Inventory Model with Time Dependent Demand Rate under Inflation When Supplier Credit Linked to Order Quantity

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1 Int. J Bui. Inf. h. Vol- No. Db 0 Invntoy Mol with i Dpnnt Dan Rat un Inflation Whn Suppli Cit Link to O Quantity R. P. ipathi Dpatnt of Mathati, Gaphi Ea Univity, Dhaun (UK), Inia E-ailtipathi_p0@iffail.o 74 Abtat - hi tuy vlop an invntoy ol un whih th uppli povi th puha a piibl lay in paynt, if th puha o a lag. Shotag a not allow an fft of th inflation at an lay in paynt a iu. In thi pap, w tablih an invntoy ol fo nontioating it an ti-pnnt an at un inflation whn uppli off a piibl lay to th puha, if th o i gat than o qual to a ptin. W thn obtain optial olution to fin optial o, optial plnihnt ti an optial total lvant ot. Finally, nuial xapl a givn to illutat th thotial ult an a th nitivity analyi of paat on th optial olution. Kywo: Invntoy; finan; ti-pnnt; an at; inflation. Intoution Lag nub of ah pap/atil ha bn pnt by any autho fo ontolling th invntoy of tioating an non-tioating it. Dtioating it uh a volatil liqui, bloo bank, iin, fahion goo, aioativ atial, photogaphi fil, t. Non-tioating it uh a what, i, y fuit, t. It i oon auption to any invntoy yt i that pout gnat ha infinitly long liv. Gnally, alot all it tioat ov ti. Oftn th at of tioation i low an th i littl n to oni th tioation fo tining th onoi lot iz. Fo ngligibility all tioating pout, th tioation at ay b nglt fo o all ti intval. h a any it in th al wol that a ubjt to a ignifiant at of tioation. Hn, th fft of tioation annot b nglt in th iion po of poution lot iz. h lo of utility u to ay i uually a funtion of th on-han invntoy. Rntly, gat intt ha bn hown in vloping athatial ol in th pn of Intnational Jounal of Buin & Infoation hnology IJBI, E-ISSN: Copyight Exlingh, Pub, UK ( ta it. Kingan (98), Chapan (985) an Dallnbah (986) hav tui th fft of th ta it on th optial invntoy poliy. In toay optition buin tanation, it i oon to obtain that th tail a allow o it pio bfo thy ttl th ount with th wholal. hi povi to th uto to pay th wholal iiatly aft iving th pout, but inta, an lay thi paynt until th n of th allow pio. h uto pay no intt uing th piibl ti fo paynt, but intt will b hag if th paynt i lay byon that pio. Gha an Sha (96) ha tablih a ol fo an xponntially aying invntoy. Covt an Philip (97) xtn Gha an Sha ol fo two-paat Wibull itibution tioation at. ng (00) iu an obtain an EOQ ol in whih tioation at i zo. Goyal (985) vlop an EOQ ol un onition of piibl lay in paynt. H igno th iffn btwn th lling pi an th puha ot an onlu that th onoi plnihnt intval an o gnally ina aginally un th piibl lay in paynt. Dav (985) ot Goyal ol by auing th fat that th lling pi i naily high than it puha pi. Aggawal an Jaggi (995) thn xtn Goyal ol fo tioating it. Jaal t al. (997) futh gnaliz th ol to allow fo hotag an tioation. Hwang an Shinn (997) vlop th optial piing an lot izing fo th tail un th onition of piibl lay in paynt. Chang an Dy (00) xtn th ol by Jaal t al. to allow fo not only a vaying tioation at of ti but alo th baklogging at to b invly popotional to th waiting ti. Chang t al. (00) thn xtn ng ol, an tablih an EOQ ol fo tioating it in whih th uppli povi a piibl lay to th puha if th o i gat than o qual to a ptin. h wok of Covt an Philip (97) xtn by Elay an i (98) by allowing hotag an uing ti vaying an at. In thi tuy a ingl it i oni.

