OPTIMUM ORDER QUANTITY FOR DETERIORATING ITEMS IN LARGEST LIFETIME WITH PERMISSIBLE DELAY PERIOD S. C. SHARMA & VIVEK VIJAY

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1 Iraioal Joural of Mahaics a opur Applicaios Rsarch (IJMAR) ISSN(P): ; ISSN(E): 9-86 Vol. 6, Issu, Aug 6, Pv. L. OPIMUM ORDER QUANIY FOR DEERIORAING IEMS IN LARGES LIFEIME WIH PERMISSIBLE DELAY PERIOD S.. SHARMA & VIVEK VIJAY Dpar of Mahaics, Uivrsiy of Rajasha, Jaipur, Rajasha, Iia ABSRA I his rsarch papr w vlop a opiu orr quaiy ol icluig powr par a, rioraio, a lifi a lay prio. I h propos ol rioraio is ivrsly proporioal o i. hr is axiu lif i of prouc a supplir pri o railr a crai i lii for lay h rvu. Afr his i irs is charg. hr is paricular cycl i. A urical xapl is also prs i his papr. KEYWORDS: Drioraio, Holig os, Orrig os, Purchas os, Maxiu Lif i, Prissibl Dlay i Pay, ycl i, Irs Ear a Irs harg Rciv: Ju, 6; Accp: Jul, 6; Publish: Jul 5, 6; Papr I.: IJMARAUG6 INRODUION I h pas rsarch ay ivory ol has b vlop wih a wihou rioraio. I h pracical siuaio ay proucs riora i o i, which is aufacur lik foo is, chicals, Pharacuicals, phoography, paprs c. a ay of proucs has xpiry a. h a ra ay b cosa, i p, sock lvl p or pric p c. W hav lii spac for aiai h sock lvl. Du o low spac, h orr has o plac frquly ha icrass h cos. Now if w sor h larg ubr of is for fuur a h aags of is ar possibl u o ay facors lik sorag coiios, wahr coiio, iscs biig. Soi supplir prs araciv policis o larg sal (lik gifs or prissibl i lii for pay). If supplir pris for lay i pays h afr his i h will charg high irs fro railr. Origial Aricl h firs ap o scrib opial polics for rioraig is was a by Ghar a Schrar [], by EOQ ol assuig xpoial cay. ovr a Philip [] vlop a ivory ol for wo parar wibull isribuio for cosa a ra wihou shorags. Goswai a hauhuri [] hav vlop a EOQ ol for rioraig is wih shorags a a liar r i a. Hariga [] givs a opial EOQ ols for rioraig is wih i varyig a. g, hag, Dy a Hug [5] vlop a opial rplish policy for rioraig is wih i varyig a a parial backloggig. Goyal [6] has giv cooic orr quaiy ol ur coiio o prissibl lay i pays. Aggarwal a Jaggi [7] hav vlop orrig policis of rioraig is wih prissibl lay i pays. Jaal, Sarkar a Wag [8] hav irouc a orrig policy for rioraig is wih allowabl shorag a prissibl lay i pays. Soi a Shah [9] hav vlop a opial orr policy for sock p a ur progrssiv pay sch. g, Kroya, Skouri a Lou [] hav giv a coprhsiv xsio of opial orrig policy for sock p a ur progrssiv pay sch. g, Mi ior@jprc.org

2 S.. Shara & Vivk Vijay a Pa [] has vlop cooic orr quaiy ol wih ra cri fiacig for o crasig a. Sarkar [] has vlop a EOQ ol for pay lay a i varyig rioraio ra. Sigh a Shrivasava [] irouc a EOQ ol for prishabl is wih sock p sllig ra a prissibl lay i pay a parial backloggig. Mishra S. S. a Mishra P. P. [] ivsiga pric riaio for a EOQ ol for rioraig is ur prfc copiio. Shara a Pri [5] vlop opiu orrig irval for rao rioraio wih sllig pric a sock p a ra a shorags. I h prs ol w vlop a opiu orr quaiy ol wih powr par a a rioraio. hr is axiu lif i of prouc a supplir pri o railr a crai i lii for lay h rvu. Afr his i irs is charg. A urical xapl is also availabl. Assupios a Noaios Orrig cos pr orr. Purchasig cos pr ui. S Sailig pric. h Holig cos pr ui. I c Irs charg pr yar i socks by supplirs. I Irs ar by ivs pr yar. I ( ) Ivory lvl a i. θ Drioraio ra p o i, ( ) Maxiu lif i i yars of i. Supplir prissibl lay prio. D Powr par a. ycl i oal cos pr yar. Mahaical Mol I, () ( ) I ( ). Ipac Facor (J):.879 NAAS Raig:.8

