A fuzzy mixture two warehouse inventory model with Linear Demand
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1 nninl Junl f pplicin nnvin in Engining & Mngmn JEM Si: Emil: i@ijim.g iijim@gmil.cm Vlum ssu Fuy SSN 9 - fuzzy mixu w wus invny ml wi Lin Dmn K Mli Ysv Sing Dpmn f Mmics B.K. Bil nsiu f Engining &cnlgy Pilni jsn sc Scl Singni Univsiy Pci Bi Junjunu jsn BS is pp ls wi fuzzy s w wus invny ml wi lin mn. Diin s in wuss cnsi iffn u cng in nvinmn. Sgs n llw. n l lif n gll m siuins sm pms li ing cs ling css n iing cs flucu wi i cul vlus. S pms n ssum cnsn. l wi suc yp f unciny cnsi fuzzy ml in wic ling css ssum in wuss ing cs n iing cs in fuzzy num wic is psn y ingul nums. in l invny cs in cisp nvinmn s wll s fuzzy nvinmn wi lp f Sign isnc m. numicl xmpl is pvi illus pps cisp ml n fuzzy ml wic sws ffcs f fuzzinss f pms n piml sluin. Kyws: Lin mn iin ling cs isp ml Fuzzy ml n Sign isnc M.. NDUN n ls fw cs invny mls v n wily ppli in usinss wl. Hwv n f wnsss f cun invny mls is unlisic ssumpin ll ims puc f g quliy. n cisp nvinmn ll pms in l invny cs suc s ling cs ing cs s-up cs iin n mn c. nwn n v fini vlu wiu miguiy. Sm f usinss siuins fi suc cniins u in ms f siuins n in y--y cnging m scni pms n vils igly uncin impcis. cncp f sf cmpuing cniqus fuzzy lgic ws fis inuc y Z 965. Bllmn n Z 9 vlp iffnc wn nmnss n fuzzinss y swing fm ls wi unciny ging mmsip nn-mmsip f n lmn in s wil l is cncn wi g f unciny y wic n lmn lngs s. Hly 96 cnsi n invny ml wi w sg fciliis. is gnlly ssum ling cs in is g n ling cs in. Hnc ims s fis in n nly xcss f sc is s in. Fu ims f ls li n ims f. Zimmmnn 95 s givn viw n fuzzy s y n is pplicins. is lng isy f gul pgss in vlpmn f invny mls. P 9 n Vujsvic l 996 vlp invny mls in fuzzy sns in wic ing cs n ling cs psn y fuzzy nums. P s psn css s pzil fuzzy nums. il Vujsvic l s iscuss ing cs y ingul fuzzy num n ling cs y pzil fuzzy num Y n L 999 psn fuzzy invny ml wi n wiu c f fuzzy quniy wi pzil fuzzy num.. K n. K. Hsu psn l siz- pin invny ml wi fuzzy mns. Hsi cnsi w fuzzy pucin-invny mls: n f cisp pucin quniy wi fuzzy pms n n f fuzzy pucin quniy. Hsi us g mn ingin psnin m f fuzzifying fuzzy l invny cs. J. S. Y n J. ing vlp n invny wiu c wi fuzzy l cs n fuzzy sing cs ffuzifi y cni n sing isnc. ng l. iscuss fuzzy mixu invny ml wi vil l-im s n pilisic fuzzy s n ingul fuzzy num. ng l. 6 psn ml in wic y cnsi l-im mn s fuzzy nm vil ins f pilisic fuzzy s. Du l. cnsi cninuus viw invny sysm w nnul vg mn ws s fuzzy nm vil. l-im mn ws ls ssss y ingul fuzzy num. Yung l. iscuss pcumn plnning