FUZZY EXPECTED VALUE MODEL WITH INSPECTION ERRORS AND TWO LEVEL OF TRADE CREDIT IN ONE REPLENISHMENT CYCLE Olha Yegorova

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nnonl Jounl "nfoon odl nd Anly" Volu u 7 FUZZY X VALU OL WH SO RRORS A WO LVL OF RA R O RLSH YL Olh Yoo A: n h ono od quny odl h o ll of d d n on lnhn yl lu of ony non o lnnd kod nd l un offd. n ho ol dnd lln fo ood quly lln fo df n d nd n nd ond fuzzy l. Follon xd lu odl on nd fuzzy xd lu odl onud. Fuzzy ulon loyd o h xd lu of fuzzy l nd xu un on l. n od o ol h fuzzy xd lu odl n loh d on h fuzzy ulon dnd. Kyod: OQ f quly lfon o doon nnoy kodn d d fuzzy ulon n loh. A lfon Kyod:.6.5 odl lon noduon ff nnoy nn on of h n u fo ny d ony. h donl ono od quny odl dly ud y don k nnoy onol ool n l-old nonnl. ly ud h h uy u y fo h uhd oon h d. So l n y h n od u fo ono on nd u d d. Bfo h nd of h d d od h l n ll h ood uul nu nd n n. un l l y dl of h ono od quny (OQ) odl h d d h n offd n h nf lu. A lo of h ok ho h n h ffo n h oh nonnl. Fo xl n OQ odl und h ondon of l dly n yn udd n [Goyl 985 hun 998]. Rnly Hun [Hun ] nd Sh l. [Sh ] odfd h uon o o ll of d d. Al nd J [Al 995] hun nd Lo [hun ] Shh nd Rykundly [Shh 9] hy nd dhn [hy ] dl h h ol of dnn h ono od quny fo doon und l dly n yn. hn nd y [hn ] ulhd h fo don h l klon nd l dly n yn. Hou nd Ln [Hou 9] ud h flo ond OQ odl h don und l dly n yn. An nlyl of h h ffo n h fuzzy nonn fod on OQ nd ono oduon quny odl hd don y Hu [Hu ] Yoo [Yoo ]. Whl h don l l o h on n h oh nonn h dnd nd nnoy o ondd fuzzy l. Sl oh onnd h onn uh ud ll. A ful oon of h n o l h h no ondd nnoy odl und h ondon of d d h hun o n nn o. W no h Shll [Shll 988] xndd h OQ odl y ddn h uon h df of knon ooon n n non lo nd h fxd nd l non o nud nd n fndn nd on h

8 nnonl Jounl "nfoon odl nd Anly" Volu u df. Slh nd J [Slh ] dlod n ono od quny odl fo h h ndo ooon of h n lo df. Bu hun o n h nn o nod n h odl h hn n uffu nd Khn [uffu 5]. L Khn. l [Khn ] ood n OQ h df non o nd l un h ho no llod df old dound h nd of h % nn o. o duon n n no y Hu [Hu ]. l h oduon o ofn f. hfo n od o od ood o uo nd k h on k dlon of uh dqu odl ndd h oly of lfon nd don o h hnn xnl. Bd ol nnoy ol h ond oh h ul nd l on o onl hn ho ho h ond only fo on. h f xnd h ono od quny odl fo doon h o ll of d d n on lnhn yl non o lnnd kod nd l un n oh oh nd fuzzy nonn uh h h dnd lln n d nd n nd u fuzzy nu. A ondd ol h onn nd unny nu ny o fo lzon of hnoloy hh ll llo o hon h quny of h nly nd oz h lulon o. ln oly hoy ood y Zdh [Zdh 978] nd dlod y ny h uh uo nd d [uo 988] nd Y [Y 99]. Rnly B. Lu nd Y. K. Lu [Lu ] nd n u nd dly u. oo Lu [Lu ] ood dly hoy. fnon. L fuzzy l h h funon x. hn h oly ny nd dly u of h fuzzy n n n ly y [Lu ] o u x x u x o fnon. h xd lu of fuzzy l dfnd [Lu ] x d d () fnon. h o funon of dfnd [Lu ] fnon. f u u. (5) nul fuzzy nu h n lf dh nd h dh hn h funon h h follon fo (6) lh. () () ()