3 Opiu Orr Quaiy for Drioraig Is i Largs Lifi wih Prissibl Dlay Prio 5 ior@jprc.org Bouary coiio is I () Now soluio of iffrial quaio () is A I Usig bouary coiio (), w hav I () Now holig cos h I H h as : if I his cas railr ar irs pr cycl wih rur ra I. hrfor h aual irs ar pr cycl is giv as Irs ar D D SI [ ] SI Now h oal cos pr ui i (Purchasig cos orrig cos holig cos) Irs ar h [ ] SI Now o fi opial cycl i, a > h [ ] SI

4 6 S.. Shara & Vivk Vijay Ipac Facor (J):.879 NAAS Raig:.8 [ ] SI h as : if < Now irs charg pr cycl is giv as Irs charg c I I I c A irs ar i i o si D si Now h oal cos pr cycl is h c I si Now o fi opial cycl i, a >

5 Opiu Orr Quaiy for Drioraig Is i Largs Lifi wih Prissibl Dlay Prio 7 ior@jprc.org h c I si h 6 I c si Nurical Exapl hr is urical xapl o s h ol a is soluio. W ak so valus as cosa a suy h ffc o oal cos oal cycl i a o of parar. abl & Graph : I cas, Parars ar Rs, S Rs,, h 5 Rs, I.5 Rs, I c Rs, a

6 8 S.. Shara & Vivk Vijay abl & Graph : I cas, Parars ar Rs, S Rs,, h 5 Rs, I.5 Rs, I c Rs, a abl & Graph : I cas, Parars ar Rs, S Rs,, h 5 Rs, I.5 Rs, I c Rs, a abl & Graph : I cas, Parars ar Rs, S Rs,, h 5 Rs, I Rs, I c. Rs, a Ipac Facor (J):.879 NAAS Raig:.8

7 Opiu Orr Quaiy for Drioraig Is i Largs Lifi wih Prissibl Dlay Prio 9 abl & Graph 5: I cas, Parars ar Rs, S Rs,, h 5 Rs, I Rs, I c. Rs, a abl & Graph 6: I cas, Parars ar Rs, S Rs,, h 5 Rs, I Rs, I c. Rs, a ONLUSIONS I his ol, w vlop a opiu orr quaiy ivory ol for rioraig is wih powr par a. I h ol w suy h ffc of oal cos a suiabl cycl i wih iffr parars. I boh ior@jprc.org

8 S.. Shara & Vivk Vijay cass h oal cos icrass as h parar,, icrass. Shorags ar o allow a o rplish. I prs ol w us rioraio, a, sock lvl, holig cos a rioraio cos. I pracical siuaio hr ar ay ohr facors which ar rsposibl o chag h oal cos. his ol ca x wih ohr ffciv facors a i coul b o i fuur rsarch. REFERENES. P. M. Ghar a G. P. Schrar (96): A ol for xpoial cayig ivory, J. I. Eg., 8-.. R. B. ovr a G. S. Philip (97): A EOQ ol wih wibull isribuio rioraio, AIIE ras. 5, -6.. Goswai a K. S. hauhuri (99): A EOQ ol for rioraig is wih shorags a a liar r i a. J. Opr. Rs. Soc., 5-.. M. A. Hariga (996): A opial EOQ ols for rioraig is wih i varyig a, J. Opr. Rs. Soc. 7, J.. g, H. J. hag,. Y. Dy a. H. Hug (): A opial rplish policy for rioraig is wih i varyig a a parial backloggig. Opr. Rs. L., S. K. Goyal (985): Ecooic orr quaiy ol ur coiio o prissibl lay i pays. J. Opr. Rs. Soc. 6, S. P. Aggarwal a. K. Jaggi (995): Orrig policis of rioraig is wih prissibl lay i pays. J. Opr. Rs. Soc. 6, M. Jaal, B. R. Sarkar a S. Wag (997): A orrig policy ol for rioraig is wih allowabl shorag a prissibl lay i pays. J. Opr. Rs. Soc. 8, H. Soi a N. H. Shah (8): Opial orr policy for sock p a ur progrssiv pay sch. Eur. J. Opr. Rs. 8, 9-.. J.. g, I. P. Kroya, K. Skouri a K. R. Lou (): A coprhsiv xsio of opial orrig policy for sock p a ur progrssiv pay sch. Eur. J. Opr. Rs. 5, J.. g, J. Mi a Q. Pa (): Ecooic orr quaiy ol wih ra cri fiacig for o crasig a. Oga, B. Sarkar (): A EOQ ol for pay lay a i varyig rioraio ra. Mah. opu. Mol 55, Sigh D. a Shrivasava R. K. (9): A EOQ ol for prishabl is wih sock p sllig ra a prissibl lay i pay a parial backloggig. Aca icia Iica, Vol. XXXV M, No., -.. Mishra S. S. a Mishra P. P. (8): Pric riaio for a EOQ ol for rioraig is ur prfc copiio. opurs a Mahaics wih Applicaios 56, Shara A. K. a Pri (): Opiu orrig irval for rao rioraio wih sllig pric a sock p a ra a shorags. Gaia Sash, Vol. 5 No., Ipac Facor (J):.879 NAAS Raig:.8

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