f im-vil mn in mnufcuing sysm s n sf cmpuing cniqus. Sing n Sing cnsi fuzzy invny ml f fini f plnismn using sign isnc m... u 9 iscuss fuzzy cnmic quniy invny ml. Hlim l. ss l sizing plm in n unlil pucin sysm wi scsic mcin wn n fuzzy pi im. y fuzzifi cs p uni im using sign isnc m. Yng l. iscuss n piml pucin-invny ml f iing ims wi mulipl-m mn. Mli n Sing cnsi n invny ml f iing ims wi sf cmpuing cniqus n vil mn. Li l Vlum ssu Fuy Pg
2 nninl Junl f pplicin nnvin in Engining & Mngmn JEM Si: Emil: i@ijim.g iijim@gmil.cm Vlum ssu Fuy SSN 9 - min n cnmic quniy f iing ims wi w-sg fciliis n is n wn wus n in n wus w ci is lin quniy. Mli Sing n Gup psn fuzzy s w wuss invny ml f iing ims. Hsi n Dy iscuss pucin invny ml f iing ims wi im-vying mn n fini plnismn y llwing psvin cnlgy cs s cisin vil in cnjuncin wi pucin plicy. n is pp w v psn n invny ml wi w wuss f iing ims. H w v w wuss f suy-n wn wus n scn n wus. ling cs f n wus is ig n ling cs f wn wus. ling cs n iing css f w wuss cnsi s fuzzy nums. ingul yp f fuzzy num is us f psning fuzzy pms. l invny css in in cisp s wll s fuzzy ml wi lp f numicl xmpl.. NN ND SSUMPNS invny ml is s n fllwing ssumpins: ing cs p invny ling cs in p uni p im uni invny ling cs in p uni p im uni iing cs p uni p im uni im wic invny lvl in cs z = lng f cycl im. mximum invny lvl in uing. lvl f invny in im lvl f invny in im lvl f invny in im l cs p im uni. { Sign psns fuzzinss f pms} n iin fllwing nins us: invny sysm ls wi singl im. Sgs n llw. mn is -. iin in is n in is. l im is z ngligil. ingul Fuzzy Num: L = is ingul fuzzy num w =- = = +. mmsip funcin f is wis. MHEML MDEL SP MDEL invny lvl ny insn f im uing is sci y fllwing iffnil quin:... i uny cniins = = n =. Sluins f v quins :. Vlum ssu Fuy Pg
3 nninl Junl f pplicin nnvin in Engining & Mngmn JEM Si: Emil: i@ijim.g iijim@gmil.cm Vlum ssu Fuy SSN 9 - Vlum ssu Fuy Pg ccing givn cniins =... quin sws lin wn &. Nx l lvn invny cs p cycl cnsiss f fllwing lmns:. ing cs p cycl is =.... nvny ling cs p cycl in is givn y H. 9. nvny ling cs p cycl in is givn y H.. Diin cs p cycl in is givn y D. 6. Diin cs p cycl in is givn y D. f l invny cs p uni im is givn y D D H H.. Susiuing Equin in v quin w g l lvn invny cs p uni im is minimum if n.. FUZZY MDEL n v ml w vlp cisp ml in wic ssum ll pms fix s cnsi f iin in n ssum is cnsn u in l lif n gll m siuins y flucu wi wn cul vlus. S pms n ssum cnsn. l wi suc yp f unciny cnsi fuzzy ml in wic ling css ssum in wuss ing cs n iing cs in fuzzy num wic is psn y ingul nums. iscuss is fuzzy ml us y sign isnc m.
