Analysis of purchasing activity with discounted cash flow inventory models
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1 őelyanulmányk Vállalagazdaságan néze 093 Budapes Fıvám é Fax: Analyss f puasng avy w dsuned as flw nveny mdels me Dbs Gyöngy Vöösmay 32. sz. őelyanulmány HU SSN auguszus Budapes vnus Egyeem Vállalagazdaságan néze Fıvám é 8. H-093 Budapes Hungay
2 Analyss f puasng avy w dsuned as flw nveny mdels me Dbs Gyöngy Vöösmay Depamen f Lgss and Supply an anagemen nsue f Busness Enms vnus Unvesy f Budapes Budapes vnus Egyeem 093 Budapes Fıvám é 8. Beszezés evékenység elemzése dszknál pénzáamlású készlemdellel Abszak. A klasszkus éelnagyság pbléma ké fnsabb készleezés kölsége agad meg: endelés és készleaás kölségek. Ebben a dlgzaban a vállalak készpénz áamlásának a beszezés evékenysége gyakl aásá vzsgáljuk. Ebben az elemzésben a készpénzáamlás egyenlısége asználjuk amely nagyban emlékeze a készleegyenleeke. Eljáásunkban a beszezés és endelés flyama dszknálva vzsgáljuk. A kölségfüggvény lneás készpénzaás a pénzkadás asznleeıség és lneás kamakölségbıl áll. Bemuajuk a vzsgál mdell pmáls megldásá. Az pmáls megldás egy számpéldával lluszáljuk. Kulsszavak: Neó jelenéék Dszknál as flw Készpénzáamlás pbléma Készleezés mdell Beszezés Absa. e lassal enm de quany mdel as w ypes f ss: deng and nveny ldng ss. n s pape we y nvesgae e effe f puasng avy n as flw f a fm. n e examnans we use a as flw deny smla a f n nveny mdelng. n u appa we analyze e puasng and deng pess w dsuned ss. e s funn f e mdel nsss f lnea as ldng lnea ppuny s f spendng as and lnea nees ss. We sw e pmal slun f e ppsed mdel. e pmal sluns wll be pesened by numeal examples. Keywds: Ne pesen value dsuned as flw as balane pblem nveny mdels puasng 2
3 . ndun e as balane mdel was fs analyzed by Bauml 952. He as appled e lassal EOQ nveny mdel nvesgae e demand f a fm f as. s mdel s a deemns as mdel. Oe deemns as balane pblems was examned by ensng Gaska and n 978. ey ave analyzed a smple as balane pblem smla a f aggegae pdun plannng pblems e analyss s seekng f an pmal slun and e plannng zns. and and n 982 ave suppled a fue examnan f e deemns as balane pblem n den f e plannng zns. Se and mpsn 970 ave mdeled a w-asse dynam as balane pblem. ey ave slved e pblem w e elp f Pnyagn s maxmum pnple. e slun s a bang-bang pmal nl. An nduy as managemen ape s pesened n exbk f Rss and Wesefeld 988 e fs sas as balane mdel was naed by lle and O 966. s bas mdel was genealzed n seveal den e.g. Eppen and Fama Ggs 968 Neave 970 Peus 972 Heyman 973 Kamn 975 nsanndes 976 ndefu and Sneewess 978 nsanndes and Rad 978. ese sas mdels ae slved w dynam pgammng and unde dffeen s suue. e menned mdels ae ally examned by Daellenba and asked wee ese mdels f e pae. Oe papes nvesgae e as managemen paes n e nex f as flw e.g. Gman ses and We 979 s 983 Sas and Hll 983 Vksn 985 and Pemaanda A gd ndun n e sas as managemen pblems ae suppled by ape 990 w pesens e bas mdels w slun ppsns. sensn 988 as examned e apal ss n e nveny mdels. n s wk sensn as nvesgaed e effe f dsunng n as flw nveny mdels. Ou appa s smla a f sensn. e am f e pape s analyze e allan f as n puasng avy. e ppsed mdel s a dynam as flw mdel w dsuned ss. e as flw deny nsss f as ansfe ed and as equemens. e gal funn as ee lnea elemens as ldng as ansfe and nees ss. We slve s pblem w lnea pgammng. e send pa f e pape sws paamees vaables and gal funn f e mdel. e nex ape aaezes sme ppees f e pmal slun. e fu pa pesens sme numeal examples and las we summaze e esuls f e pape. 2. e mdel e paamees f e mdel: - dsun ae - leng f e plannng zn - 0 nal as level - avalable quany f mney f puasng n e plannng zn - p pe f e pdu seve n e ped 3
