Receved n revsed format: October 12, 2015 Accepted November 25, 2015 Avalable onlne November Keywords: S Sgma Fuzzy logc Proect selecton MADM Modfed dgtal logc TOPSIS VIKOR S Sgma s a strategc approach of sgnfcant value n achevng overall ecellence. It helps to accomplsh the organzatons strategc am through the effectual use of proect controlled methodology. As S Sgma s a proect controlled approach, t s necessary to prortze proects whch gve utmost economc benefts to the frm. In real practce, S Sgma proects selecton s very tough assgnment because poor proect selecton also happens even n the well-managed organzatons and ths can weaken the success and trustworthness of the S Sgma practce. The present study ams to develop a proect selecton approach based on a combnaton of fuzzy and MADM technque to help organzatons determne proper S Sgma proects and dentfy the prorty of these proects manly n automotve companes. VIKOR and TOPSIS methods have been used to select the proper S Sgma proect composed wth fuzzy logc. In ths contet, seven crtcal parameters have been consdered for selecton of fnest alternatve. The weghts of evaluaton crtera are obtaned usng the MDL (modfed dgtal logc) method and fnal rankng s calculated through prmacy nde obtaned by usng fuzzy based VIKOR and TOPSIS methodology. A factual case study from automotve ndustry s used to nvestgate the effcacy of the planned approach Growng Scence Ltd. All rghts reserved. 1. Introducton In ths compettve era customers wants superor qualty products and servces, so organzatons look for ways to mprove ther functonal performance to deal wth customer epectatons. In the chase of mproved performance and customer utmost satsfacton, S Sgma has been acknowledged as a wellorganzed methodology that efforts to mprove organzatonal performance through spottng on customer requrements (Lnderman et al., 2003). It s a commandng mprovement tool that can be used to drve and contnuously mantan transformatonal rase n the busness. It s an organzed approach to mprove processes and servces, snce t s based on scentfc and statstcal tools to create sgnfcant reducton n varatons (Johannsen et al., 2011). It has been accepted as a governng strategy that employs an ncessant mprovement methodology to reduce process varablty and forced out capacty waste nsde the processes usng qualty and statstcal technques (Rath et al., 2015). S Sgma * Correspondng author. Tel: , mob: , Fa: E-mal address: raeevrath_1443@ntkkr.ac.n rath.415@gmal.com (R. Rath) 2016 Growng Scence Ltd. All rghts reserved. do: /.dsl

2 256 mproves organsatonal performance n order to boost customer's satsfacton on products and servces. Many bg corporatons lke Motorola, General Electrc, Du Pont, Alled Sgnal, Honeywell, Sony etc. have mplemented S Sgma and saved mllons of dollars (Trechler et al., 2002). As per many researchers; t s a statstcally based mprovement methodology that helps to mprove company s processes by elmnatng waste, costs and by mprovng effectveness of the processes (Snee, 2004). It can be consdered as a busness strategy wth an am to reduce producton costs and make consderable mprovements n processes and savngs through combned attempts of statstcal and management approaches n an ntegrated manner (Hensley & Dobe, 2005). It s a breakthrough strategy used for process mprovement by usng a set of prearranged tools and statstcal technques to evaluate process performances (Tang et al., 2007). It makes a deep analyss and an effcent decson makng whch ams for the optmal soluton rather than a merely good one. The strategy s popular among manufacturng organsatons not only for ts stout tool set but also for ts well organsed applcaton of DMAIC methodology (Go & Scara, 2014). It ncludes all essental elements for certfyng a qualty manufacturng, startng from the desgn to control, usng qualty tools nto a system. S Sgma was evolved by Motorola Corporaton on the manufacturng floor n 1980s. S Sgma am at Motorola was not ust to manufacture defect free products, but to remove defects throughout the corporaton. They defned S Sgma as a qualty enhancement methodology wth an obectve of droppng the number of defects to 3.4 parts per mllon opportuntes. It was a move to refashon the capablty and use of qualty make-up n ndustral amphtheatre (Chakrabarty & Chuan Tan, 2007). It s a statstcally supported process mprovement busness strategy that targets to lessen defects by dentfyng and elmnatng causes of varaton n processes. S Sgma methodology make avalable the tools and technques to buld up the potental and decrease the defects n any busness practce (Goh, 2002). The name S Sgma has evolved from the Greek alphabet sgma (σ). The Greek alphabet s used to symbolze standard devaton n statstcs and to evaluate the varablty. The performance of any busness s delberated by ther resultant sgma level. In statstcs t s defned as s standard devatons from mean value and n a parametrc way shall nclude 99.99% of the yeld (Goh, 2002). S Sgma was ust a qualty mprovement practce and works on contnuous mprovement approach, when t was ntated n md 1980s. But wthout the drectonal support ths approach was not so popular at that tme. In late 1990s n net generaton of S Sgma; a new phase was adoned by General Electrc to S Sgma approach named as Defne n order to recognze and prortze problems n a rght drectonal way. The addton of ths phase completes the DMAIC methodology now etensvely used to successfully carry out S Sgma proects. Defne phase s the key step n selectng the best possble proect by focusng on the customer necesstes (Antony, 2006). As S Sgma s a proect drven approach, t s necessary to prortze proects whch gve greatest