Inventory Management Model with Quadratic Demand, Variable Holding Cost with Salvage value
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1 Asr Rsr Journl of Mngmn Sins ISSN 9 7 Vol. 8- Jnury Rs. J. Mngmn Si. Invnory Mngmn Modl wi udri Dmnd Vril Holding Cos wi Slvg vlu Mon R. nd Vnkswrlu R. F-Civil Dp of Mmis Collg of Miliry Enginring Pun INDIA GIAM Sool of Inrnionl Businss GIAM Univrsiy Viskpnm INDIA Avill onlin : Rivd 6 Oor rvisd 8 Novmr pd nd Dmr In is ppr invnory mngmn modl for drioring produs wi qudri funion of im s r of dmnd. Hr driorion is onsidrd s wiull driorion r. Sorgs r llowd. slvg vlu is lso usd for driord ims in sysm. ol os is luld y onsidring vril olding os. Suil vlus for prmrs onsidrd in numril xmpl. Snsiiviy nlysis is lso disussd. Kywords: udri dmnd wiull driorion r slvg vlu sorgs. Inroduion Rsrrs d n dvlopd invnory modls y ssuming onsn dmnd r for ims lik lroni goods vgls food suffs fsionl los. sin dmnd r is lwys fluuing nd inroduing nw produs will r mor in dmnd. Du o usomr s oi nd rrivl of nw produ in mrks normlly som produ my dlin in dmnd r. Amping pnomnon of im-vrying dmnd prn in drioring invnory modls yilds vry mu rl im ppliion. So fr in dvloping Invnory modls r r wo kinds of im-vrying dmnds nmly disr im nd Coninuous im. Mny of oninuous im invnory modls wr dvlopd y onsidring lik linrly inrsing /drsing dmnd prns. Gr nd Srdr sudid n invnory mngmn modl inorporing r of dmnd is dying xponnilly. Covr nd Pilip sudid n invnory modl wi driorion r is im dpndn. Aggrwl disussd n invnory modl for sysm wi r of driorion is onsn. Dv nd Pl proposd n EO modl for im proporionl dmnd wi onsn driorion. D nd Couduri sudid n invnory modl onsidring rndd invnoris y ssuming sorg. Hrig disussd n invnory modl for imvrying dmnd of drioring produs y onsidring sorgs r llowd 6. Ckrori nd Couduri proposd n invnory modl for drioring ims of linr dmnd lso in ll yls sorgs r llowd 7. Giri nd Cuduri sudid urisi modl for drioring ims of im vrying dmnd nd oss wi sorgs 8. Goyl nd Giri orougly sudid survy of rn rnd in drioring invnory modls 9. Mondl. l disussd EO modl for mlioring produs y onsidring pri dpndn dmnd. You proposd n invnory sysm for ims wi im nd pri dpndn dmnds. Ajn Roy proposd n EO modl wi dmnd r is pri dpndn nd inorporing vril olding os wi rsp o im y onsidring wi / wiou sorgs of drioring produs. Misr nd Sing sudid n invnory modl im dpndn dmnd of drioring ims onsidring pril klogging. Misr proposd n invnory modl of onsn dmnd wi Wiull r of driorion. H inorpord vril olding os onsidring sorgs nd slvg vlu. Viks Srm nd Rk sudid n EO modl for im dpndn dmnd for drioring produs wi Wiull driorion r lso onsidring sorgs. Vnkswrlu nd Mon proposd n EO modl wi - prmr Wiull driorion im dpndn qudri dmnd nd slvg vlu 6. Vnkswrlu nd Mon dvlopd n EO modl for im vrying driorion nd pri dpndn qudri dmnd wi slvg vlu 7. Mon nd Vnkswrlu sudid n invnory mngmn modls wi vril olding os nd slvg vlu 8. Mon nd Vnkswrlu proposd n invnory modl for im Dpndn qudri dmnd wi slvg onsidring driorion r is im dpndn 9. In is ppr w v onsidrd n ordr lvl invnory prolm wn dmnd r is qudri funion of im wi Wiull driorion nd vril olding Cos is inorpord. Sorgs r llowd. im orizon is infini. Slvg vlu lso onsidrd for opiml ol os. Suil numril xmpl nd snsiiviy nlysis is lso don. Inrnionl Sin Congrss Assoiion 8
2 Rsr Journl of Mngmn Sins ISSN 9 7 Vol. 8- Jnury Rs. J. Mngmn Si. Inrnionl Sin Congrss Assoiion 9 Assumpions nd noions W inorpord following noions nd ssumpions o dvlop mmil modl: r of dmnd D ny im is ssumd o D R of rplnismn is infini Ld im is zro A ordring os pr ordr θ - -Prmr Wiull Driorion r < θ < C os pr uni pr ordr r > r> olding os pr uni I is invnory lvl im. q is ordr quniy in on yl γ*c γ < slvg vlu ssoid wi driord unis during yl im NDU numr of drioring unis pr ordr wi on yl im π os of sorgs pr uni pr ordr Formulion nd soluion of modl govrning diffrnil quion wi dsris vriion of invnory w.r.o o im is ; d d θ θ d d ; wi. Equion is linr firs ordr quion n On ingrion ov quion yilds k wr k is n ingrl onsn. Hr w v xpndd nd ignord igr ordr rms s is smll. Using givn oundry ondiions soluion of ov diffrnil quion is givn y Sin w g Solving quion nd is soluion is givn y In yl im numr of drioring unis NDU is givn y NDU d D 6 wr D is r of Dmnd. numr of driord unis NDU Cos du o driorion CD C 7 Slvg vlu SV γ C 8 Invnory im vrying olding os IHC in inrvl is