nnonl Jounl "nfoon odl nd Anly" Volu u 9 fnon 5. Fo h fuzzy l dd n fnon h dly of h n dfnd d on h dfnon n () [Lu ] fnon 6. f d (7) lh. zodl fuzzy nu h lf odl ll h odl ll с lf dh nd h dh d hn h funon h h follon fo (8) d d lh. fnon 7. Fo h fuzzy l dd n fnon 6 h dly of h n dfnd d on h dfnon n () [Lu ] (9) d d d. n h h h nul fuzzy l ud o odl h fuzzy n d n nd nd zodl fuzzy l ud o odl h fuzzy dnd lln of ood quly nd lln of df. ol dfnon d ony hh oly do no h okn l ln o lnh nnoy y un of d d. Allol uhn o of nnoy n fo n o x. h ul off h l d od of -dy. un h h l u nl nu nn ou h n nd ony un. A h nd of h od h l y off ll un old kn h fo dy-o-dy xn nd yn fo h n h on h unold ok h h n ony un un of. B n ould lo o fo h d of f h l y off ll un old dun o. uh od xud h onn nny. kn no oun h oll dnon of un of oduon с d fo holdn nnoy ny hou h y W. Suly lo h

nnonl Jounl "nfoon odl nd Anly" Volu u hyl h hl hy k od n h nnoy. f un y found dun odu quly onol. o nu n dqu ll of d onu h xu llol nu of df n h lo hould no xd u un. no ould noly lfy nondf o df o noly lfy df o non-df. Sul o ok (k u dfny) o l h nufun fon. oduon o of df hh ond fo l quly l do no nlud o h uhn o of h nnoy lo nd hy ll no und o h ul. Oh xndu du o k n non ood non no y y h l. nd unfoly dud on h nl n dn lnhn. Sho llod. h h lfon df nd ho und y h onu k n ok nd old h nd of h oon yl. uod h h nflon ony un ll n. ny dn h ono od quny nd lnh of on yl h h xu nu on l. odl foulon knon h h lnhn un un nd dnd un un. L u u h h nu of h lfd df nludd ho h non-df nd noly lfd df (h oly ) nd ho h df nd lfd df (h oly ). hu h h nu of h lfd df n on yl () nd h nu of h lfd non-df n on yl () h h oly h h df h oly of lfyn non-df df h oly of lfyn df non-df. Slly qul uu of h ond fo l quly l. h nu of h h n ond fo l quly l nd lfd df () nd h nu of h h n ond fo l quly l nd lfd non-df () h lnhn of h h n ond fo l quly l un un h oly h on ond fo l quly l df h oly of lfyn non-df on ond fo l quly l df h oly of lfyn df on ond fo l quly l non-df. h ooon of h uo ho ould lk o klon d h h n fo h nx lnhn. n h uon h klon dfnd B h h hh h h lnhn n d h klon.

nnonl Jounl "nfoon odl nd Anly" Volu u All h flo ln ll ld o h of h nn un dound y onnuou h fo o oon h olu of ony nold n h on of ok h follon no. n h n doun of h nflon 5% k () 5% nd du h oonn of h flo h h n h un l doun n h k. f h oun of ony hn h o h luld Н k d (5) h h lu of ony h nnn of h lnnn hozon H lnnn hozon. o dn ol h flo ond nnoy nn ny k no oun no only h oun of h flo u lo on of yn nd nu odn o h on oon. h nnoy odl. h nnoy y ol follo: un of h nnoy y h lnhn un un hn h ho ll o. Fo F. on n h h kn o fll h kod h. un lnhn od nnoy ll dlnn only du o h dnd nd doon h h n of dod un n of dod nd ou fo h nnoy. A oon nnoy ll of l o ul hould dful h ln of l nd xu l nnoy ll ll uuld. Af h nnoy ll du o h dnd nd doon o zo o nl nd kodn od nnoy ll n. Lo l F.. Bho of h nnoy ll o h h nnoy ll of l o h f od n yl dnd y follon dffnl quon:

