Price Dependent Quadratic Demand Inventory Models with Variable Holding Cost and Inflation Rate
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1 Pric Dndn Qudric Dmnd nvnory Modls wi Vril Holding os nd nlion R SBN: 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.
2 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 ]
3 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
4 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
5 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
6 wl MS nrnionl onrnc on Mngmn l Rrdd Dclin Modl.E. > B< nd < S.No c Q l Rrdd Grow Modl > B< nd > Prmrs % cng ng in % ng in % ng in c. % ng in Q % -5% % % % % % % % % c -5% % % % ll -5% % % % % % % % % % % % % % % l Rrdd Dclin Modl > B< nd < Prmrs % cng ng in % ng in % ng in c. % ng in % -5% % % % %
7 wl MS nrnionl onrnc on Mngmn 7 c ll -5% % % % % % % % % % % % % % % % % % % % % % % Rrncs. Buzco J Economic ordr quniis wi inlion. Or. Rs.Q. Vol Misr R.B no on oiml invnory mngmn undr inlion Nvl Rs. Logis. Vol 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 Pdmnn G. nd Vr P. 99. n EOQ modl or ims wi soc dndn consumion r nd xonnil dcy. Enginring oss nd Producion Economics 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 Mondl B. Buni.K. Mii M. n invnory sysm o mlioring ims or ric dndn dmnd r omurs nd ndusril Enginring You S.P. 5 nvnory olicy or roducs wi ric nd im dndn dmnds Journl o orions rsrc sociy 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 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 Sisnr Sn nd K.S.udry. Soc-Rviw EOQ Modl wi Soc-Dndn Dmnd Qudric Driorion R dvncd Modlling nd Oimizion vol. No 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 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 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 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 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.
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