3 Rsr Journl of Mngmn Sins ISSN 9 7 Vol. 8- Jnury Rs. J. Mngmn Si. Inrnionl Sin Congrss Assoiion rd rd o IHC d r d IHC 6 8 r 9 Ordring Cos A Sorg os d π π ol os C of sysm is givn y C OCIHCSCCD-SV 6 8 γ π C r A nssry ondiions for minimizing ol os is C C nd > C C C Numril Exmpl By puing propr unis of prmri vlus for A C.9.6 r.. π γ. Using MAHCAD Sofwr opiml vlus invnory sysm r.9. q.8 C 7.6. Snsiiviy Anlysis From is modl w nlyz rousnss of prmr vlus A π C nd γ on opiml yl im C ol os nd EO of is modl. From l- infrns r s follows: i. Ordring quniy nd yl im inrss drss wrs nd ol os C inrs drs wi inrs drs in vlus of u r of ng is insignifin. ii. W noi ngs in vlus of yl im ordring quniy nd ol sysm os r similr wn prmrs nd r ovr siming or undrsiming. Howvr prmr s disin ff on ll s vlus. iii. ff of on yl im nd ordring quniy is qui similr wil i is diffrn on ol sysm os. Bu r of ng on s vlus is lmos sm. iv. ff of prmrs A nd C on opimum ol os vlu is similr u nging r is signifin in s of A. yl im nd ordring quniy inrs drs wi n inrs drs in s of A u ff is qui opposi in s of C. v. ff of prmrs γ nd π on opimum yl im ordring quniy nd ol os is qui opposi wn w inrs or drs vlus of s wo prmrs. vi. ol os is igly snsiiv n nd ordring quniy wn vlus of ll prmrs r undr-simd or ovr-simd y %. Conlusion W v dvlopd n EO modl for drioring produs y ssuming r of dmndd is qudri wi rsp o im. In is ppr driorion r follows -prmr Wiull disriuion. W v solvd is modl wi vril olding os nd sorgs. Anlyzing is modl C ol os is ig snsiiviy n yl im nd ordring quniy wn vlus of ll prmrs r ovrsimd or undrsimd.
4 Rsr Journl of Mngmn Sins ISSN 9 7 Vol. 8- Jnury Rs. J. Mngmn Si. l- Snsiiviy nlysis for prmrs A π C nd γ -% o % Prmr % ng q C A C γ π All prmrs Rfrns. Gr P.M. nd Srdr G.F. An Invnory modl for xponnilly drioring ims J. of Indusril Engg Covr R.P nd Pilip G.C. An EO modl for ims wi Wiull disriuion driorion AIIE rnsions Aggrwl S.P. A no on n ordr-lvl invnory modl for sysm wi onsn r of driorion Opsr Dv U. nd Pl L.K. S i - poliy invnory modl for drioring ims wi im proporionl dmnd J. of Op. Rs. Soiy D M. nd Cuduri K. A no on urisi for rplnismn of rndd invnoris onsidring sorgs J. of Op. Rs. Soiy Hrig M. An EO modl for drioring ims wi sorgs nd im-vrying dmnd J. of Op. Rs. Soiy Ckrori. nd Cuduri K.S. An EO modl for ims wi linr rnd in dmnd nd sorgs in ll yls In. J. of Prod. Eonomis Inrnionl Sin Congrss Assoiion
5 Rsr Journl of Mngmn Sins ISSN 9 7 Vol. 8- Jnury Rs. J. Mngmn Si. 8. Giri B.C nd Cuduri K.S. Hurisi modl for drioring ims wi sorgs In. J. of Sys. Si Goyl S.K nd Giri. B.C. Rn rnds in modling of drioring invnory E. J. of Op. rs. -6. Mondl B. Buni A.K nd Mii M. An invnory sysm of mlioring ims for pri dpndn dmnd r Comp. nd Ind. Engg. -6. You S.P. Invnory poliy for produs wi pri nd im dpndn dmnds J. of Op. Rs. Soiy Ajn Roy An Invnory modl for drioring ims wi pri dpndn dmnd nd im-vrying olding os AMO-Adv. Mod. nd opm. 8. Misr V.K nd Sing L.S. Drioring invnory modl wi im dpndn dmnd nd pril klogging App. M.l Si Vinod Kumr Misr Invnory modl for im dpndn olding os nd driorion wi slvg vlu nd sorgs J. of M. nd Comp. Si Viks Srm nd Rk Rni Cuduri An invnory Modl for drioring ims wi Wiull Driorion wi im Dpndn Dmnd nd sorgs Rs. J. of Mgm Si Vnkswrlu R. nd Mon R. An Invnory Modl wi Wiull Driorion im Dpndn udri Dmnd nd Slvg Vlu AIMS - Prodings Bnglor 7. Vnkswrlu R. nd Mon R. An Invnory Modl for im Vrying Driorion nd Pri Dpndn udri Dmnd wi slvg vlu Ind. J. of Compuionl nd App.d M Mon R nd Vnkswrlu R. Invnory Mngmn Modls wi Vril Holding Cos nd Slvg Vlu IOSR J. of Busi. nd Mgm IOSR-JBM 7-9. Mon R. nd Vnkswrlu R. Invnory Modl for im Dpndn Driorion im Dpndn udri Dmnd nd Slvg Vlu J of In. M.Soy In prss Inrnionl Sin Congrss Assoiion
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