benefts to the organzaton. Prortzng and selectng the S Sgma mprovement proects are most complcated tasks n real lfe stuatons (Snee & Hoerl, 2003). S Sgma proects may be dssmlar n goals, vagueness, ntrcacy, length and n several other aspects. Every proect ncludes varous amounts of msgvngs and there s no rsk free proect (Fundn & Cronemyr, 2003; Su & Chou, 2008). Proect selecton s a key element for successful mplementaton of S Sgma. Busness enttes should select S Sgma proects n such a manner that they are drectly attached to the targets and plans, snce varous productve areas of enhancement struggle for lmted resources. S Sgma proect selecton s one of the most commonly argued ssue n the lterature these days because most of the S Sgma proects get faled due to mproper selecton of mprovement proects (Banuelas et al., 2006). Proect selecton s the process of estmatng ndvdual proects, and then choosng most essental proect to mplement S Sgma, so that the targets of the company wll be accomplshed. Rght S Sgma proect selecton s tself a task, f t s correctly conceded that the probable profts of S Sgma can mprove sgnfcantly (Banuelas Coronado & Antony, 2002). Proect selecton has been referred to as a very crucal act n any S Sgma proect and lterature revew shows that t has been frequently taken up very carelessly. Many of the corporatons dd not have any proect selecton technque that helps n well-tmed concludng of the proects. Approprate proect selecton ncreases the success rate and acceptance of

3 R. Rath et al. / Decson Scence Letters 5 (2016) 257 S Sgma n any busness. An approprate proect selecton s a very mportant task for accomplshment of S Sgma strategy due to the fact that wrong proect selecton can gravely affect the total effcency and productvty of any ndustry. For flourshng of S Sgma eecuton, the mportance of approprate proect selecton cannot be mstreated. Successful S Sgma proect eecuton can provde valuable outputs by utlzng varous resources. Whenever varous S Sgma proects are contradctory for mplementaton, organzaton s payng attenton n recognzng those proects that outcome n the utmost proft to the organzaton. Present study manly emphasze on Selecton of the rght S Sgma proect n an automotve manufacturng unt n Inda, whch s always the most crucal tasks n the successful eecuton of S Sgma n any busness. When there are no clear edges n outlooks of decson makers (S Sgma epert, producton manager, techncal and fnancal eperts etc.) whle selectng S Sgma proect. It becomes necessary to compute the best possble soluton n terms of selectng approprate proect usng a decson makng approach. In many decson makng methods estng n the lterature, only quanttatve crtera have been consdered for S Sgma proect selecton (De Boer et al., 2001). Varous domnant factors are frequently not consdered durng decson makng, lke; partal nformaton, qualtatve decsve factor and vagueness lkngs (Zhang et al., 2009). Therefore, n ths paper fuzzy MADM s used to recognze the proper S Sgma proect that outcomes n the utmost proft to the corporaton. Fuzzy MADM s a combned applcaton of fuzzy set theory and mult attrbute decson makng (MADM) approach to accomplsh most effcent proft and effectveness (Shemshad et al., 2011; Vats & Vash, 2013). MADM has capablty to selects the best alternatve from to the estng resources (Agalgaonkar et al., 2005). MADM approach has been effectvely used n a lot of decson makng tasks n ndustral and research feld (Gwo-Hshung, 2010). It ncludes a varety of decson makng technques lke; Analytc Herarchy Process (AHP) (Rath et al., 2015), VlseKrterumska Optmsaca I Kompromsno Resene (VIKOR) (Tong, Chen, & Wang, 2007), Technque for Order Preference by Smlarty to Ideal Soluton (TOPSIS) (Yong, 2006), Addtve Weghtng (AW) (Modarres & Sad-Nezhad, 2005), Weghted Product Method (WPM) (M. Wang, Lu, Wang, & La, 2010) and many more, and among these, VIKOR and TOPSIS are the outstandng approaches for decson makng n comple stuatons (Oprcovc & Tzeng, 2004). There are varous applcatons for the VIKOR and TOPSIS approaches as reported n lterature n varous sectors lke; materal selecton (Anokumar et al., 2015), supply chan, suppler selecton (Wu & Lu, 2011), health care sector (Zeng et al., 2013), renewable energy proect selecton (San Crstóbal, 2011), machne tool selecton (Önüt et al., 2008) and many more(dev, 2011; Önüt & Soner, 2008). Current study deals wth the selecton of rght S Sgma proect for mprovement to reduce down tme n Escorts Auto Products dvson of Escorts Group Inda. It nvolves the selecton of mprovement proect from s alternatves at selected ste. The purpose of ths paper s to eplot the capablty of VIKOR and TOPSIS approach to select rght S Sgma proect that wll mproves overall operatonal performance under fuzzy envronment usng modfed dgtal logc (MDL) weghts. 2. Evaluaton Crtera for S Sgma Proect Selecton The proect selecton problem wth havng a common factors and conflctng crtera can be well resolve by MADM methods, snce these methods are used for solvng paradocal plans wth dfferent selecton parameters (qualtatve and quantatve both). For a proper and most favourable selecton of S Sgma proect, the decson maker should need proper selecton crtera to be consdered. For ths seven crtcal parameters were recognzed at selected ste n Inda. The recognzed parameters are taken out from the vews of decson makers and ecavated from lterature based upon the requrements and prospects of the ndustry where the fnal S Sgma proect wll be eecuted (Ayağ & Özdemr, 2011; Nguyen et al., 2014). Alternatves should be assessed accordng to consdered crtera, and the decson maker s preference must be epressed by weghts to agreed crtera.

