Inventory Management Models with Variable Holding Cost and Salvage value
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1 OSR Journl of Business nd Mngemen OSR-JBM e-ssn: -X p-ssn: 9-. Volume ssue Jul. - Aug. PP - nvenory Mngemen Models wi Vrile Holding os nd Slvge vlue R.Mon R.Venkeswrlu Memics Dep ollege of Miliry Engineering- Pune ndi GAM Scool of nernionl Business -GAM Universiy Viskpnm ndi Asrc: nvenory mngemen models re developed for deerioring iems wen e demnd re is ssumed o e liner funcion of ime nd e deeriorion re is proporionl o ime. e model is solved wen sorges re llowed. e slvge vlue is used for deeriored iems in e sysem. A numericl exmple is ken o discuss e sensiiviy of e models. Key words: Deeriorion re liner demnd slvge vlue sorges ime-dependen models. nroducion e ssumpion of consn demnd re is no lwys pplicle o mny invenory iems like elecronic goods vegeles food suffs fsionle cloes ec. since flucuions in demnd re. nroducing new producs will rc more in demnd during e grow pse of eir life cycle. is eviden some produc my decline due o e inroducion of new producs due o e preference or influencing cusomer s coice. So i is wor emp e penomenon o develop deerioring invenory models wi ime-vrying demnd re pern. n developing nvenory models wo kinds of ime-vrying demnds so fr i oninuous ime & ii discree ime. Mny coninuous ime invenory models ve een developed king in o e considerion like linerly incresing /decresing demnd [i.e. D = + [ or ]. Gre nd Scrder 9 sudied n invenory model for exponenilly decying. over nd Pilip 9 developed n invenory model for ime dependen re of deeriorion. Aggrwl 9 proposed n order level invenory model for sysem wi consn re of deeriorion. Dve nd Pel 9 sudied lo size model for ime proporionl demnd wi consn deeriorion. De nd ouduri 9 sudied eurisic pproc for replenismen of rended invenories wi sorges. Hrig 99 developed n invenory model of deerioring iems for ime-vrying demnd wi sorges. krori nd ouduri 99 proposed n EOQ model for deerioring iems of liner rend in demnd wi sorges in ll cycles. Giri nd uduri 99 developed eurisic model for deerioring iems of ime vrying demnd nd coss considering sorges. Goyl nd Giri sudied survey of recen rend in deerioring invenory model. Mondl e. l developed n invenory model of melioring iems for price dependen demnd re. You sudied e invenory sysem for e producs wi price nd ime dependen demnds. Ajn Roy proposed n invenory model for deerioring iems wi price dependen demnd nd ime vrying olding cos wi nd wiou sorges. Misr nd Sing sudied n invenory model for deerioring iems wi ime dependen demnd nd pril cklogging. Recenly Misr developed n invenory model wi Weiull re of deeriorion nd consn demnd. He incorpored vrile olding cos considering sorges nd lso slvge vlue. Viks Srm nd Rek developed n invenory model for ime dependn demnd for deerioring iems wi Weiull re of deeriorion nd sorges. n is pper we consider n order level invenory prolem wi ime-dependen deeriorion wen e demnd re is liner funcion of ime. Sorges re llowed in is cse nd e ime orizon is infinie. e opiml ol cos is oined considering e slvge vlue for deeriored iems. e sensiiviy nlysis is done wi numericl exmple.. Assumpions nd noions e memicl model is developed on e following ssumpions nd noions: i e demnd re D ime is ssumed o e D = +. ii Replenismen re is infinie nd led ime is zero. iii A e ordering cos per order is known nd consn. iv θ = θ is e deeriorion re < θ <. v e cos per uni vi +α > α> e olding cos per uni vii is e invenory level ime. viii e order quniy in one cycle is q. Pge
2 nvenory Mngemen Models wi Vrile Holding os nd Slvge vlue Pge ix e slvge vlue γ* γ < is ssocied wi deeriored unis during cycle ime. x D e numer of deerioring unis per order wi one cycle ime. xi π is e sorge cos per uni per order. Formulion nd soluion of e model e differenil equion wic descries e insnneous invenory level ime cn e wrien s d d d d wi e iniil condiion e soluion of equion using iniil condiions is given y = e + K e K Using e condiion = we ge e vlue of K. Now susiuing is vlue in e ove equion e soluion is oined s Using = Q we oin Q e soluion of equion using e oundry condiion is V. nvenory Model wi sorges e ol cos of e invenory sysem consiss of e following cos:. rrying cos/olding cos per cycle = d
3 nvenory Mngemen Models wi Vrile Holding os nd Slvge vlue 9 Pge.9. H. Ordering cos O = A. e numer of unis deeriored during is cycle ime is D were d D Q D D. os due o deeriorion =*D D. Sorge cos S = d S 9. Slvge Vlue SV of deeriored unis = D * SV ol os = nvenory Holding cos + Ordering cos + + Sorge cos + os due o deeriorion Slvge vlue..9. A e necessry condiion for minimizing e ol cos is nd ie.
