Decision making about selection and grading of suppliers by using fuzzy Topsis (case study: Havasan company)

Transcription

1 Interntonl Reserch Journl of Apple n Bsc Scences 03 Avlble onlne t.rbs.com ISSN 5-838X / Vol 4 (9): Scence Explorer Publctons Decson mng bout selecton n grng of supplers by usng fuzzy Topss (cse stuy: Hvsn compny) Soleymn Irnzeh Al Abr Hzeh Kml Khllpour 3. Scentfc Bor Member n Assocte Islmc Az Unversty Mhb Brnch Deprtment of Mngement Mhb Irn. MSc Stuent of Inustrl Mngement Islmc Az Unversty Mhb Brnch Deprtment of Mngement Mhb Irn 3. Scentfc Bor Member n Assstnt Islmc Az Unversty Mhb Brnch Deprtment of Mthemtcs Mhb Irn Corresponng uthor eml: hze@yhoo.com ABSTRACT: Supply chn hs gne ttenton of mny reserchers. In toy compettve orl supplers not only try to mprove omestc contons but lso choose the best mrets n supplers (ccorng to globlzton phenomenon). The ssue of evluton s mportnt n supply chn. In orer to ncrese customer stsfcton n reuce costs orgnztons shoul conser supply chn from provng prmry cru mterls to fnl consumer. Selecton of the best optons n bove ecson mng proceure requres the nlyss of mny crter hch orgnztons encounter th mult crter ecson mng proceure. In ths reserch fuzzy mult crter ecson mng proceure hs been pple.the sttstcl populton nvolves ll supplers of tems n prts of Hvsn Compny. In ths reserch frstly the mportnt crter n evluton of tems supplers ere collecte by questonnre n the mn crter ere chose n ther mportnce gre s specfe by other questonnre; consequently the supplers ere gre n ten groups by usng Fuzzy Topss. In ths reserch the nlyss n grng of group A s one of the stue compny supplers hve been propose. Keyors: Decson mng Fuzzy theory Fuzzy Topss Supply chn INTRODUCTION In the pst commercl ssues ere consere mng to ncrese the benefts; but toy ths nex coul not be the only y to solve the problems. The rt of toy ecson mers s to use mult obectve problems such s ecresng the costs n ncresng the qulty of servce. Such problems re more complex thn the erler ones. The mentone gols shoul be compre n gre th fferent nces. It cn be refer to selecton of the best supplers s mult crter ecson mng ssue. Snce 990 supply chn mngement n process of selecton of supplers hve been consere sgnfcntly n purchse mngement. Most of fctores see supplers th hgh mngement effcency n competton poer. Purchse s the mn ctvty n supply chn. Toy concurrent to promoton n purchse methos ecson mng n selecton of the best suppler hve been complcte. Customer stsfcton meetng customers nees n prortes requre the rp n pproprte selecton of supplers. It cn be refer to fuzzy Topss metho s the best metho of selecton of supplers. In most cses humn thnng s uncertn n ths uncertnty ffects the ecson mng ssues. In such contons the fuzzy Topss ecson mng pproch s choose s the best metho. MATERIALS AND METHODS Decson mng Precton evluton n comprson of the current soluton results n selecton of soluton for chevng n optml gol s clle ecson mng. Decson mng s ugment n selecton beteen to or mny thngs or soluton tht everyboy oes t n hs lfe n or plce n socety th ny poston n responsblty n t