4 258 S.no Parameters Code descrpton 1 Down Tme Cost C 1 It s a man factor for nvestgatng crtcal reasons of breakdown. It ncludes the cost of breakdown, mantenance, repar and all actvtes necessary to meet all ts functonal requrements throughout the servce lfe. It becomes crtcal to estmate such costs. 2 Repar Tme C 2 It s the Porton of breakdown tme durng whch one or more eperts are workng on a system to affect a repar. Repar tme ncludes preparaton tme, fault detecton tme, fault correcton tme and fnal bnd up tme. 3 Relablty C 3 It s the prme factor for selectng crtcal reasons of breakdown n manufacturng unts. It defnes of how relable a system s. It shows the falure rate of each parameter responsble for breakdown n automotve manufacturng. Relablty s an attrbute of any that consstently performs accordng to ts specfcatons. 4 Reecton C 4 It s also a key factor for nvestgatng crtcal reasons of capacty wastage. It ncludes the wastage of capacty due to reecton (n-process or fnal) durng producton. 5 Productvty C 5 Productvty s a prme measure of the effcency of any producton system. Productvty s a crucal factor n measurng and estmatng producton performance of frms. 6 Workng Envronment C 6 Workng envronment go beyond ust energy effcency and attempt to rate an effort wth regard to the total envronmental stewardshp of a unt. It ncludes mnmum wastage, low energy consumpton and user frendly envronment. In ths regard workng envronment s sgnfcantly more encompassng than ust energy. A healthy workng envronment on shop floor mproves ts productvty. 7 Safety C 7 There are common hazards assocated wth the use of shop floor equpment and tools. Workng safely s the frst thng because the safe way s the correct way. The costs of accdents and ll health to engneerng shop floors may be dsproportonately hgh. Many employees are key workers whose losses through nury or ll health severely dsrupt producton and lowers productvty and proftablty. 3. Methods 3.1 Modfed Dgtal Logc All the selected parameters have ther dfferent effect for selecton of an approprate S Sgma proect whch s consdered as the optmum for the applcaton, therefore cannot be allocated equal weghtng. So t turns out to be essental to fnd out the prorty of each parameter as per the frm s resources. MDL s well recognzed method to compute the weghts of selecton crtera n such crcumstances. It s the amended verson of Dgtal logc method. It has varous ncredble advantages over dgtal logc (Dehghan-Manshad et al., 2007). It ncludes epert vews to allocate prmary prortes value as 1, 2 and 3 for less, equvalent and more sgnfcant parameters, respectvely. Further, MDL decson table was created wth par wse comparson based on the vews of decson makers. Before constructng the MDL table, t s necessary to work out the number of lkely postve decsons usng equaton N= n (n 1)/2, where n s the number of parameters. Further summaton of all postve decsons (P) for a parameter on normalzaton drects to fnal weght (W) as: W P n 1 P (1)

5 3.2 Fuzzy Logc R. Rath et al. / Decson Scence Letters 5 (2016) 259 Fuzzy Logc s manly a multvalue logc that allows ntermedary values to be defned between conventonal assessments lke true/false, good/bad, yes/no etc. Such values can be devsed mathematcally and processed by computers. Ths made an attempt to apply a more human thnkng n the programmng of computers. The mportance of fuzzy logc estmates from the fact that the maorty of approaches of human beng- reasonng are appromate n nature. Fuzzy approach was ntroduced to deal wth the problems where there are no clear lmts between the two parameters (Zadeh, 1965). Fuzzy approach was used for multple attrbute decson makng where the emphass s on possblty rather than probablty (Rbero, 1996). Fuzzy logc s based on a set theory. It comprses of a membershp functon wthn the nterval [0,1] whch epress the level of sgnfcance of an element for beng the member of the set (Bevlacqua, Carapca, & Gacchetta, 2006). A feature of fuzzy logc whch s of partcular mportance n epert systems s that t provdes a systematc structure for dealng wth fuzzy values, e.g., most, many, few, not