nnonl Jounl "nfoon odl nd Anly" Volu u d (6) h h oundy ondon. h oluon fo h o dffnl quon (6). ln 5 с (7) h fnl oluon of o quon n y. ln (8) Hn n ddud fo (8) h (9) ln () ln ()

nnonl Jounl "nfoon odl nd Anly" Volu u ln () () h lnh of h yl. W y lo ddu h ono od quny Q () Ou o xz un on l un hh n xd x nd d un d h R K R... (5) u o h onn - nn oun on ol oduon o nno nfny y h n u nd lo l on h xu nn n x (6) - hou h h o od lon W d (7) - holdn o nno o hn ol oduon o h С (8) - odn ood of h uo u (9) h R l nu n y d d d d d d d d d R k k k k k oh

nnonl Jounl "nfoon odl nd Anly" Volu u oh oh oh K h odn o h uh o n y d d d d d d k k k oh oh oh

nnonl Jounl "nfoon odl nd Anly" Volu u 5 oh h (non) nn o n y d k h o fo un h on o ul n y d d k k h h nnoy holdn o yl n y d d d d h d d h k k k k k h d h doon o n y d k ou d d h ho o yl du o klo n y d d d k k h un h oouny o du o lo l yl n y d d k u un d h o of n df d с k d d

nnonl Jounl "nfoon odl nd Anly" Volu u 6 nd h o of on non-df d k nd nd n d n y d d d d k k oh oh n nd n y d d d d d d k k oh oh lln un of ood quly lln un fo df с uhn o un nn (non) o un с h o fo un h on o ul ony un h holdn o of l ony un un h holdn o of f quly ony un un d doon o ony un ou nly o of lln dod o uo ony un h un ho o ony un un u o of lo l ony un d o of n df nd o of on non-df. Hn ou ol

nnonl Jounl "nfoon odl nd Anly" Volu u 7. x 9 8 7 6 5 () u o h onn n x W d h С u h... n y q. (5). Fuzzy xd lu nnoy odl. n h h ondd h dnd lln n d nd n nd fuzzy l o kl h ly n o ff y. Whn h ( uon) d fuzzy l h o nnoy xon o fuzzy nd hy h un on l o fuzzy l on h dly X X. L nd dfnd y zodl nd nul fuzzy nu uh h nd h nd d on h u udn. f h don k n o dn ol n nd nnoy ol uh h fuzzy xd lu of h un on l xl fuzzy V n onud follo

nnonl Jounl "nfoon odl nd Anly" Volu u 8 x 9 8 7 6 5 () u o h onn x n W d h С u h nd d un d h R K R.... x on d ou h ulon hnqu o h fuzzy nd oluon hodoloy fo fuzzy xd lu odl lon h hol ul o dnfy lol ol oluon fo. Fuzzy ulon hnqu n o-non nnoy y fqunly h don k n o onol h fuzzy nu on l n h lnhn yl uh h h l lu of h fuzzy nu on l xl. Slly n odl () nd o fnd h o o uh h f h onn nd h xl lu. Fo h fxd lu of fuzzy ulon hnqu [lzdh ] loyd o h fuzzy uh dnd lln n d nd n nd. S. S nd nlzd G nd. O S. W ndoly n qun fo h -ll of fuzzy l G... h uffnly ll o nu.

