Pric Dndn Qudric Dmnd nvnory Modls wi Vril Holding os nd nlion R SBN: 978-8-97-8-9 R. Vnswrlu Gim Univrsiy rngvjl_v@yoo.co.in M. S. Rddy BVSR Enginring ollg nvnsrinu@gmil.com n m is md o dvlo n invnory modl or risl ims wn dmnd r is qudric uncion o ric nd r o driorion is linr uncion o im. is lso ssumd olding cos is linr uncion o im. Undr insnnous rlnismn wi zro ld-im EOQ is drmind or oimizing ol roi undr inlion r. snsiiv nlysis is rsnd wi numricl xml nd.. nroducion is ru uni ric nd or invnory rld coss r dndn on im. Howvr mos o invnory modls in lirur v considrd uni ric nd invnory rld coss o indndn o im nd consn ovr riod undr considrion. Buzco [] modiid clssicl EOQ modl incororing consn inlion r undr dirn ricing olicis. Misr [] Gu l [] Vr nd Pdmnn [] r som o uors wo v sudid invnory modls wi scil rrnc o inlion r. is wll nown dmnd r o ny roduc is lwys in dynmic s. is vriion is du o im or ric or vn wi insnnous lvl o invnory. n conomic lo siz modl or ric dndn dmnd undr quniy nd rig discouns ws dvlod y Burwll [5]. n invnory sysm o mlioring ims or ric dndn dmnd r ws considrd y Mondl l []. You [7] dvlod n invnory modl wi ric nd im dndn dmnd. jn Roy [8] s dvlod n invnory modl or drioring ims wi ric dndn dmnd nd im vrying olding cos. nvnory modlrs so r v considrd wo ys o ric dndn dmnd scnrios linr nd xonnil. linr ric dndn dmnd imlis uniorm cng in dmnd r o roduc r uni ric wrs xonnil ric dndn dmnd imlis vry ig cng in dmnd r o roduc r uni ric. s wo scnrios r qui unusul in rlisic siuions. us qudric ric dndn dmnd my n lrniv roc o xising wo scnrios. So i is rsonl o ssum dmnd r in crin commodiis du o ssonl vriions my ollow qudric uncion o im [i.. D = + + ; c ]. uncionl orm givn ov xlins cclrd grow/dclin in dmnd rns wic my ris du o ssonl dmnd r Knr nd uduri [9]. W my xlin dirn ys o rlisic dmnd rns dnding on signs o nd. Bndri nd srm [] v sudid Singl Priod nvnory Prolm wi Qudric Dmnd Disriuion undr nlunc o Mring Policis. Knr nd uduri [9] v discussd n ordr-lvl invnory rolm wi dmnd r rrsnd y coninuous qudric uncion o im. Sn nd uduri [] v dvlod soc-rviw invnory modl or risl ims wi uniorm rlnismn r nd soc-dndn dmnd. Klm l [] v sudid rolm o roducion lo-siz invnory modl or Wiull drioring im wi qudric dmnd qudric roducion nd sorgs. n ordr lvl EOQ modl or drioring ims in singl wrous sysm wi ric dndd dmnd in non-linr qudric orm s n sudid y Pr l []. Vnswrlu nd Mon [] sudid invnory modl or im vrying driorion nd ric dndn qudric dmnd wi slvg vlu. Vnswrlu nd Rddy [5] dvlod im dndn qudric dmnd invnory modl undr inlion. Rcnly Vnswrlu nd Rddy [] sudid invnory modls wn dmnd is im dndn qudric dmnd nd dly in ymns is cl. n is r w ry o dvlo n ingrd modl wic conins o risiliy nd inlion nomn wi ric dndn qudric dmnd siuion. invnory driorion is ssumd o consn. soluions o modls r rsnd nd lso discussd snsiiviy o modls nd.. ssumions nd Noions mmicl modl is dvlod on ollowing ssumions nd noions: i Slling r D im is ssumd o D c. Wr is iniil r o dmnd is r wi wic dmnd r incrss nd c is r wi wic cng in r dmnd r isl incrss. ii Rlnismn r is inini nd ld im is zro. iii is slling ric r uni.