2 Intl. Res. J. Appl. Bsc. Sc. Vol. 4 (9) cn be mportnt. Decson mng s sgn of groth n mturty n responsblty tng (Moenyn n Age 0). Crter of ecson mng All bses ssurng gol n formng ts consttuents bloc consere by ecson mer n orer to ncrese the optmlty n stsfcton re clle crteron. Crter re scle for gol n ts mesurng tool. In other hns crter re stnrs n rules use for ugment n ncte the level of effectveness. More coverge of gols by crter les to hgh probblty of chevng gol (Atte 00). Mult crter ecson mng In toy orl complexty of most of ecson mng envronments necessttes conserton of comprehensve spects n employment of nvuls th fferent slls experences recors n scentfc veponts. All of these cses entfy the necessty of pplcton of tem n mult crter ecson mng methos. In some cses t s probble tht crter re n contrst together n ncrese of one fctor reuces nother fctor; so t s necessry to fn n opton tht offers more benefts. In generl mult crter ecson mng methos re ve nto to ctegores: -Multpurpose ecson mng moels -Mult nces ecson mng moels Evluton moels for mult nces ecson mng Irreprble moels Compenstory moels Domnton moel Sclng sub group Copng subgroup Coornton subgroup Lexcogrphc Omsson metho SAW Topss Lner llocton Mxm n Smple n recprocl ntercton MRS ELECTRE Specl stsfctory Collectve stsfctory Clssfe eghte set LINMAP MDS Permutton metho Fgure. Mult nces ecson mng ccorng to compenstory n rreprble clssfcton

3 Intl. Res. J. Appl. Bsc. Sc. Vol. 4 (9) Multpurpose ecson mng moels In these moels severl gols re consere concurrent for optmzton. The best seprton of multpurpose ecson mng s progrmmng of n el problem tht Chrnes n Cooper offere for the frst tme. Its mthemtcl moel s s follos: :{f (x)f (x)...f (x)} Optmze n S. t. G ( x ) 0... m Mult nces ecson mng moels In these moels n opton s selecte mong severl optons. In generl efnton t nvolves evluton prortzton n selecton mong present optons (Azr n Rbzeh 00). Iel Smlr opton metho (TOPSIS) In efnton of ths metho el soluton n el smlr soluton re use. Iel soluton s the best soluton n t s tre to pproch to el opton. In orer to mesure smlr to el soluton of n opton the stnce from el n non el soluton s mesure n then the optons re clssfe bse on the rto of stnce from non el soluton to stnce from el soluton (Att 00). B-vlue logc In most of the scences le mthemtcs n logc t s ssume tht there re efne bounres n confnements n prtculr subect oes not plce n ths confnement. Cses le ll or noboy lve n e mn or omen blc or hte 0 or re such phrses. In ths scence every sttement s correct or ncorrect; the rel phenomen re hte or blc. Everythng s ve nto yes or no ctegores n there s no meum sttement. In ths phlosophy t cn not be completely truthful or lr beng young n ol n everythng hs efne bounry. Mult vlue logc In orer to vo from b-vlue logc the mult vlue logc s offere by Lusecz (930). In ths logc the sttements re vlue ccorng to n. So n ths logc the reltes re shon better thn Arstotle logc. Thus n vlue logc s propose tht every sttement coul hve ny vlue of {0 /n /n }. It s obvous tht f n s selecte s bg number etermnton sttement s ner to relty (Atte 0). Fuzzy mult crter ecson mng In clssc mult crter ecson mng metho t s tre to mesure the effect of fferent fctors on ecson mng. But most of the fctors re not possble th clssc mthemtc logc. In other hn there s uncertnty n rel orl; so n most cses there s problem n fferent steps. Thus some prt of mult crter ecson mng problem s fuzzy. In such contons f problem s formulte by certn t the response s not ccurte. So n moels th rnom n fuzzy t the clculton shoul be one n logc y n uncertnty be consere. Moelng of uncertnty n ecson mng problems s one th fuzzy set theores. Lmtton n clssc methos hs le to proposton of fuzzy mult crter ecson mng methos. Fuzzy smlr el opton metho (FTOPSIS) In the clssc fuzzy smlr to el opton metho the efne vlues re use for etermnton of crter n grng of optons. In most cses humn thnng s ccompne by uncertnty n t ffects on ecson mng. In ths cse t s better to use fuzzy ecson mng metho. Fuzzy smlr el opton metho s the best opton tht mtrx n eghts re evlute bse on vrbles offere by fuzzy numbers; so the problems of clssc metho re resolve.