very many, etc. In ths way, fuzzy logc ncludes both establshed logc and probablty theory, and makes t lkely to deal wth dssmlar vagueness wthn sngle conceptual framework.e. lngustc varables. These varables are used for all comparsons, whch has been assgned numercal values wthout any engma. A lngustc varable s a varable whose value are words or sentences n a natural or artfcal language (Zadeh, 1975). The man applcaton of the lngustc approach le n the realm of humanstc system especally n the felds of artfcal ntellgence, human decson processes, pattern recognton, lngustcs, psychology, economcs and related areas (Bellman & Zadeh, 1970). There are dfferent fuzzy numbers dependng on ther stuaton. Some of whch are trangular fuzzy numbers, trapezodal fuzzy numbers, ntersecton of two trangular fuzzy numbers etc (Mahdav-Amr & Nasser, 2007). In present study trapezodal fuzzy numbers were used ( b 1, b 2, b 3, b 4) for { b 1, b 2, b, b 3 4 R ; b 1 b 2 b 3 b 4 }as shown n fg 1. It s often convenent to work wth trapezodal fuzzy numbers because of ts smplcty and nformaton processng. The membershp functon µ b () of trapezodal fuzzy number s defned as; µ b () = b1, b1, b2 b2 b1 1, b2, b3 b4, b3, b4 b4 b3 0, otherwse (2) Fg. 1. Trapezodal fuzzy number

6 TOPSIS Technque for order preference by smlarty to an deal soluton (TOPSIS) method was presented by Hwang and Yoon n 1981 (Yoon & Hwang, 1995). TOPSIS uses dfferent weghtng schemes and dstance metrcs to compares results of dfferent sets of weghts appled to set of multple crtera data (Olson, 2004; Önüt & Soner, 2008). The basc prncple s that the chosen alternatve should have the shortest pathway from the deal soluton and the ecessve dstance from the negatve deal soluton. The deal soluton s a soluton that takes advantage of the beneft crtera and lessens the cost crtera, whereas the negatve deal soluton epands the cost crtera and mnmzes the beneft crtera. Beneft crtera s for mamzaton, whle the cost crtera s for mnmzaton. The best alternatve soluton s one, whch s closest to the deal soluton and farthest away from the negatve deal soluton (Wang & Elhag, 2006). 3.4 VIKOR VlseKrterumska Optmsaca I Kompromsno Resene (VIKOR) method was developed for mult attrbute decson makng of ntrcate systems, manly n crcumstances where the decson makers are not capable to set preferences (Oprcovc & Tzeng, 2004). VIKOR prortze alternatves and determnes the compromse soluton (feasble soluton), whch s the nearest to the deal, and a compromse soluton means a concord set up by mutual compromses (Chen & Hwang, 1992). For any problem, a feasble soluton wth contradctory crtera can help the decson makers to make an ultmate decson. Ths method uses lnear normalzaton to elmnate the unts of crteron functon. Ths method provdes robust prortzaton because t actvely reflects the vews of numerous collectons and reflects vagueness n the nput data. 4. Applcaton of proposed Methodology Ths secton eplans the steps nvolved n the subectve fuzzy VIKOR and fuzzy TOPSIS approach for rght S Sgma proect selecton n an automotve ndustry. The approach utlzes MDL weghts for par wse comparson among all consdered crtera followed by fuzzy logc approach wth VIKOR and TOPSIS methods to obtan best alternatves. It ncludes followng steps: Step 1: calculaton of MDL weghts. As dscussed n secton 3.1, MDL weghts (W) are calculated for all proect selecton parameters. Ths gves the weghts of dfferent crtera. Step 2: Descrbe lngustc varables, approprate membershp functon and equvalent fuzzy numbers. A set of fuzzy rates s requred n order to compare all the alternatves for each crteron. These fuzzy terms are assgned by the decson makers and responsble for ntra crteron comparsons of the alternatves. Step 3: Constructon of decson matr. Let p be the parameters and q be the alternatves. For k number of decson makers n the proected model for the aggregated fuzzy ratng for C crteron s represented as k = { k1, k2, k3, k4}.for =1, 2,...p; =1, 2.q; k =1, 2.k, k s calculated as (Shemshad et al., 2011), mn b k 1 b k 1 b k ma b k k1 k 2 k 3 k 4 (3)