nnonl Jounl "nfoon odl nd Anly" Volu u 9 S. lul fo... G.... S. S....... S 5. Rndoly n fo. S 6. f hn h O O x x...... nd. Oh h O O x x....... S 7. R 5 nd 6 fo O. S 8. lul d d і. O So f h onud OQ n fuzzy n nd knon h h V n old h n oh. Ho h odl nd o old h h hu loh on h olxy of ol. h l hu loh nd fo oluon of nu uh Gn Aloh [Gold 989] oluony S [Rhn 99] nd An olony Aloh [oo 996]. H n od o ol h V hoo Gn Aloh h foundon o dn n loh hh n fuzzy ulon nd Gn Aloh h h fuzzy ulon loyd o h xl nu on l nd Gn Aloh ud o fnd h ol oluon. Gn loh d on h fuzzy ulon Gn loh of h d oy of oluony loh hh onlly ood y Gold [Gold 989]. hu ozon hnoloy d on uh nul oluon hn oo uon nd nul lon. ll no GA h n ufully ld o d n of

5 nnonl Jounl "nfoon odl nd Anly" Volu u lon. h ohn uy of GA nd lon o ol nnoy onol ol n found n [lzdh ]. n h follo h n h of h n loh loyd n h h dd. n h h hooo h n of h unflld od klo nnoy ll of l nd xu nnoy ll of l. hfo ny o hooo o n l lu of h l nd. h lnh of h o dnd on h qud on. oo nfl hooo h on h do no fy h onn of h odl n () no ondd. h oo oo o n hooo fo of ld hooo of h n non. h nu of l oo oon fo ny-odd d: on-on oo oon oo n -on oo unfo oo. n h h nl on oo h dffn ol of.5.6.7 ulzd. h uon oo hn h lu of ndo ld ln of h hooo. o do h ndo nu R n nd fo h n. f R l hn dnd uon oly hn h uon ou n h n. Oh do no. n xzon ol h o dqu h oluon h h o funon (fn lu) ll. hfo h f hooo ll k n offn non h l oly. h fuzzy ulon ud o lu h o funon of h h. h lon oo nu h lon of ll-fon hooo fo h oduon o. h o oul hnqu o dul of ood nddul ounn nd l. h l dn nd dn of xly l h ou o-don no lo. Fo ll y of lon only fo l od [H 99] n hoy h h h o of ou don. Alo h oh lon hod uh n ndn oudn nd ooonl lon. Son ondon fo h odl ozon n dfnd n f dffn y: - By nn h ol nu of h non - Ahn of ny lu of fn-funon - Sl oulon on of dnl ln - By nodun o nu uh h h ozon od f h ondon f x f n fulflld f x nd f n n xu nd nu o funon lu ly. Bfo n h ozon loh ny l h lu n h on ondon (o h nu of non) h oulon z L nd un h nly funon hod ond onnd ol o n unonnd. n ho h nold n h GA loh ud n h h. S h nd ndoly h nl oulon of z L (h nddul hould fy h onn).. lul h fn lu fo h hooo.. Sl n nddul fo n ool y ounn lon hod un l.. Aly oo oo o h ld of hooo h oly. 5. Aly uon oo o ndoly ld hooo h oly.