4 - x equed quany f e pdu seve n e ped - e as equemens n e ped - e ldng s f as - ppuny s f spendng as buy pdus and seves - nees ae f ed. e vaables f e mdel: - avalable as level n me nnnegave - as ansfe pad f pdus and seves n ped nnnegave - ed equemens n ped nnnegave. Le us assume a as equemens f e fm ae gven f e puasng depamen. f e pes p and e equed quanes x f pdus and seves ae knwn n any ped en ese equemens an be alulaed as fllws: n p x wee numbe n s e numbe f e sum f pdus and seves. n s mdel we assume a e as flw f e puasng depamen an be mdeled as an nveny balane equan. e nveny balane equan nsss f e sum f spen as by puasng depamen and used ed edued by e as equemens defned abve: 2 0 s gven and equal ze. Le us assume a e puasng depamen dspses f a gven quany f mney:. 2 We assume a e vaables f e mdel ae nnnegave: e gal funn f e mdel s e sum f e dsuned ped ss: mn. 4 We wll analyze e pmal slun f mdel -4. 4
5 5 3. Ppees f e pmal slun f e mdel -4 del -4 s a lnea pgammng pblem. Befe we slve s pblem we gve sme ppees f e mdel. We nvesgae e dependene f e mdel n e paamees. Fs we examne e dependene f pmal slun n e s paamees and. en we analyze e slun n dependene n avalable as and e sum f e equed as f puasng. Le us assume a e pmal slun f mdel -4 s { }.e nex ppey sws a e pmal nveny level s ze alng e plannng zn. Ppey. n e pmal slun e as levels ae ze n e plannng zn: Pf. a s assumed a >. Le us efmulae e gal funn a fllws: [ ]. n s fmula usng we an we. 5 Subsung 5 n e efmulaed gal funn we ave [ ]. 0 e gal funn as a lwe bund: 0 beause e as levels and as ansfes ae n lwe en ze. s lwe bund s aeved f values and 2 ae equal ze. s means n s ase a s bee bw fm a bank e equed mney and nves e avalable as. e pmal slun en: b Nw we an assume a. We we e gal funn as [ ].
![e nex ppey sws a e pmal nveny level s ze alng e plannng zn. Ppey. n e pmal slun e as levels ae ze n e plannng zn:... 2 0. Pf. a s assumed a >. Le us efmulae e gal funn a fllws: [ ].](/docs-images/49/17982655/images/page_5.jpg "n s fmula usng we an we. 5 Subsung 5 n e efmulaed gal funn we ave [ ]. 0 e gal funn as a lwe bund: 0 beause e as levels and as ansfes ae n lwe en ze. s lwe bund s aeved f values and 2 ae equal ze.")
6 6 n s fmula subsung 5 e gal funn an be wen n e fllwng way: [ ]. 0 e lwe bund f s s funn s 0. s lwe bund s aeved f e. we ave aaned e pmal slun. s pmal slun lds f. f > en e pmal slun as e nex fm: and me ped s defned as. W ese alulans we ave pven e ppey. Usng e pf f Ppey. we ave w addnal ppees. Ppey 2. f > en n e pmal slun e meanng f s ppey s a f e un s f as ansfe s geae an e nees ae en s bee use bank lan and n spend e asse f e fm. able. Opmal slun f e mdel n dependene f paamees >
7 > Ppey 3. f en n e pmal slun a f and b f > 0 and < and wee s d ppey sws a s me anal spend e asse f e fm f e nees ae s n smalle an e ppuny s f spendng as. e esuls an be summazed n able. 4. Numeal examples able pesens ee dffeen ases f e pmal sluns. We nsu pblems demnsae e sluns w e elp f daa fm e able 2. ase. n s ase e ppuny s f as ansfe 2 s geae an e nees ae 0.5. e slun f s ype f mdels s bwng fm a bank and usng e asse f e fm f e nvesmens. e pmal slun en e mnmal ss ae $ ase 2. e ppuny ss 0.5 ae lwe an en nees ae. n s mdel s 2 bee spend e avalable as f puasng. e sum f e equed as 20 s lwe an e avalable asse 30. e pmal slun en e mnmal ss ae $