7 Thus the obtaned decson matr (M) s shown as: M q q2 1 p 2 p qp R. Rath et al. / Decson Scence Letters 5 (2016) 261 Step 4: Normalzaton The frst essental requrement of any comparson s that all quanttes beng contrasted should be on the same scale. Therefore, aggregated fuzzy ratng was normalzed n ths step. Mathematcally, normalzaton was carred out usng the followng Equatons:,,, , , 2 2, 3 3, 4 4, J J (4) (5) where ma( ), J; mn( ), J where J corresponds to hgher desred value and J corresponds to lower desred value. Step 5: Defuzzfcaton Defuzzfcaton s a method of convertng fuzzy output to crsp value (enumerated result) n fuzzy logc by real valued functons. It s performed to obtan the crsp values for each crteron correspondng to each alternatve. The nput for the procedure s the cumulatve set and the output s a sngle number. Ths provdes a quanttatve value for the lngustc varables and fuzzy numbers assgned based on the verbal reasonng of the decson makers. Followng equaton lead to the crsp values: f = Defuzz() =. d ( ). d ( 1)/( 2 1) ( 4 )/( 4 3). /( ). d d ( )/( ). d d d d (6) = (1/ 3)( 4 3) (1/ 3)( 2 1) The crsp values, thus obtaned are ntegrated wth MDL weghts to calculate fnal rankng usng VIKOR and TOPSIS approach as dscussed below.

8 262 VIKOR Approach Steps Step 6: Determnaton of deal and negatve deal solutons; The deal soluton f * and negatve deal soluton f are determned as f * = {ma f } (7) f - = {mn f } (8) Step 7: Calculaton of utlty and regret measures S R n W 1 Ma W * f f (9) ; * f f * f f (10) ; * f f where S and R represent the utlty and regret measures, respectvely and W s the relatve weght assgned to the Jth parameter usng MDL. Step 8: Calculaton of VIKOR nde S S * * S R R (11) 1 * * S R R Q = v v ; where Q represents th alternatves VIKOR value, v s the group utlty weght, t s generally consdered as 0.5(unsupervsed) and; S * = mn (S); (12) S =ma (S); (13) R * = mn (R); (14) R =ma (R); (15) S Sgma Proect wth least value of VIKOR nde Q s preferred. TOPSIS Approach Steps Step 5: Normalzed the matr as gven below: r m 1 f f 2 ; (16) Step 6: Calculate the weghted normalzed decson matr as gven: V r W dagonal (17) mn nm

9 Step 7: Calculate the postve deal and negatve deal soluton: The postve deal soluton V V R. Rath et al. / Decson Scence Letters 5 (2016) 263 V and negatve deal soluton V are as gven below: V, J, mnv, J, 1,2,3... m; ma 2 1 (18) V, J, mav, J, 1,2,3... m; mn 2 1 (19) where J1 and J2 represents hgher best and lower best crtera respectvely. Step 8: Calculate the dstance respectvely d and d from the postve deal soluton and negatve deal soluton 0.5 n d, V V, 1,2,3 m 0.5 n d, V V, 1,2,3 m (20) (21) Step 9: Calculaton of TOPSIS rank nde: C d d d (22) S Sgma Proect wth hghest rank nde 5. Results and Dscusson C are preferred. Proect selecton decson n S Sgma methodology s a very challengng assgnment. The proect selecton n early phase of S Sgma requred hgh profcency n decson makng to select proper proect from all gven alternatves. In ths study, n branstormng sessons wth decson makers lke producton manager, supervsors, machne operators and fnancal eperts etc; t s concluded that selecton of the optmal S Sgma proect from the accepted s mportant proects (alternatves) for mprovement depends on seven selecton crtera (parameters) as dscussed n Secton 2, whch carred a sgnfcant mpact on selecton of alternatves. It has been closely observed that mpact of these parameters dffer from shop floor of ndustry to ndustry. As these parameters are dentfed, the net step s to prortze these parameters, as to whch of these have more mpact on the dentfed alternatves. MDL approach was used to prortze these parameters and n order to compare these dstnct parameters, numerc prorty values are assgned to the parameters on a scale of 1-3 and a set of par wse matr was made to carry out comparson. Table 1 Subectve weghts of the evaluaton crtera calculated usng MDL Parameters C 1 C 2 C 3 C 4 C 5 C 6 C 7 Postve Decson Weghts Rank Down Tme Cost(C 1) Repar Tme(C 2) Relablty(C 3) Reecton(C 4) Productvty(C 5) Workng Envronment(C 6) Safety(C 7)

