h Asalian Sociy fo Opaions sach www.aso.og.a ASO Bllin Vol 33 ss 4 Pags 4-48 A Coninos viw nvnoy Mol fo Dioaing s wih Sochasic Dan an Pic Discon on Backos Manisha Pal an Sjan Chana Dpan of Saisics Univsiy of Calca nia Eail: anishapal@gail.co Dpan of Saisics Halia Gov. Collg nia Asac h pap sis a coninos viw invnoy ol fo ioaing is whn an is ano an only a facion of h n an is acklogg. a i is ass o consan an h invnoy anag offs a pic iscon on ackos o p csos o wai. Kywos: Coninos viw invnoy ol; ponnially ioaing is; sochasic an; fi la i; pic iscon on ackos.. nocion n classical invnoy ols wih shoags i is gnally ass ha h n an is ih coplly los o coplly acklogg. Howv i is qi possil ha whil so csos lav ohs a willing o wai ill flfiln of hi an. n so siaions h invnoy anag ay off a iscon on ackos an/o cion in waiing i o p csos o wai. Oyang al. 999 consi cion in la i an oing cos in a coninos viw ol wih paial ackoing. Dan an Hsian si invnoy ols wih acko iscon an ano la i. Chang al. 4 iscss a isiion f poc fo i invnoy ol wih acko iscon an vaial la i. al. 7 si an invnoy policy involving ack-o iscons an vaial la i an Uhayaka an Pavai 8 consi a coninos viw ol wih only fis wo ons of h la i an known an oain h opi acko pic iscon an o qaniy in ha siaion. Pal an Chana si a inisic invnoy ol wih pissil lay in payn an pic iscon on ackos. S also Chng an Hang 998 vino al. 993 Ki al. 99. h Asalian Sociy fo Opaions sach 4
4 ASO Bllin Vol 33 ss 4 Pags 4-48 n his pap w consi a coninos viw invnoy ol fo ioaing is whn an is ano an a pic iscon is off o csos who a willing o wai fo ackos. a i is ass o fi an h an a of ioaion is also consan. h pap is oganiz as follows. Scion givs h noaions s an h asspions a in h sy. Scion 3 folas an analyzs h ol. n scion 4 a snsiiviy analysis is cai o hogh an apl. Finally concling aks a a in scion 5.. Noaions an Mol Asspions h invnoy ol consi is a coninos viw ol. h following noaions an asspions hav n s h.. Noaions = invnoy lvl a i poin = facion of h an acko ing sock o = pp on on acko aio θ= a of ioaion = fi la i X = ano an ing la i = pc lngh of a plnishn cycl = h o qaniy a ach o poin = sock high which iggs off an o = pc i akn fo sock o co own o K = oing cos p o p = pchas cos p ni h = holing cos p ni p ni i s = fi shoag cos p ni sho p ni i s = los sals cos p ni an los = pic iscon on ni acko off = aginal pofi p ni. Asspions h asspions govning h ol a as follows:. h ol consis only on i in invnoy.
4 ASO Bllin Vol 33 ss 4 Pags 4-48. h sock on han ioas a a consan a. h is no pai o placn of ioa is. 3. Dan is ano wih an an a. 4. Shoags a allow an a facion of n ans ing sock-o is acklogg. 5. a i is fi. 6. Dan ing la i follows an ponnial isiion wih paa. 7. Only on o can osaning a any poin of i. 8. Ding h sock-o pio h acko facion is icly popoional o h pic iscon off y h invnoy anag on ni acko. hs wh. 3. Mol Folaion an Analysis h invnoy policy is o plac an o fo is whnv h sock high cos own o. W ass h planning pio o of infini lngh so ha h ol is si ov a plnishn cycl. A plnishn cycl fins h i inval wn wo consciv spplis of h o qaniy. no h invnoy lvl a i poin in h plnishn cycl. s consi h siaion wh h sock on han a h n of h la i is ga han o qal o zo. hn sinc plion of sock occs owing o an an ioaion h following iffnial qaions will fin ansiions in invnoy ing h la i: / wih onay coniion =. H - = h la i. Hnc. say. Sinc w s hav hs h iffnial qaions fining ansiions in invnoy ing a plnishn inval will as follows: i fo /.
43 ASO Bllin Vol 33 ss 4 Pags 4-48 ii Fo / / wh is h i akn fo sock on han o has ing h la i whn. n i h onay coniion givs an h onay coniion givs ln ln. n ii fo h onay coniions w g. Sinc h laionship wn an is oain as ln. h pc invnoy ing a cycl is hn givn y
44 ASO Bllin Vol 33 ss 4 Pags 4-48 E = f f [ { }{ } { Ei ln - Ei }] wh Ei. h n of nis ioaing p cycl is hfo E. Sinc shoag occs ov h pio [ ] whn h la i an cs an nos h acko aio h n of ackos p cycl is givn y S [ f h pc n of los sals ing a cycl is { ln Ei Ei }] hs h oal pc cos p ni pc lngh of a plnishn cycl is givn y C [ K h p E ss s ] ln
45 ASO Bllin Vol 33 ss 4 Pags 4-48 [ ] [ [ { ln[ ] C k s S s h E P E s k Ei }] [ ln { }{ } s Ei h P { }]] ln[ ] Ei Ei N Fo givn h opial vals of an which iniiz C s saisfy C an C which giv C P h.. }}] ] [ { { } } { { [ C Ei P h s Ei s Fo. an. an a oain as non-lina fncions of. Hnc C can pss as a fncion of alon iniizing which w oain h opi vals of an hnc of an.