4 nvenory Mngemen Models wi Vrile Holding os nd Slvge vlue Pge.9*.* nd.9. A Provided.9*.*.9. A
5 nvenory Mngemen Models wi Vrile Holding os nd Slvge vlue..9 V. Numericl Exmple By puing proper unis of prmeric vlues for A = = = = θ =. =. α =.9 π= γ =. Using MAHAD Sofwre e opiml vlues e invenory sysem re =. =.9 =.9. V. Sensiiviy Anlysis We will sudy e effec of cnges mde in e vlues of e prmeers A α γ nd π on e opiml cycle ime ol cos nd EOQ of ese models. We ve e following inferences cn e mde from le-: Decrese in e prmeers A nd π decreses e ol opiml sysem cos. Similrly e increse in ese prmeers increses e ol opiml cos. e effec of ese prmeers is more pronounced on e ol cos of e sysem. e effec of e prmeers nd α on e ol opiml cos is similr u e re of cnge is more in cse of prmeer. e ol opiml cos of e sysem is no effeced y e cnges in e prmeers nd γ. my e conclude e slvge vlue for deeriored iems is no effecing o e ol cos. le- Prmeer % cnge A α γ π Pge
6 nvenory Mngemen Models wi Vrile Holding os nd Slvge vlue V. onclusions We ve developed invenory mngemen models for deerioring iems wen e demnd re is ssumed o e liner funcion of ime. is ssumed e deeriorion re is proporionl o ime. We ve solved e model due o sorges. is noed e slvge vlue for deeriored iems is insignificn in e ol opiml cos of e sysem. References [] Gre P.M. nd Scrder G.F. An nvenory model for exponenilly deerioring iems Journl of ndusril Engineering 9 - [] over R.P nd Pilip G.. An EOQ model for iems wi Weiull disriuion deeriorion AE rnscions 9 - [] Aggrwl S.P A noe on n order-level invenory model for sysem wi consn re of deeriorion Opserc 9 - [] Dve U. nd Pel L.K. S i- policy invenory model for deerioring iems wi ime proporionl demnd. Journl of Operionl Reserc Sociey 9 - [] De M. nd uduri K. A noe on e eurisic for replenismen of rended invenories considering sorges. Journl of Operionl Reserc Sociey 9 9- [] Hrig M An EOQ model for deerioring iems wi sorges nd ime-vrying demnd. Journl of Operionl Reserc Sociey [] krori. nd uduri K.S An EOQ model for iems wi liner rend in demnd nd sorges in ll cycles nernionl Journl of Producion Economics [] Giri B. nd uduri K.S Heurisic model for deerioring iems wi sorges nernionl Journl of Sysem Science99-9 [9] Goyl S.K nd Giri. B.. Recen rends in modeling of deerioring invenory Europen Journl of Operions reserc Vol. pp.-. [] Mondl B. Buni A.K nd Mii M. An invenory sysem of melioring iems for price dependen demnd re ompuers nd ndusril Engineering - [] You S.P. nvenory policy for producs wi price nd ime dependen demnds Journl of Operionl Reserc Sociey - [] Ajn Roy An nvenory model for deerioring iems wi price dependn demnd nd ime-vrying olding cos AMO- Advnced modeling nd opimizion volume numer [] Misr V.K nd Sing L.S Deerioring invenory model wi ime dependen demnd nd pril cklogging Applied Memicl sciences -9 [] Vinod Kumr Misr nvenory model for ime dependen olding cos nd deeriorion wi slvge vlue nd sorges. e Journl of Memics nd ompuer Science Vol. No. - [] Viks Srm nd Rek Rni uduri An invenory Model for deerioring iems wi Weiull Deeriorion wi ime Dependen Demnd nd sorges Reserc Journl of Mngemen Sciences Vol. - Pge
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