8 able 2. Paamees f e mdels ase. ase 2. ase { } ase 3. e ppuny ss ae lwe an en nees ae.5. n s mdel s bee spend e avalable as f puasng as was n ase 2. e sum f e equed 2 as 77 s lwe an e avalable asse 30. means a e puasng depamen mus bw sme mney fm a bank. e sum f e bwed as s equal 2 $ 43. s knwn n s mdel a 25 < 30.e. n e 0 0 ped ee ae use f asse and bwng. e pmal slun en { } and { } mnmal ss ae $ e 8
9 5. nlusns n s pape we ave nvesgaed a dsuned as flw puasng mdel. n e pmal slun f e mdel e as levels ae equal ze n e plannng zn. e as ansfe s equal ze n e mdel f e ppuny ss f ansfe ae ge an a f nees ae. f e nees ae s ge an e ansfe ss en s pmal spend all avalable as and f s neessay bw sme mney fm a bank. s bas mdel an be genealzed n seveal ways. A pssble genealzan s ake n aun e dae f paymen. n s mdel fm we ave n examned e ne pesen value epesenan f e as flw deny. ndun f s em an be nea e eal wd pae. Refeenes. Bauml W.J. 952: e ansans demand f as: An nveny ee appa Quaely Junal f Enms and S. n.e. 982: A pefe plannng zn pedue fa a as balane pblem anagemen Sene nsanndes G.. 976: Sas as managemen w fxed and ppnal ansans ss anegemen Sene nsanndes G.. Rad S.F. 978: Exsene f pmal smple ples f dsuned-s nveny and as managemen n nnuus me Opeans Resea Daellenba H.G. 974: Ae as managemen pmzan mdels wwle? Junal f Fnanal and Quanave Analyss Eppen G.D. Fama E.F. 968: Sluns f as-balane and smple dynampfl pblems e Junal f Busness Eppen G.D. Fama E.F. 969: as balane and smple dynammpfl pblems w ppnal ss nenanal Enm Revew Eppen G.D. Fama E.F. 97: ee asse as balane and dynam pfl pblems anagemen Sene Ggs N.. 968: Opmal as balane levels anegemen Sene Gman L.J. ses E.A. We.. 979: An assessem f pae as managemen paes Fnanal anagemen/spng Haley. W. Hggns R.. 973: nveny ply and ade ed fnanng anagemen Sene Heyman D.P. 973: A mdel f as balane managemen anagemen Sene ndefu K. Sneewess. 978: Subpmal ples f sas as balane pblems: A mpasn f lnea desn ules and llng zen deemns pmzans Zesf fü Opeans Resea Kamn J.L. 975: Opmal pfl evsn w ppnal ansan s anegemen Sene ensng J. Gaska S. n. 978: Peve plannng-zen f a deemns as balane pblem Opeans Resea
10 6. lle.h. O D. 966: A mdel f e demand f mney by fms Quaely Junal f Enms s J.R. 983: e le f as balanes n fm valuan Junal f Fnanal and Quanave Analyss Neave E.H. 970: e sas as balane pblem w fxed ss f neases and deeases anagemen Sene Peus E.L. 972: Equvalen fmulans f e sas as balane pblem anagemen Sene Pemaanda : A dffusn appxman mdel f managng as n fms: An alenave appa e lle-o mdel Eupean Junal f Opeanal Resea Rbek A.A. eew D. Jnes J.. 965: Opmal s em fnanng desn anagemen Sene Rss S.A. Wesefeld R.W. 988: pae fnane mes /sby llege Publ. S. Lus e al. 23. Sas W.L. Hll N.. 983: A genealzed as flw appa s-em fnanal desns e Junal f Fnane Se S.P. mpsn G.L. 970: Applans f maemaal nl ey fnane: delng smple dynam as balane pblems Junal f Quanave and Fnanal Analyss ape.s. 990: Appled sas mdels and nl n managemen N- Hlland Amsedam e al. 26. sensn A. 988: apal ss n nveny mdels A dsuned as flw appa Pdun-Enm Resea n Lnköpng PROFL 8 Lnköpng 27. Vksn R.G. 985: Smple pmal ply f as managemen: e aveage balane equemen ase Junal f Fnanal and Quanave Analyss
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