4 Intl. Res. J. Appl. Bsc. Sc. Vol. 4 (9) Steps of Fuzzy smlr el opton metho Step -Formng ecson mtrx If trngulr fuzzy numbers re use ( b c ) ( n). If trpezo numbers re use ) x~ s effcency of tht ( m) s relte to ~ x ( b c s effcency of ( m) n ( n). If ~ x ( b c ecson mer commttee hs member n fuzzy grng of th ecson mer s one ) (trngulr fuzzy numbers) for... n... m. Accorng to combntory fuzzy grng crter x~ (bc ) the optons re obtne bse on follong reltons: Mn { } () b b () c Mx {c } (3) If ecson mer commttee hs member n fuzzy grng of th ecson mer s one ( ~ x ( b c )) (trpezo fuzzy numbers) s for x~ ( b c )...n... m the optons re obtne bse on follong reltons: Mn { } (4) b b (5) c c (6) Mx { } (7) ~ x ~ x ~... x n ~ x ~ x ~ ~... xn D... ~ x ~ m x ~ m... xmn. Accorng to combntory fuzzy grng crter Step -Determnton of crter eghts In ths step the mportnce coeffcent of fferent crter re etermne s follos: ~ [ ~ ~... ~ n ] If trngulr fuzzy numbers re use ech component of ll be efne s ~ ( 3) n f trpezo fuzzy numbers re use ech component of ll be efne s ~ ( 3 4). If ecson mer commttee contn member n the th coeffcent of ecson mer ~ ( 3 ) s for n combntory fuzzy grng ~ ( 3) cn be obtne s follos: Mn { } (8)

5 Intl. Res. J. Appl. Bsc. Sc. Vol. 4 (9) (9) 3 Mx {c 3 } (0) If ecson mer commttee contn member n the th coeffcent of ecson mer ~ ( 3 ) s for n combntory fuzzy grng ~ ( 3) cn be obtne s follos: Mn { } () () 3 3 (3) 4 Mx {c 4 } (4) Step 3-Scle up fuzzy ecson mtrx In orer to scle up n ths step lner converson of scle s use for converson of fferent crter nto comprble scle. If fuzzy numbers re trngulr scle up ecson mtrx rrys re clculte for negtve n postve crter from follong reltons: b c (5) c c c (6) c b here n these reltons: c mx c (7) mn (8) If fuzzy numbers re trpezo scle up ecson mtrx rrys re clculte for negtve n postve crter from follong reltons: ~ b c (9) r (0) c b here n these reltons: mx () mn () Thus scle up fuzzy ecson mtrx (R) s s follos: R ~ [ ]... m ;... n (3) mx

6 Intl. Res. J. Appl. Bsc. Sc. Vol. 4 (9) Or R ~ m m m s number of optons n n s number of crter. n n mn Step 4-Determnton of eghte fuzzy ecson mtrx Accorng to fferent crter eghts eghte fuzzy ecson mtrx s obtne from multplcton of mportnce coeffcent of ech crteron n fuzzy scle up mtrx s follos:. ~ (4) here ~ s mportnce coeffcent of C. So ecson mtrx s s follos: [v ~ ] mx...my...n (5) n Or n m m mn If fuzzy numbers re s trngulr so for crter th postve n negtve spects e hve: b c ( ) b c. ~ c c c c c c ~ ( ) r. ~ c b c b If fuzzy numbers re s trpezo so for crter th postve n negtve spects e hve: ~ ~ b c b c r ( ) ~ r. ~ c b. ( ) Step 5-Fnng fuzzy el soluton (FPISA) n fuzzy nt el soluton (FNIS A-) Fuzzy el soluton (FPIS A) n fuzzy non el soluton (FNISA-) re efne s follos: A {... n } (6) A { ~... v n } (7) here s the best vlue mong ll optons n s the orst vlue mong ll optons. Mx... m... (8) { 3 } n { }... m... n Mn (9) Optons n A n A- ncte the best n the orst optons. Step 6-Clculton of stnce from fuzzy el n non el Dstnce from fuzzy el n non el s clculte from follong reltons: 4 c b 3 4

