Inventory Model with Quadratic Demand under the Two Warehouse Management System

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Prin : - nlin : - A K Mlik l. / nrnionl Jornl of Enginring nd hnology JE nnory Modl wih Qdri Dmnd ndr h wo Wrhos Mngmn ysm A K Mlik Dipk Chkrory Kpil Kmr Bnsl nd * ish Kmr Assoi Profssor Dprmn of Mhmis B.K. Birl nsi of Enginring &hnology Pilni jshn ndi jndrmlik@gmil.om srh holr Dprmn of Mhmis inghni Unirsiy Phri di Jhnjhn jshn ndi dipkhkrory@gmil.om Hd srh & Pliion M Unirsiy C Cmps Modingr drkpilnsl@gmil.om Assoi Profssor Dprmn of Mhmis D.. PG Collg Mr U.P. skg@gmil.om *Corrsponding hor: skg@gmil.om Asr- h oji of his mnsrip is o dlop n mhmil modl for wo wrhoss. Hr w ssm wo wrhoss sysm on is wn Wrhos W nd ohr is n Wrhos W; d o ssonl prod for soring h rw mril/prods. h proposd sdy is mn for qdri dmnd nd ril holding oss in whih shorgs r no llowd. h solion oind y h proposd pproh illsri n xmpl for h opimm ol innory os nd opimm innory ll. Kywords: Qdri dmnd W nd W Vril holding nd driorion.. DUC Moid y h rn onriions Ghr nd hrdr Cor nd Philip md in h fild of h ppliion of innory modls in indsris h oj of his work will o insig h opimm innory poliy nd opimm ll for h innory mngmn sysms. Firs Hrly proposd hniqs for wo wrhoss innory mngmn sysm in whih h holding os of h rn wrhos is lrgr hn h holding os of h W. Pkkl nd Ahry prsnd mhod for soling wo wrhos innory mngmn sysm for drioring ims. Apr from h lo of work hs n don o dlop wo-wrhoss innory mngmn sysm wih drioring ims y h rsrhrs lik L nd M Khrn nd Chdhry Yng Mlik l. i nd Xi Mlik l. L nd Hs ingh nd Mlik & rkr l. nd ohrs. ingh nd Mlik formld wo sorg innory modl wih linr driorion nd xponnil dmnd. Gp l. prsns n innory modl wih wo wrhoss nd prodion r is fnion of dmnd. ingh nd Mlik dlopd wo shops innory sysm wih ril holding os. n prsnd n innory modl wih ril drioring r wih opiml slling pri. ingh l & dlopd mhmil wo wrhos innory mngmn sysm. Also l prsnd qdrilly yp dmnd innory modl wih ril driorion nd h wo wrhoss mngmn sysm. Kmr l. proposd wo wrhos mngmn sysm wih ril dmnd. Vshish l disssd wo wrhos innory modl wih qdri dmnd nd ril holding os. hrm nd Bnsl dlopd n innory modl for non-insnnos drioring ims. Moid y his id in his ppr w h prsnd qdri dmnd wih wo wrhoss innory modl for h drioring ims. Hr w ssm wo wrhoss sysm wih ril driorions in h oh h wrhoss. Holding os is fnion of im nd onsidrd; h holding os of W is highr hn W. hrfor h ol innory os of his mngmn sysm is opimizd wih nmril xmpl. D:./ij//i/ Vol o Jn-Jl

. A AD AUMP Following noions nd ssmpions r sd o dloping his modl:. h Dmnd D= -- whr >.. h driorion rs in rn wrhos nd own wrhos is nd ; nd dfind y = + nd = + rspily.. h holding oss in rn wrhos nd own wrhos is h nd g; nd dfind y h=h +h nd g=g +g rspily.. horgs r no prmid in his modl. C rdring os pr ordr yl Mximm innory ll in rn wrhos Mximm innory ll in own wrhos C d Drioring os in oh h wrhoss pr ni im in whih no driorion ors C ol innory os pr ni im. MAHEMACAL MDEL Aording o o mniond h noion nd ssmpions mniond nd r h innory lls for h rn nd own wrhoss rspily. h piis of rn wrhos nd own wrhoss r nd nis rspily. n [ ] h innory ll drs d o dmnd only nd = + h innory ll oms zro fr sisfying h dmnd nd driorion. n im priod [ + ] h nnory ll drss d o oh h dmnd nd driorion h nnory ll drss d o driorion. n [ + + + =] h nnory ll drss d o oh h dmnd nd driorion nd = h innory ll oms zro fr sisfying h dmnd nd driorion. h following diffrnil qions showing h hior of innory lls in rn wrhos nd own wrhoss: D D d d D d d Wih h ondry ondiions. h olion of h o sysm of qions w g. Whr. D o oniniy of h innory lls nd w h. Prin : - nlin : - A K Mlik l. / nrnionl Jornl of Enginring nd hnology JE D:./ij//i/ Vol o Jn-Jl