nnonl Jounl "nfoon odl nd Anly" Volu u 5 6. Rl h un oulon y h uln n fl oulon. 7. lul h o funon. 8. f h on ondon o. Oh o o. onluon n h oh lnhn nnoy odl dlon. onln on odl fo doon h o ll of d d n on lnhn yl lu of ony non o lnnd kod nd l un h n ood. W h ondd h OQ nnoy ol y hzn h dnd h lln fo ood quly h lln fo df n d nd n nd h fuzzy l nd onud h fuzzy xd lu odl. Alyn h fuzzy ulon hnqu h d h xd lu of fuzzy o nd n. Wh h fuzzy xd lu odl hd o ol h nly hod nd h dnd n loh d on h fuzzy ulon o ol. So nu fo fuu ok follo: - h holdn o o oh of h ol y k unn fo (oh o ouh) ll - o oh doon funon h hn xonnl y ondd fo h doon - o oh -hu loh uh l y loyd o ol h ol - oluony hnolo of d Ozon [Snyyuk ] n ondd n ff hnqu o ol h ol. Blohy [Al 995] S.. Al.K. J. Odn ol of don und l dly n yn. n: Jounl of Oonl Rh Soy 6 658-66. [hun 998] K.J. hun. A ho on h dnon of ono od quny und ondon of l dly n yn. n: Jounl of nfoon nd Ozon Sn 5 9-5. [hun ] K.J. hun J.J. Lo. Lo-zn don und d d dndn on h odn quny. n: ou & Oon Rh (6) 99-98. [oo 996]. oo V. nzzo A. olon. An y: ozon y olony of oon n. n: non on Sy n nd yn B 6() 9- [uo 988]. uo H. d. oly hoy: An Aoh o ouzd on of Unny lnu Yok 988. [uffu 5] S.O. uffu. Khn. of non o on h fon u of nl non ln. n: nnonl Jounl of oduon Rh () 95-967. [Gold989]. Gold. Gn loh n h ozon nd hn lnn Addon-Wly Rdn A 989. [Goyl 985] S.K. Goyl. ono od quny und ondon of l dly n yn. n: Jounl of Oonl Rh Soy 6() 5-8. [H 99] R.. H. And lol onn oof fo l of n loh Wn hnh Un 99. [Hou 9] K.L. Hou L.. Ln. A h flo ond OQ odl h don und l dly n yn. n: Jounl of Ald Sn 9 79-79. [Hu ]. J.-. Hu L.-F. Hu. o Q odl h f oduon o non o lnnd kod nd l un. n: ou & ndul nnn 6 89-.

5 nnonl Jounl "nfoon odl nd Anly" Volu u [Hun ] Y.F. Hun. Ol l odn ol n h OQ odl und d d fnnn. n: Jounl of Oon Rh Soy 5(9) -5. [Khn ]. Khn.Y. J. Bonny. An ono od quny (OQ) fo h f quly nd non o. n: nnonl Jounl of oduon ono () -8. [Lu ] B. Lu Y. K. Lu. xd lu of fuzzy l nd fuzzy xd lu odl. n: non on Fuzzy Sy () 5 5. [Lu ] B. Lu. Unny hoy: An noduon o Axo Foundon Sn-Vl Bln. [Rhn 99]. Rhn. oluon Sy Bln Fonn-Holzoo 99. [Slh ].K. Slh.Y. J. ono oduon quny odl fo h f quly. n: nnonl Jounl of oduon ono 6() 59-6. [Shh 9].H. Shh. Rykundly. Ol nnoy ol fo Wull doon und d d n dlnn k. n: ndu Jounl of nn & Sol Sn () -. [Sh ] A. Sh R. Gol.K. u. Ol oly fo OQ odl h o ll of d d n on lnhn yl. n: An Jounl of Oon Rh 5-58. [Snyyuk ] V.. Snyyuk. ooonl oon unny n nonln ull ozon ol. n: Afl nlln 7-. [lzdh ] A. A. lzdh S.. Akhn k.-b. Aynzhd. A hyd hod of fuzzy ulon nd n loh o oz onnd nnoy onol y h oh lnhn nd fuzzy dnd. n: nfoon Sn 5-. [hy ].K. hy L.. dhn. An OQ odl fo h Wull doon h l dly n yn nd od l lu. n: nnonl Jounl of ndul nnn ouon 5-. [Y 99] R. R. Y. On h olon of qul oly u. n: non on Fuzzy Sy () 8 9. [Yoo ] O.V. Yoo. Fuzzy nnoy odl: ol dlon. n: n-uon Jounl of n hnolo /(58) -. [Zdh 978] L. A. Zdh. Fuzzy fo hoy of oly. n: Fuzzy S nd Sy -8. Auho' nfoon Olh Yoo n hky S hnolol Uny Shhnko Bld. l.6 hky 86 Ukn -l: yooo@l.o o Fld of Snf Rh: nlln ouon fuzzy odln hnolo nd don kn n ono

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