7 Intl. Res. J. Appl. Bsc. Sc. Vol. 4 (9) S ( )... m (30) S n n ( )... m here s stnce beteen to fuzzy numbers. If ( bc) n ( bc) re trngulr fuzzy numbers the stnce of to numbers equls to: v ( M ~ M ~ ) [( ) + (b b ) + (c c ) ] (3) 3 Also f ( bc) n ( bc) re trpezo fuzzy numbers the stnce of to numbers equls to: v ( M ~ M ~ ) [( ) + (b b ) + (c c ) + ( ) ] (33) 4 Step 7-Clculton of smlrty nex S CC... m (34) S + S Step 8-Grng of optons In ths step the optons re gre ccorng to level of smlrty of nex so tht optons th hgh smlrty nex hve hgher perorty (Atte 0). Supply chn Supply chn nvolves ll ctvtes relte to proucton n converson from supplyng r mterls to elverng to fnl consumer n lso nformton trnsfer relte to these ctvtes. In generl supply chn s chn contns ll ctvtes relte to proucts from preprng of prmry mterls to elverng to the fnl consumer (Gozt 008). Supply chn mngement Supply chn mngement s conucton of ctvtes of supply chn n relte nformton by mprovement of supply chn reltons for chevng relble n controllble compettve vntge. So t s process of ntegrton of ctvtes of supply chn n relte nformton by mprovement of supply chn reltons n coornton of ctvtes n supply chn proucton n elvery. The offere efnton nvolves subects of nformton system rrngement scheulng of proucton clssfcton of orers control of nventory rehousng n customer servces (Gozt 008). Supply chn ecson mngs Supply chn mngement ecson mngs re clssfe nto to groups of strtegc n opertonl ones. Strtegc ecson mngs re long term n they re relte to compny n rect supply chn polces. In other hn opertonl ecson mngs re short term n emphsze on ctvsts. There re fve ecson mng bounres: - loclzton - Proucton 3- Inventory 4- (Trnsportton) Dstrbuton 5- Informton (Gzvt 008) Questons The questons re s follos: - Wht supplers hve hgh scores ccorng to fuzzy Topss moel? - Does fuzzy Topss metho evlute n select supplers ccorng to evlutons n grng of Hvsn compny experts n the pst yers? RESULTS AND DISCUSSION (3) In ths secton the results of group A s one of the stue compny groups re nlyze:

8 Intl. Res. J. Appl. Bsc. Sc. Vol. 4 (9) Investgton on supplers by help of experts Rtngs supplers by experts for fferent crter s lste n Tble (). Tble. Rtngs supplers by experts ccorng to crter Y6 Y5 Y4 Y3 Y Y X3 X X X3 X X X3 X X X3 X X X3 X X X3 X X G G G G G B M G VG G G G G VG VG G G M A G G G G G M VG M G G G M G VG G M M M A G G G VG G G G M G M M M VG G M M M M A3 G G G G G B G G VG VG VG M G M M B M M A4 M VG G G G M G M G VG G M VG M G M M M A5 Y Y Y0 Y9 Y8 Y7 X3 X X X3 X X X3 X X X3 X X X3 X X X3 X X G G M VG VG G G G M M G G VG VG B G G M A VG G G VG M G G G M M G G VG VG M VG M M A G G M G G M VG G G B M M G VG B G M G A3 G G M VG G M G M G M M M VG VG M G G VG A4 M VG G G G M G M M M M M G M VB G M VG A5 - Converson of the bove tble from qulttve s fuzzy Expert opnon bse on fuzzy numbers re efne n Tble (). Tble. Certfe nvuls from qulttve s fuzzy A A A3 A4 A5 X ( ) ( ) ( ) ( ) ( ) Y X ( ) ( ) ( ) ( ) ( ) X3 ( ) ( ) ( ) ( 3 5 ) ( ) X ( ) ( ) ( ) ( ) ( ) Y X ( ) ( ) ( ) ( ) ( ) X3 ( ) ( ) ( ) ( ) ( ) X ( ) ( ) ( ) ( ) ( ) Y3 X ( ) ( ) ( ) ( ) ( ) X3 ( ) ( ) ( ) ( ) ( ) X ( ) ( ) ( ) ( ) ( ) Y4 X ( ) ( ) ( ) ( ) ( ) X3 ( ) ( ) ( ) ( ) ( ) X ( 3 5 ) ( ) ( ) ( 3 5 ) ( ) Y5 X ( ) ( ) ( ) ( ) ( ) X3 ( ) ( ) ( ) ( ) ( ) X ( ) ( ) ( ) ( ) ( ) Y6 X ( ) ( ) ( ) ( ) ( ) X3 ( ) ( ) ( ) ( ) ( ) X ( ) ( ) ( ) ( ) ( ) Y7 X ( ) ( ) ( ) ( ) ( ) X3 ( ) ( ) ( ) ( ) ( ) X ( 3 5 ) ( ) ( 3 5 ) ( ) ( 3 ) Y8 X ( ) ( ) ( ) ( ) ( ) X3 ( ) ( ) ( ) ( ) ( ) X ( ) ( ) ( ) ( ) ( ) Y9 X ( ) ( ) ( ) ( ) ( ) X3 ( ) ( ) ( 3 5 ) ( ) ( ) X ( ) ( ) ( ) ( ) ( ) Y0 X ( ) ( ) ( ) ( ) ( ) X3 ( ) ( ) ( ) ( ) ( ) X ( ) ( ) ( ) ( ) ( ) Y X ( ) ( ) ( ) ( ) ( ) X3 ( ) ( ) ( ) ( ) ( ) X ( ) ( ) ( ) ( ) ( ) Y X ( ) ( ) ( ) ( ) ( ) X3 ( ) ( ) ( ) ( ) ( ) 3- Anlyss of t s fuzzy Topss metho:

9 Intl. Res. J. Appl. Bsc. Sc. Vol. 4 (9) Step -- Formng ecson mtrx The ecson mtrx s presente n Tble (3). As cn be seen n the reltve mportnce of ech crteron of lterntves n eghts of crter usng fuzzy numbers trngulr specfe. Crter Tble 3. Weghte ecson mtrx Fuzzy eghts Items W A5 A4 A3 A A Y ( ) (753) (74.33) (753) (753) (96.333) Y ( ) (973) (95.673) (973) (97.675) (98.335) Y3 ( ) (973) (97.673) (753) (96.333) (975) Y4 ( ) (96.333) (97.675) (96.333) (973) (973) Y5 ( ) (96.333) (95.67) (97.675) (96.333) (95.67) Y6 ( ) (973) (975) (975) (975) (975) Y7 ( ) (973) (97.675) (96.333) (96.333) (96.333) Y8 ( ) (94.33) (97.673) (96.33) (97.673) (97) Y9 ( ) (753) (753) (74.33) (96.333) (96.333) Y0 ( ) (95.673) (96.333) (97.675) (96.333) (96.333) Y ( ) (96.333) (973) (96.333) (973) (98.335) Y ( ) (973) (96.333) (96.333) (97.675) (96.333) Step 3- Scle up fuzzy ecson mtrx Scle up fuzzy ecson mtrx s lste n Tble (4). Tble 4. Scle up fuzzy ecson mtrx A5 A4 A3 A A Y (.33.67) ( ) (.33.67) (.33.67) (3.) Y ( ) ( ) ( ) (.8.53) (.8.67) Y3 ( ) ( ) (.40.6) ( ) (.8.4) Y4 ( ) (.8.53) ( ) ( ) ( ) Y5 ( ) (.8.30.) (.8.53) ( ) (.8.30.) Y6 ( ) (.8.4) (.8.4) (.8.4) (.8.4) Y7 ( ) (.8.53) ( ) ( ) ( ) Y8 ( ) (3.56) (3.0.33) (3.56) ( ) Y9 (.33.67) (.33.67) ( ) (3.) (3.) Y0 ( ) ( ) (.8.53) ( ) ( ) Y ( ) ( ) ( ) ( ) (.8.67) Y ( ) ( ) ( ) (.8.53) ( ) Step 4- Determnton of crter eghts Weghte fuzzy ecson mtrx s lste n Tble (5). Tble 5. Weghte fuzzy ecson mtrx A5 A4 A3 A A Y (..80.5) (..0.7) (..80.5) (..80.5) ( ) Y ( ) ( ) ( ) ( ) ( ) Y3 ( ) ( ) ( ) ( ) ( ) Y4 ( ) ( ) ( ) ( ) ( ) Y5 ( ) ( ) ( ) ( ) ( ) Y6 ( ) ( ) ( ) ( ) ( ) Y7 ( ) ( ) ( ) ( ) ( ) Y8 ( ) ( ) ( ) ( ) ( ) Y9 (..50.7) (..50.7) (..30.3) ( ) ( ) Y0 ( ) ( ) ( ) ( ) ( ) Y ( ) ( ) ( ) ( ) ( ) Y ( ) ( ) ( ) ( ) ( ) Step 5- Fnng fuzzy el soluton (FPISA) n fuzzy nt el soluton (FNISA-) Fuzzy el soluton n fuzzy nt el soluton s clculte n Tble (6). Step 6- Clculton of stnce from fuzzy el n non el Dstnce from fuzzy el n Dstnce from fuzzy non el for ech crteron clculte for supplers s lste n Tble (7) n Tble (8).