wl MS nrnionl onrnc on Mngmn iv r o inlion is consn v uni cos nd or invnory rld cos r sujcd o sm r o inlion sy. is imlis ordring quniy cn drmind y minimising ol sysm cos ovr lnning riod. vi is ordring cos im. vii is consn r o driorion. viii dnos uni cos im. ix is invnory lvl im. x Q is ordring quniy im = xi is r uni olding cos xcluding inrs crgs r uni r yr.. Formulion nd Soluion o Modl ojciv o modl is o drmin oimum roi or ims ving ric dndn qudric dmnd nd r o driorion ollows linr uncion o im wi no sorgs. invnory lvl dls s im sss du o dmnd nd driorion during nd du o dmnd only during riod. invnory lvl im dirnil quions wic dscris invnory lvl im r givn y d.. d d d ogr wi = nd =. soluion o quions nd L us considr Ordring Quniy is Q. n Q Q L dnos uni cos im. i.. wr is uni cos im zro. L dnos Ordring cos im. wr i.. is ordring cos im zro. ol sysm cos during lnning riod is sum o Mril cos ordring cos nd rrying cos. ssum = m* Wr m is n ingr or numr o rlnismns o m during riod nd is im wn rlnismns. Ordring cos during riod is... m ] Ordring os is... m wr m. Mril cos during riod is... m ]
wl MS nrnionl onrnc on Mngmn ]... [ m Q ]... [ m Q... m Q Q Similrly rrying os/olding cos during riod is d Bu w v in riod rrying os/olding cos is d d d ol cos ovr riod is = Ordring cos + Mril cos + rrying cos d d Q d d Q sorgs r no llowd n Sls rvnu r cycl is givn y d d D ol roi r uni im = / Sls rvnu ol cos
wl MS nrnionl onrnc on Mngmn ol roi is mximum i i.. c c nd Oiml vlu o is oind solving quion y MHD c c
wl MS nrnionl onrnc on Mngmn 5 lso sisying ollowing condiion nd is ound oimliy condiions r sisid or ollowing wo css viz. i < nd c > wic givs rrdd grow in dmnd modl ii < nd c < givs cclrd dclin in dmnd modl. Numricl Exml o dmonsr civnss o modls dvlod numricl xml is n wi ollowing vlus or rmrs. =5 = 5 c =. = 5 = θ =. i =.5 =. MHD ouu is rsnd in l- nd l- wic conins oimum vlus o im ordring quniy Q nd ol roi o sysm or vrious vlus o inlion rmr nd driorion rmr θ. s ls rovid crin imorn insigs ou rolm undr sudy. Som osrvions r s ollows: viour o o modls dvlod r is lmos similr in nur u r o cng is sligly dirn. oiml vlus o cycl im ordring quniy nd ol cos incrss wi n incrs in inlion r rmr. For som riculr vlus o θ wn inlion r incrss rom.5 o. cycl im nd ordring quniy incrss wil ol roi lso incrss in o modls. For som riculr vlus o wn θ incrss rom.5 o. cycl im nd ordring quniy dcrss wrs ol roi incrss in o modls.. Snsiiv nlysis W now sudy snsiiviy o modls dvlod o xmin imlicions o undrsiming nd ovrsiming rmrs individully nd ll ogr on oiml vlu o cycl im ordring quniy nd ol sysm roi. rsuls r sown in l- nd l-. ollowing osrvions r md rom s wo ls: i ordring quniy Q uni ric nd ol sysm roi incrss dcrss wi incrs dcrs in vlu o rmr wr s cycl im is invrsly rld wi rmr. ii ncrs dcrs in vlus o rmrs nd c dcrs incrs ric r uni ordring quniy nd ol roi wil cycl im incrss dcrss wi nd dcrss incrss wi c. Howvr r o incrs/dcrs is mrginl in cs nd. ordring quniy Q uni ric nd ol sysm roi incrss dcrss wi dcrs incrs in vlu o rmrs nd. iii oimum vlu o ol roi ordring cos nd cycl im is mrginl u uni ric rmin consn o cngs in rmrs iv ol roi o sysm is mor snsiiv n cycl im nd ordring quniy wn vlus o ll rmrs r undr-simd or ovr-simd y 5%. l Rrdd Grow Modl.E. > B< nd > S.No c Q 5-5..5 5.787 9.58 8 5 5-5.. 5.785 9.95 9 7 5-5..7 5.78 9.5 9 9 5-5..8 5.78 9. 79 5 5-5..9 5.78 9.8 8 5-5.. 5.778.7 99