10 264 Table 1 summarzes the relatve decson matr formed on the bass of par-wse comparson and the weghts are calculated for consdered crtera. Relablty comes out as the leadng S Sgma proect selecton parameter; whle workng envronment was found to be the least domnant parameter for selecton. Bar chart shows the contrbuton of all mportant parameters towards the selecton of proper S Sgma proect as demonstrated n Fg. 2. The herarchcal structure for the selecton of proper proect s shown n Fg. 3. Level 1 specfes our target on selecton of the proper S Sgma proect that has to be selected from the dentfed s mportant proects (alternatves) for mprovement specfes n level 2. Level 3 specfes that the proect selecton alternatves are entrely nterdependent on crtcal selecton parameters; ths shows the ntrcacy of the problem. Furthermore, ths s a tme consumng practce and consderable knowledge of both technologcal as well as economc aspects s needed n ths case Workng Envronment Safety Down Tme cost Repar Tme Relablty Reecton Productvty Fg. 2. Contrbuton of all mportant parameters towards the selecton of proper S Sgma proect Fg. 3. Schematc herarchcal structure for the selecton of proper S Sgma proect

11 R. Rath et al. / Decson Scence Letters 5 (2016) 265 Further net, comparson of all alternatves wth each parameter was carred out based on fuzzy logc approach. Lngustc varables were used for the selecton of proper S Sgma proect, these varables further converted nto correspondng fuzzy numbers. Table 2 presents the converson of lngustc varables nto fuzzy numbers for ths problem. The hghest range of lngustc varable s termed etremely hgh (EH) and the least s termed as etremely low (EL). Table 2 Lngustc varables and correspondng fuzzy numbers Lngustc Varable Fuzzy number Etremely Hgh (EH) (0.8, 0.9, 1.0, 1.0) Very hgh (VH) (0.7, 0.8, 0.8, 0.9) Hgh (H) (0.5, 0.6, 0.7, 0.8) Above average (AA) (0.4, 0.5, 0.5, 0.6) Average (A) (0.2, 0.3, 0.4, 0.5) Very low (VL) (0.1, 0.2, 0.2, 0.3) Etremely low (EL) (0.0, 0.0, 0.1, 0.2) Table 3 Lngustc decson matr of proper S Sgma proect selecton for all evaluaton crtera Producton Shops Evaluaton Crtera (Parameters) (Alternatves) C 1 C 2 C 3 C 4 C 5 C 6 C 7 Metal Fnshng Shop(S 1) H H VL H VL A A Sho. Machne Shop(S 2) EH VH VL EH VL VL EL Sho. Assembly Shop(S 3) H H A AA A AA H TFF Assembly Shop(S 4) A A AA VL H H H TFF Grndng Shop(S 5) VL A VH AA VH VH VH HCP Shop(S 6) H A VL H A VL A A Lngustc decson matr of specfed alternatves was constructed for all evaluaton crtera durng branstormng sesson wth decson makers as shown n table 3. For ths problem a sngle decson matr has been created rather than havng a dfferent decson matr for each decson maker (as per dscusson wth decson makers). Further, Fuzzy values thus obtaned are fnally transformed nto crsp values usng equaton 6. Crsp values thus obtaned from aggregated fuzzy ratngs are shown n table 4. Further net, estmated crsp values were analyzed wth VIKOR approach, usng equaton 7 to 15 and crsp values were further analyzed wth TOPSIS approach usng equaton 16 to 22 to fnd out the rank ndces of all alternatves. Table 4 Calculated crsp values for assgned fuzzy numbers Producton Shops Evaluaton Crtera (Parameters) (Alternatves) C 1 C 2 C 3 C 4 C 5 C 6 C 7 S S S S S S

12 266 Table 5 Calculated VIKOR and TOPSIS rankng Producton Shops (Alternatves) VIKOR Inde VIKOR Rank TOPSIS Inde TOPSIS rank Metal Fnshng Shop(S 1) Sho. Machne Shop(S 2) Sho. Assembly Shop(S 3 ) TFF Assembly Shop(S 4) TFF Grndng Shop(S 5) HCP Shop(S 6) Table 5 dsplays subsequent rank ndces and ranks for all S Sgma proects (alternatves). The rankng of alternatves obtaned by VIKOR and TOPSIS approach are appromately same. Ths shows the robustness of the obtaned results. Current study shows that the compromse soluton, closest to the deal s obtaned as Sho machne shop (S 2) as t s VIKOR and TOPSIS rank s hghest among all selected alternatves. Therefore ths shop has been selected as key prorty proect for further mprovement usng S Sgma strategy. In current study producton managers are gven a decson makng tool to determne the approprate S Sgma proect at an early decson phase. Furthermore, the qualty status of the selected ndustry has been etensvely mproved through eecuton of the S Sgma proect. 