4 nninl Junl f pplicin nnvin in Engining & Mngmn JEM Si: Emil: i@ijim.g iijim@gmil.cm Vlum ssu Fuy SSN 9 - Vlum ssu Fuy Pg 5. SGNED DSNE MEHD is m w us ingul fuzzy num f ling css ing cs n iing cs. Supps fllwing fuzzy nums: [ - + ] w n [ - + ] w n [ ] w 5 n 5 6 [ - + ] w n. sign isnc f v fuzzy nums is 5 6 Using quin w v l invny fuzzy cs p uni im y sign isnc m is Hnc fin pimum sluin f ny picul siuin wi lp f v quins. 6. NUMEL EXMPLE n illus v sluin pcu cnsi n invny sysm wi fllwing :. isp Ml = = = =.6 =. =.6 =.55 =56 =65. s cn sv in v illusins l cs is vy snsiiv cngs in mn. i incs in mn p pimum im f invny in im f invny in n l cs incss. Bu mn p is vy snsiiv if incss n l cs css vy fs. ncss in f iin in pimum im n l cs incs n n cs u incs in
5 nninl Junl f pplicin nnvin in Engining & Mngmn JEM Si: Emil: i@ijim.g iijim@gmil.cm Vlum ssu Fuy SSN 9 - f iin in pimum im n l cs cs n; n incs. n iing cs ling css f n incss n l s is incss. ncs in ing cs s n puc significn cngs in piml sluin. ngs in Fuzzy Ml Sign Disnc M = = = =.6 =. * =5.655 * =.6 * =6 =565. ngs in * * * Vlum ssu Fuy Pg
6 nninl Junl f pplicin nnvin in Engining & Mngmn JEM Si: Emil: i@ijim.g iijim@gmil.cm Vlum ssu Fuy SSN s cn sv in v illusins l cs is vy snsiiv cngs in mn. ncs in mn p pimum im * f invny in im * f invny in n l cs incss. Bu mn p is vy snsiiv if incss n l cs css vy fs. ncss in f iin in pimum im * n l cs incs n * n * cs u incs in f iin in pimum im * is cs n; * * n l cs incs. ncs in ing cs s n puc significn cngs in piml sluin. n iing cs ling css f n incss n l s is incss.. NLUSNS is pp ls fuzzy s invny ml f iing ims wi lin mn n w wus fciliis. pps ml cn us in invny cnl f iing ims suc s fsinl ims micins f ims lcnic cmpnns suc s mil mcins cicui ys n fsinl cmmiis c. H w us numicl xmpl illus pps cisp ml n fuzzy ml wic sws ffcs f fuzzinss f pms n piml sluin. n cmpisn cisp ml fuzzy ml is giving s piml sluin. n fuu suy i is p fu incp pps ml in m lisic ssumpins suc s pilisic mn iin sgs n ling cs li s sc pnn pucin pnn xpnnil mp yp quic wiull iin pil clgging. EFEENES [] Z L Fuzzy Ss nfmin n nl -5. [] Bllmn. E. n Z L.. 9. Dcisin-ming in fuzzy nvinmn. Mngmn Scinc B-B6. [] Hly V. nl. 96. n EQ ml w lvls f sg. psc [] H. J. Zimmmnn 95. Fuzzy S y n s pplicins. Kluw-Nij Hingum Nlns. [5] K. S. P Fuzzy s ic inpin f cnmic quniy E nscins n Sysms Mn n ynics 9 -. [6] M. Vujsvic l EQ fmul wn invny cs is fuzzy nninl Junl f Pucin Ecnmics [] Y J.S. n L H.M Fuzzy invny wi wiu c f fuzzy quniy wi pzil fuzzy num. Fuzzy Ss n Sysms 5 -. [] Hsi.H.. pimizin f fuzzy pucin invny mls. nfmin Scincs [9]. K n. K. Hsu. L siz- pin invny ml wi fuzzy mns mpus n Mmics wi pplicins vl. pp.9-. [] J. S. Y n J. ing. nvny wiu c wi fuzzy l cs n fuzzy sing cs ffuzifi y cni n sing isnc Eupn Junl f pinl sc -9. [] H.. ng J. S. Y n L. Y. yng. Fuzzy mixu invny ml wi vil l-im s n pilisic fuzzy s n ingul fuzzy num Mmicl n mpu Mling vl.9 pp.