10 Intl. Res. J. Appl. Bsc. Sc. Vol. 4 (9) Tble 6. Fuzzy el soluton n fuzzy nt el soluton ( ) ( ) Y ( ) (...) Y ( ) (.6.6.6) Y3 ( ) (.6.6.6) Y4 ( ) (.6.6.6) Y5 ( ) (.6.6.6) Y6 ( ) (.6.6.6) Y7 ( ) (.6.6.6) Y8 ( ) (.7.7.7) Y9 ( ) (...) Y0 ( ) (.6.6.6) Y ( ) (.6.6.6) Y ( ) (.6.6.6) Tble 7. Dstnce from fuzzy el A5 A4 A3 A A Y Y Y Y Y Y Y Y Y Y Y Y ( ) Tble 8. Dstnce from fuzzy non el A5 A4 A3 A A Y Y Y Y Y Y Y Y Y Y Y Y ( ) Step 7- Clculton of smlrty nex Dstnce from fuzzy el Dstnce from fuzzy non el n Smlrty nex clculte for supplers s lste n Tble (9). Tble 9. Smlrty nex A5 A4 A3 A A ( ) ( ) ( CC ) Step 8- Grng of optons Accorng to the computtons ere crre out supplers re rne s n Tble (0).

11 Intl. Res. J. Appl. Bsc. Sc. Vol. 4 (9) Tble 0. Grng of optons A5 A3 A4 A A CONCLUSION The ssue of selecton of supplers s mportnt problem n successful mplementton of supply chn. In generl ths ssue encounters th vgue n mplct t n usng fuzzy set theores for nvestgton on uncertnty seems necessry. As t s shon usng fuzzy Topss s pproprte for evluton n selecton of supplers. In ths metho qulttve n quntttve crter cn be conser concurrent n selecton process. By clculton of reltve closeness the supplers re gre n the best one s etermne. Improvement of ths metho shoul be consere for problem of selecton of the best n effcent supplers n support system shoul be evelope n fuzzy n future reserches. REFERENCE Atte M. 00. 'Fuzzy mult crter ecson mng'. Shhrou Unversty of Technology Shhrou st eton. Atte M. 00. 'Mult crter ecson mng' Shhrou Unversty of Technology Shhrou st eton. Azr A Rbzeh A. 00. 'Prctcl ecson mng (MADM pproch)'. TehrnNegh Dnesh uplcton st eton. Gzvt J 'Mngement of equpments n mterls supply' Rhnegsht Novn Publcton Tehrn st eton. Momen M. 0. 'Ne ssues n reserch on operton'. Molef Publcton Tehrn 4 th eton. Moneyn D Aghe M. 0. 'Decson mng n mngement'. Sfr Arehl Publcton Tehrn st eton. Smch-Lev D Kmnsy P 'Desgnng n Mngng the Supply Chn- Concepts Strteges n cse stues' Mc Gro- Hll Publshng Ne Yor NY pp.85-00