6. Conclusons S Sgma Proects of an automotve manufacturng unt are prortzed n present study. MADM methods are used for selecton of proper S Sgma proect n Indan automotve ndustry. In ths regard, s proects (alternatves) of the partcular unt are ranked on the bass of selecton crtera. Modfed dgtal logc (MDL) method s used to calculate weghts of all nfluencng parameters for evaluaton of proper S Sgma proects n an automotve ndustry. Relablty and workng envronment have been found to be most and least crtcal parameters, respectvely. Further, the prorty order of S Sgma proects s determned usng fuzzy VIKOR and fuzzy TOPSIS approach ntegraton wth MDL weghts. Sho machne shop was found to be the most favourable S Sgma Proect for mprovement at selected ste. The results of the applcaton reveal that the proposed approach can effcently be used n practce for proper S Sgma proect selecton problem. Present study valdates the effcacy of fuzzy logc wth VIKOR and TOPSIS approaches for proper S Sgma proect selecton n Indan automotve ndustry. References Agalgaonkar, A., Kulkarn, S., & Khaparde, S. (2005). Mult-attrbute decson makng approach for strategc plannng of DGs. Paper presented at the Power Engneerng Socety General Meetng, IEEE. Anokumar, L., Ilangkumaran, M., & Vgnesh, M. (2015). A decson makng methodology for materal selecton n sugar ndustry usng hybrd MCDM technques. Internatonal Journal of Materals and Product Technology, 51(2), Antony, J. (2006). S sgma for servce processes. Busness Process Management Journal, 12(2), Ayağ, Z., & Özdemr, R. G. (2011). An ntellgent approach to machne tool selecton through fuzzy analytc network process. Journal of Intellgent Manufacturng, 22(2), Banuelas Coronado, R., & Antony, J. (2002). Crtcal success factors for the successful mplementaton of s sgma proects n organsatons. The TQM magazne, 14(2), Banuelas, R., Tennant, C., Tuersley, I., & Tang, S. (2006). Selecton of S Sgma proects n the UK. The TQM Magazne, 18(5),

13 R. Rath et al. / Decson Scence Letters 5 (2016) 267 Bellman, R. E., & Zadeh, L. A. (1970). Decson-makng n a fuzzy envronment. Management scence, 17(4), B-141-B-164. Bevlacqua, M., Carapca, F., & Gacchetta, G. (2006). A fuzzy-qfd approach to suppler selecton. Journal of Purchasng and Supply Management, 12(1), Chakrabarty, A., & Chuan Tan, K. (2007). The current state of s sgma applcaton n servces. Managng Servce Qualty: An Internatonal Journal, 17(2), Chen, S.-J., & Hwang, C.-L. (1992). Fuzzy multple attrbute decson makng methods: Sprnger. De Boer, L., Labro, E., & Morlacch, P. (2001). A revew of methods supportng suppler selecton. European Journal of Purchasng & Supply Management, 7(2), Dehghan-Manshad, B., Mahmud, H., Abedan, A., & Mahmud, R. (2007). A novel method for materals selecton n mechancal desgn: combnaton of non-lnear normalzaton and a modfed dgtal logc method. Materals & desgn, 28(1), Dev, K. (2011). Etenson of VIKOR method n ntutonstc fuzzy envronment for robot selecton. Epert Systems wth Applcatons, 38(11), Fundn, A., & Cronemyr, P. (2003). Use customer feedback to choose S Sgma proects. Go, E., & Scara, J. (2014). Process mprovement through S Sgma wth Beta correcton: a case study of manufacturng company. The Internatonal Journal of Advanced Manufacturng Technology, 71(1-4), Goh, T. N. (2002). A strategc assessment of S Sgma. Qualty and Relablty Engneerng Internatonal, 18(5), Gwo-Hshung, T. (2010). Multple attrbute decson makng: methods and applcatons. Multple Attrbute Decson Makng: Methods and Applcatons. Hensley, R. L., & Dobe, K. (2005). Assessng readness for s sgma n a servce settng. Managng Servce Qualty: An Internatonal Journal, 15(1), Johannsen, F., Lest, S., & Zellner, G. (2011). S sgma as a busness process management method n servces: analyss of the key applcaton problems. Informaton Systems and E-Busness Management, 9(3), Lnderman, K., Schroeder, R. G., Zaheer, S., & Choo, A. S. (2003). S Sgma: a goal-theoretc perspectve. Journal of Operatons management, 21(2), Mahdav-Amr, N., & Nasser, S. (2007). Dualty results and a dual smple method for lnear programmng problems wth trapezodal fuzzy varables. Fuzzy sets and systems, 158(17), Modarres, M., & Sad-Nezhad, S. (2005). Fuzzy smple addtve weghtng method by preference rato. Intellgent Automaton & Soft Computng, 11(4), Nguyen, H.