- [] ng H.. Y J. S. n Quyng L.Y. 6. Fuzzy mixu invny ml invlving fuzzy nm vil l-im n fuzzy l mn. Eupn Junl f pinl sc [] Yung K. L.. p n D. ng. Sf mpuing Bs Pcumn Plnning f im-vil Dmn in Mnufcuing Sysm. nninl Junl f umin n mpuing -. [] Du P. y D. n y... ninuus viw invny ml in mix fuzzy n scsic nvinmn. ppli Mmics n mpuin 9-9. [5] Sing S.. n Sing.. Fuzzy nvny Ml f fini f plnismn using Sign Disnc M. nninl nscins in Mmicl Scincs n mpu -. [6].. u Fuzzy cnmic quniy invny ml nninl Junl f nnviv mpuing nfmin n nl vl.5 n.9 pp [] Hlim K.. Gii B.. & uui K.S.. L sizing in n unlil mnufcuing sysm wi fuzzy mn n pi im. nninl Junl f nusil n Sysms Engining Vlum ssu Fuy Pg 5
![nninl Junl f pplicin nnvin in Engining & Mngmn JEM Si: www.ijim.g Emil: i@ijim.g iijim@gmil.cm Vlum ssu Fuy SSN 9 - [] Yng H Su-Yng ng K.K. Li.](/docs-images/93/114276891/images/7-0.jpg "n piml pucin invny ml f iing ims wi mulipl-m mn Eupn Junl f pinl sc Vlum ssu Pgs 59-6. [9] Mli. K. n Sing Ysv. n nvny Ml f Diing ms wi Sf mpuing cniqus n Vil Dmn.")
![nninl junl f sf cmpuing n ngining 5 -. [] Mli. K. Sing Ysv n Gup S.K.. fuzzy s w wuss invny ml f iing ims. nninl junl f sf cmpuing n ngining -9. [] Jui-Jung Li Ku-Nn Hung Kun-Jn ung.](/docs-images/93/114276891/images/7-1.jpg "L-sizing cisins f iing ims wi w wuss un n -siz-pnn ci nninl Junl f Pucin Ecnmics Vlum ssu Pgs -5. [] su-png Hsi ung-yun Dy. pucin invny ml incping ffc f psvin cnlgy invsmn wn mn is flucuing wi im.")
7 nninl Junl f pplicin nnvin in Engining & Mngmn JEM Si: Emil: i@ijim.g iijim@gmil.cm Vlum ssu Fuy SSN 9 - [] Yng H Su-Yng ng K.K. Li. n piml pucin invny ml f iing ims wi mulipl-m mn Eupn Junl f pinl sc Vlum ssu Pgs [9] Mli. K. n Sing Ysv. n nvny Ml f Diing ms wi Sf mpuing cniqus n Vil Dmn. nninl junl f sf cmpuing n ngining 5 -. [] Mli. K. Sing Ysv n Gup S.K.. fuzzy s w wuss invny ml f iing ims. nninl junl f sf cmpuing n ngining -9. [] Jui-Jung Li Ku-Nn Hung Kun-Jn ung. L-sizing cisins f iing ims wi w wuss un n -siz-pnn ci nninl Junl f Pucin Ecnmics Vlum ssu Pgs -5. [] su-png Hsi ung-yun Dy. pucin invny ml incping ffc f psvin cnlgy invsmn wn mn is flucuing wi im. Junl f mpuinl n ppli Mmics Vlum 9 Pgs 5-6. D.. K. Mli ssisn Pfss f Mmics in B. K. Bil nsiu f Engining & cnlgy Pilni jsn s xpinc f ig cnl sf cmpuing n Supply in Mngmn. H s pulis m n wny sc pps in pu ninl n inninl junls. H is viw/iil mm f mny ninl n inninl junls li s PSEH nninl Junl f Sf mpuing n Engining nninl Junl f Mmicl Scinc n nninl junl f Pysicl Scincs. H is u/c-u f n s. M. Ysv Sing sc Scl in Singni Univsiy Pci Bi Dis. Junjunu jsn ni. H in M.Sc Mmics Ms f mpu pplicin M n M.c in mpu Scinc n Engining. H s n vius smin/cnfncs. His sc inss inclu nvny nl n Sf mpuing cniqus. Vlum ssu Fuy Pg 6
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