Prin : - nlin : - A K Mlik l. / nrnionl Jornl of Enginring nd hnology JE nd h mximm innory ll is L=+.. x h ol innory os for h dlopd innory modl pr yl onsiss of h following lmns: ow h ordring os for h dlopd modl is dnod s C nd dfind is C = C... h nnory holding os in n Wrhos for h dlopd modl is dnod s HC W nd dfind is HC W h d h h h h h h h h. h nnory holding os in wn Wrhos for h dlopd modl is dnod s HC W nd dfind is HC W g d g g.. g g g g g g h drioring os in n Wrhos for h dlopd modl is dnod s DC W nd dfind is DC W C d d C d. h drioring os in wn Wrhos for h dlopd modl is dnod s DC W nd dfind is DC W C d d C d. h ol innory os C pr ni im is C C HC W HC W DC W DC h ol rln innory os is minimm if C C W nd C... V. UMECAL EXAMPLE o dmonsr h o rsls for h dlopd modl w onsidrd h xmpl: = =. =. h=.+. g=.+. =.+.β.+. C = C d =. nd * =.yr. h ol innory os C is minimm whn * =. * =. opiml ordr qniy is L * = nd h ol minimm innory os C * =. V. CCLU n his ppr n mp hs n hrogh o soling his mhmil modl wih wo wrhoss. D o ssonl prod h soring of prod/ims is ry ssnil for minimizing h ol innory os. For dloping his ppr w onsidr som imporn prmrs lik qdri dmnd ril holding os nd ril drioring os ndr h wo wrhos mngmn sysm whih hs no y n disssd. h modl xplind in his sdy nds o impro h opiml ordr qniy nd ol minimizing os for mnfring nd riling indsris. For fr rsrh i wold inrsing o sdy h innory modls wih proilisi nd sohsi prodion inflion nd pril klogging n kn forwrd. ACKWLEDGME h hors wold lik o hnk h Edior-in-hif of h jornl nd iwr for hir sppor nd nfiil ommns o impromn of h ppr. h hors wold lik o xprss hir hris grid o Dr. P.. Bhngr Diror B.K. Birl nsi of Enginring & hnology Pilni jshn ndi. EFEECE [] Ghr P.M. hrdr G.P.. A modl for n xponnilly dying innory. Jornl of ndsril Enginring. -. [] Cor.P. nd Philip G.P.. An EQ modl for ims wih Will disriion driorion AE rns. -. [] Hrly V. onld.. n h EQ modl wo lls of sorg. psrh -. [] Pkkl. nd Ahry K.. A drminisi innory modl for drioring ims wih wo wrhoss nd fini rplnishmn r Eropn J. pr. s.. [] L C. nd M C.. piml innory poliy for drioring ims wih wo-wrhos nd im-dpndn dmnds Prod. Pln. nd Con.. [] Khrn. nd Chdhri K... A no on ordr ll innory modl for drioring im wih im dpndn qdri dmnd Comp. nd ps s. -. D:./ij//i/ Vol o Jn-Jl

[] Yng H.. wo-wrhos innory modls for drioring ims wih shorg ndr inflion Eropn J. pr. s.. [] Mlik A. K. ingh.. nd Gp C. B.. An innory modl for drioring ims ndr FF disphing poliy wih wo wrhos nd im dpndn dmnd Gni ndsh Vol. o. -. [] i B. nd Xi J.. A no on wo-wrhos innory modl wih driorion ndr FF disph poliy Eropn J. pr. s.. [] L C.C. nd Hs. L.. A wo-wrhos prodion modl for drioring innory ims wih im-dpndn dmnds Eropn Jornl of prionl srh -. [] ingh.. Mlik A.K.. Eff of inflion on wo wrhos prodion innory sysms wih xponnil dmnd nd ril driorion nrnionl Jornl of Mhmil nd Appliions - -. [] Mlik A. K. ingh.. nd Gp C. B..wo wrhos innory modl wih xponnil dmnd nd im-dpndn klogging r for drioring ims Gni ndsh Vol. o. -. [] ingh.. Mlik A.K..wo wrhoss modl wih inflion indd dmnd ndr h rdi priod nrnionl Jornl of Applid Mhmil Anlysis nd Appliions Vol. o. -. [] rkr. n.. nd Chdhri K.. A fini rplnishmn modl wih inrsing dmnd ndr inflion n. J. Mh. pr. s.. [] Gp C. B. Mlik A. K. nd ingh... A wo Wrhos nnory Modl for Drioring ms wih Dmnd Dpndn Prodion Gni ndsh Vol. o. -. [] ingh.. Mlik A.K.. nnory sysm for dying ims wih ril holding os nd wo shops nrnionl Jornl of Mhmil ins Vol. o. - -. [] n... piml slling pri nd lo siz wih im rying driorion nd pril klogging Appl. Mh. Comp.. [] ingh.. nd Mlik A.K.. piml ordring poliy wih linr driorion xponnil dmnd nd wo sorg piy n. J. Mh. i. -. [] ingh.. Mlik A.K. nd Gp. K.. wo Wrhoss nnory Modl wih Pril Bkordring nd Mli-Vri Dmnd ndr nflion nrnionl Jornl of prions srh nd pimizion Vol. o. -. [] ingh.. Mlik A.K. nd Gp. K.. wo Wrhoss nnory Modl for on-nsnnos Drioring ms Wih ok-dpndn Dmnd nrnionl rnsions in Applid ins Vol. o. -. [] h B. K. rkr B. Goswmi A.. A wo-wrhos innory modl wih inrsing dmnd nd im rying driorion. ini rni E -. [] Kmr Adrsh ingh Amrdp Bnsl Kpil Kmr wo wrhos innory modl wih rmp yp dmnd shorgs ndr inflionry nironmn Jornl of Mhmis -JM -. [] Vshish V. oni. Jkhr. ihg D. nd Mlik A. K.. A wo Wrhos nnory Modl wih Qdri Drsing Dmnd nd im Dpndn Holding Cos AP Confrn Prodings ; doi:./.. [] hrm M. K. nd Bnsl K. K.. nnory Modl for on-nsnnos Dying ms wih Lrning Eff ndr Pril Bklogging nd nflion Glol Jornl of Pr nd Applid Mhmis -. Appndis Prin : - nlin : - A K Mlik l. / nrnionl Jornl of Enginring nd hnology JE D:./ij//i/ Vol o Jn-Jl

Prin : - nlin : - A K Mlik l. / nrnionl Jornl of Enginring nd hnology JE D:./ij//i/ Vol o Jn-Jl

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