-T., Dawal, S. Z. M., Nukman, Y., & Aoyama, H. (2014). A hybrd approach for fuzzy mult-attrbute decson makng n machne tool selecton wth consderaton of the nteractons of attrbutes. Epert Systems wth Applcatons, 41(6), Olson, D. L. (2004). Comparson of weghts n TOPSIS models. Mathematcal and Computer Modellng, 40(7 8), do: Önüt, S., Soner Kara, S., & Efendgl, T. (2008). A hybrd fuzzy MCDM approach to machne tool selecton. Journal of Intellgent Manufacturng, 19(4), Önüt, S., & Soner, S. (2008). Transshpment ste selecton usng the AHP and TOPSIS approaches under fuzzy envronment. Waste Management, 28(9), Oprcovc, S., & Tzeng, G.-H. (2004). Compromse soluton by MCDM methods: A comparatve analyss of VIKOR and TOPSIS. European Journal of Operatonal Research, 156(2), Rath, R., Khandua, D., & Sharma, S. (2015). Synergy of fuzzy AHP and S Sgma for capacty waste management n Indan automotve ndustry. Decson Scence Letters, 4(3), Rbero, R. A. (1996). Fuzzy multple attrbute decson makng: a revew and new preference elctaton technques. Fuzzy sets and systems, 78(2), San Crstóbal, J. (2011). Mult-crtera decson-makng n the selecton of a renewable energy proect n span: The Vkor method. Renewable energy, 36(2),

14 268 Shemshad, A., Shraz, H., Toreh, M., & Tarokh, M. J. (2011). A fuzzy VIKOR method for suppler selecton based on entropy measure for obectve weghtng. Epert Systems wth Applcatons, 38(10), Snee, R. D. (2004). S Sgma: the evoluton of 100 years of busness mprovement methodology. Internatonal Journal of S Sgma and Compettve Advantage, 1(1), Snee, R. D., & Hoerl, R. W. (2003). Leadng S Sgma: a step-by-step gude based on eperence wth GE and other S Sgma companes: Ft Press. Su, C.-T., & Chou, C.-J. (2008). A systematc methodology for the creaton of S Sgma proects: A case study of semconductor foundry. Epert Systems wth Applcatons, 34(4), Tang, L. C., Goh, T. N., Lam, S. W., & Zhang, C. W. (2007). Fortfcaton of S Sgma: epandng the DMAIC toolset. Qualty and Relablty Engneerng Internatonal, 23(1), Tong, L.-I., Chen, C.-C., & Wang, C.-H. (2007). Optmzaton of mult-response processes usng the VIKOR method. The Internatonal Journal of Advanced Manufacturng Technology, 31(11-12), Trechler, D., CARMICHAEL, B., Kusmanoff, A., Lews, J., & Berthez, G. (2002). Desgn for S Sgma: 15 lessons learned. Qualty Progress, 35(1), Vats, G., & Vash, R. (2013). Pezoelectrc materal selecton for transducers under fuzzy envronment. Journal of Advanced Ceramcs, 2(2), Wang, M., Lu, S., Wang, S., & La, K. K. (2010). A weghted product method for bddng strateges n mult-attrbute auctons. Journal of Systems Scence and Complety, 23(1), Wang, Y.-M., & Elhag, T. M. S. (2006). Fuzzy TOPSIS method based on alpha level sets wth an applcaton to brdge rsk assessment. Epert Systems wth Applcatons, 31(2), do: Wu, M., & Lu, Z. (2011). The suppler selecton applcaton based on two methods: VIKOR algorthm wth entropy method and Fuzzy TOPSIS wth vague sets method. Internatonal Journal of Management Scence and Engneerng Management, 6(2), Yong, D. (2006). Plant locaton selecton based on fuzzy TOPSIS. The Internatonal Journal of Advanced Manufacturng Technology, 28(7-8), Yoon, K. P., & Hwang, C.-L. (1995). Multple attrbute decson makng: an ntroducton (Vol. 104): Sage Publcatons. Zadeh, L. A. (1965). Fuzzy sets. Informaton and control, 8(3), Zadeh, L. A. (1975). The concept of a lngustc varable and ts applcaton to appromate reasonng I. Informaton scences, 8(3), Zeng, Q.-L., L, D.-D., & Yang, Y.-B. (2013). VIKOR method wth enhanced accuracy for multple crtera decson makng n healthcare management. Journal of medcal systems, 37(2), 1-9. Zhang, D., Zhang, J., La, K.-K., & Lu, Y. (2009). An novel approach to suppler selecton based on vague sets group decson. Epert Systems wth Applcatons, 36(5),