46 ASO Bllin Vol 33 ss 4 Pags 4-48 4. Snsiiviy Analysis Sinc algaic acailiy is alos ipossil w ap o g an ia of h havio of h opial wih chang in h ol paas hogh nical apls. al : Showing h opial vals of an cosponing pc cos p ni i fo iffn vals of whn K=4 =35 p=3 h=7 s=5 s =5 = =5 =.5 =.5 C.3.958 7.457.7457.7838.547.5.883 7.49.7593.783396 6.4..5559 6.76665.7653.784336 39.33.3 9.546 4.67899.837.7885 74.5493.5 8.5644.756766.874.796 9.45.8 7.4586.857.633.84488 85.4675 al : Showing h opial vals of an cosponing pc cos p ni i fo iffn vals of h whn K=4 =35 p=3 s=5 s =5 θ=. = =5 =.5 =.5 h C..467 8.78665.7653.784336 69.39.7.4755 8.76644.7653.784335 7.4 4.9646 7.6397.7653.784335.4896.767 5.89399.7653.784335 6.838 5 9.559 4.3568.7653.784335 87.64 7 5.4639.89 4.9489.996546 63.3636 5.8585.643 4.9456.99635 87.854 al 3: Showing h opial vals of an cosponing pc cos p ni i fo iffn vals of whn K=4 =35 p=3 h=7 s=5 s =5 θ=. = =5 =.5 C. 4..5779 4.9995.99533 677.9.3 43.3659 9.3793 4.9995.99533 34.678.5.5559 6.76665.7653.784336 39.33.7.738 4.77953 8.94458.59684 4.785 5.948 3.94738 6.769847.4533 7.9988
47 ASO Bllin Vol 33 ss 4 Pags 4-48 al 4: Showing h opial vals of an cosponing pc cos p ni i fo iffn vals of s whn K=4 =35 p=3 h=7 s =5 θ=. = =5 =.5 =.5 s C.5675 6.596.4676.76457 45.46 3.55955 6.6983.663.7744 4.39 5.5559 6.76665.7653.784336 39.33 8.53965 6.86943.988.7997 33.838.5369 6.958793.368.89 3.78 al 5: Showing h opial vals of an cosponing pc cos p ni i fo iffn vals of s whn K=4 =35 p=3 h=7 s=5 θ=. = =5 =.5 =.5 s C 5.77.4439 3.979786.6539.54 3 7.454 3.747494 7.637586.597 9.7599 5.5559 6.76665.7653.784336 39.33 7.34 9.894 4.9995.99533 4.949 9.8577.57 4.9995.99533 44.867 h following osvaions a a fo als 5: a an a casing fncions of an h whil incass as /h incass. an a casing fncions of. c As s incass an incas cass. an a non-casing fncions of s. 5. Conclsion h pap sis a coninos viw invnoy ol fo ioaing is whn an follows an ponnial isiion an la i is fi. n o o ncoag csos o wai fo flfilln of hi an whn sock on han is zo h invnoy anag offs a iscon on ackos. h opial o qaniy o lvl an iscon on ackos hav n oain so as o iniiz h oal pc cos of h invnoy anag. h na of chang in h opial vals of h cision vaials wih chang in h ol paas has n invsiga hogh nical apls.
48 ASO Bllin Vol 33 ss 4 Pags 4-48 fncs. Chang B.. Oyang.Y. Chang K.W.: A no on pioic viw invnoy ol wih conollal sp cos an la i. Cops & Opaions sach. 34 549 56 4. Chng K.J. Hang C.K.: Econoic anfacing qaniy ol involving la i an sp cos cion invsn as cision vaials. nnaional Jonal of Opaions an aniaiv Managn. 4 9 6 998 3. Dan an Hsian: nvnoy ols wih acko iscons an vaial la i. nnaional Jonal of Sys Scinc. 37 95-99 4. Ki K.. Hayya J.C. an Hong J.D.: Sp cos cion in conoic pocion qaniy ol. Dcision Scincs. 3 5-58 99 5. W.C. W J.W. i C..: Opial invnoy policy involving ack-o iscons an vaial la i an. nnaional Jonal of Avanc Manfacing chnology. 349-958 967 7 6. Oyang. Chng C. Chang H.: a i an oing cos cions in coninos viw invnoy syss wih paial ackos. Jonal of h Opaional sach Sociy. 5 7 79 999 7. Pal M. an Chana S. : A inisic invnoy ol wih pissil lay in payn an pic iscon on ackos. o appa in Opsach. 8. vino J. Hly B.J Fiich W.: A ahaical ol fo h conoic jsificaion of sp i cion. nnaional Jonal of Pocion sach. 3 9 993 9. Uhayaka. Pavahi P.: nvnoy Mols wih i of Backos involving cil a i an Sp Cos. Opsach. 45-33 8