wl MS nrnionl onrnc on Mngmn l Rrdd Dclin Modl.E. > B< nd < S.No c Q 5-5 -..5. 9. 978. 98 5-5 -...9 9.7 978.95 5-5 -..7.7 9. 979.55 9 5-5 -..8. 9.587 98. 5 5-5 -..9. 9.77 98.7 97 5-5 -... 9.988 98. l Rrdd Grow Modl > B< nd > Prmrs % cng ng in % ng in % ng in c. % ng in Q % -5% -5.78.758 -.9 -.89-5% -5.5.98-8.58-7.95 5% 5.85 -.88 8.7 7.95 5% 5.878 -.8.78.77-5%.58.5597 9.58 9. -5% 5.858.99.7.95 5% -5.8 -.9 -.95 -.95 5% -.8 -.7-9.55-9. -5% -.75 -.8 -.98 -.98 c -5% -.597 -.9 -.99 -.975 5%..99.99.975 5%.7985.89.98.9-5% -.8.9785.795.77 ll -5% -.7.98.979.8789 5%.9 -.88 -.98 -.897 5%. -.598 -.9 -.98-5% -.888.9.99.897-5% -.7.958.595 5%.7 -.987 -.5 5%.888-5.5 -.99 -.98-5% -.89.985 -.5-5% -..99 -.8785 5%.8 -.99.8789 5%.9 -.97.585-5% -.5 8.5 -.977-8.9-5% -.8.585 -.7877 -.89 5%. -.95.795.5585 5% -5.78.758.87 7. l Rrdd Dclin Modl > B< nd < Prmrs % cng ng in % ng in % ng in c. % ng in % -5% -.7985.597-5.8 -.55-5%.777755 -.8-8.7-7. 5%.7779 -.7 8.789 7.777 5% 5.8588 -.78 5.9. -5%.798558 -.95 9.877755 9.999
wl MS nrnionl onrnc on Mngmn 7 c ll -5% -.97.9.98. 5% -.89.89 -.77 -.88 5%.87.9-9.87-9.555-5%.9.87.555-5% -. -.95.7. 5% -.589 -.89 -.75 -. 5% -..8 -.8 -.55-5% -.87.99.75. -5%.89 -.8.55.999 5%. -.98 -.55 -.888 5% -.978.9877 -.75 -. -5% -.7.57.7.997-5%.777 -.987.7.5557 5%.9-5.7 -.7 -.5 5% -. -.7 -.99-5% -.95.87 -.5757-5%.9.75 -.888 5%.5 -.5.85858 5% -.8 8.9985 -.8.575758-5% -.85.575 -.7-8. -5%. -.7 -.795 -.777 5%.5 -.599.95.575758 5% -.7985.597.8 7.777. Rrncs. Buzco J.. 975. Economic ordr quniis wi inlion. Or. Rs.Q. Vol. 55-558.. Misr R.B. 979. no on oiml invnory mngmn undr inlion Nvl Rs. Logis. Vol..-5.. Gu R. Vr P. nd Swru K. 985 nvnory mngmn dvlomn rviw wi scil rrnc o risiliy inlion nd soc-dndn consumion owrds coninuing Educion Vol. Oc. Nov..-7.. Pdmnn G. nd Vr P. 99. n EOQ modl or ims wi soc dndn consumion r nd xonnil dcy. Enginring oss nd Producion Economics 8.-. 5. Burwll.H. Dv D.S. Fizric K.E. Roy M.R. 997 Economic lo siz modl or ric-dndn dmnd undr quniy nd rig discouns nrnionl Journl o Producion Economics 8-55.. Mondl B. Buni.K. Mii M. n invnory sysm o mlioring ims or ric dndn dmnd r omurs nd ndusril Enginring 5-5. 7. You S.P. 5 nvnory olicy or roducs wi ric nd im dndn dmnds Journl o orions rsrc sociy 5 87-87. 8. jn Roy 8 n invnory modl or drioring ims wi ric dndn dmnd nd im-vrying olding cos MO-dvnc modling nd oimizion Vol. No.. 9. R.M.Bndri nd P.K.Srm. singl riod invnory rolm wi qudric dmnd disriuion undr inlunc o Mr olicis Eng. Scinc Vol.. No.. 7-7.. S.Krn nd K.S.uduri. no on ordr-lvl invnory modl or drioring im wi im-dndn qudric dmnd omurs nd Orions rsrc Vol..9-9.. Sisnr Sn nd K.S.udry. Soc-Rviw EOQ Modl wi Soc-Dndn Dmnd Qudric Driorion R dvncd Modlling nd Oimizion vol. No. 5-... Klm D. Sml S. K. Su & M. Misr Producion Lo-siz nvnory Modl or Wiull Drioring m wi Qudric Dmnd Qudric Producion nd Sorgs nrnionl Journl o omur Scinc & ommunicion Vol. No. Jn.. 59-.. Pr S.K. Ln.K. nd R P.. n Ordr Lvl EOQ Modl or Drioring ms in Singl Wrous Sysm wi Pric Dndd Dmnd in Non-Linr Qudric Form nrnionl Journl o omuionl nd lid Mmics Vol.5 No.. 77 88. R.Vnswrlu nd R. Mon n nvnory Modl or im Vrying Driorion nd Pric Dndn Qudric Dmnd wi Slvg Vlu Journl o omuionl nd lid Mmics 7/; :-7.
8 wl MS nrnionl onrnc on Mngmn 5. R.Vnswrlu nd M.S.Rddy im Dndn Qudric Dmnd nvnory Modls Undr nlion Glol Journl o Pur nd lid Mmics Volum Numr. 77-85.. R.Vnswrlu nd M.S.Rddy im Dndn Qudric Dmnd nvnory Modls wn Dly in Pymns is cl nrnionl Journl o Modrn Enginring Rsrc JMER Vol. No. -7.