2 Int. J Bui. Inf. h. Vol- No. Db 0 Chung (989) vlop an invntoy ol fo obtaining th optial o of tioating it in th pn of ta it uing th DCF appoah. Chung (989) pnt th iount ah flow (DCF) appoah fo th analyi of th optial invntoy in th pn of th ta it. Bian an hoa (977), Buzaott (975), Chana an Bahn (988), J t al. (98) vlop EOQ ol un ontant inflation at. Liao t al. (000) pnt an invntoy ol with tioating it un inflation whn a lay in paynt i piibl. Bhahbatt (98) vlop an EOQ ol un a vaiabl inflation at an ak-up pi. An EOQ ol un inflation an ti-iounting allowing hotag wa pnt by Ray an Chauhui (997). Mia (975) au a unifo inflation at fo all th aoiat ot an iniiz th avag annual ot to iv an xpion fo th EOQ ol. Datta an Pal (99) invtigat a finit ti-hoizon invntoy ol following th appoah of Mia (979) with a linaly ti-pnnt an at, allowing hotag an oniing th fft of inflation an ti valu of ony. Su t al. (996) vlop an invntoy ol un inflation fo initial-tok pnnt onuption at an xponntially ay. Rntly, Hou an Lin (008) iv an oing poliy with a ot iniization pou fo tioating it un ta it an ti iounting. Oth any atil an b foun by Chung t al. (005), Chung an Liao (006), Ouyang t al. (006) an Huang (007). hi tuy vlop an invntoy ol un a ituation in whih th uppli povi th puha a piibl lay of paynt if th puha o a lag, in whih an at i ti pnnt. hi pap i th gnalization of Chun- ao Chang (004) in whih tioation an an at both a ontant. W h fou on how a puha obtain an optial olution whn a uppli off a piibl lay of paynt fo lag o. In thi pap, w tablih an EOQ ol with ti-pnnt an at un inflation whn a uppli povi a piibl lay in paynt fo a lag o that i gat than o qual to th ptin Q. hi pap i oganiz a follow. In tion, w ntion th notation an auption u thoughout th tuy. In tion, th athatial ol a iv un fou iffnt ituation in o to iniiz th total ot in th planning hoizon. In tion 4, thotial ult a givn follow by nuial xapl a in tion 5. Snitivity analyi i givn in tion 6 to ontat th appliability of popo ol. h onluion an poibl futu wok i givn in lat tion 7.. Notation an Auption h following notation a u thoughout thi pap: 75 o h: h holing ot at p unit ti xluing intt hag o :Contant at of inflation p unit ti, wh 0 o P(t) = pt : h lling pi p unit at ti t, wh p i th unit lling pi at ti zo o C(t) = t : h unit puhaing ot at ti t, wh i th unit puhaing pi at ti zo an p > o S(t) = t : h oing ot p o at ti t, wh i th oing ot at ti zo. o H:h lngth of planning hoizon o I : h intt hag p $ in tok p ya by th uppli o :h piibl lay in ttling aount o Q:h o o Q : h iniu o at whih th lay in paynt i pitt. o o o o :h plnihnt ti intval : h ti intval that Q unit a plt to zo u to ti pnnt an. I(t):h lvl of invntoy at any ti t, 0 t = H/n R(t) :h annual an a a funtion of ti, wh R(t) = t, wh i a poitiv ontant i.. > 0. o Z() :h total lvant ot ov (0, H). h total lvant ot onit of th following lnt: (a) Cot of plaing o, (b) ot of puhaing, () ot of aying invntoy xluing intt hag, () ot of intt hag, () ot of intt hag fo unol it at th initial ti o aft th piibl lay, an (f) intt an fo th al vnu uing th piibl pio. In aition, th following auption a bing a:. h inflation at i a ontant. Shotag a not allow. Rplnihnt i intantanou 4. h an fo th it i known an i tipnnt 5. If Q < Q, thn th paynt fo th it iv ut b a iiatly. 6. If Q Q, thn th lay in paynt up to i pitt. Duing piibl lay pio th aount i not ttl, gnat al vnu i poit in an intt baing aount. At th n of it pio, th uto pay off all unit o, an bgin paying fo th intt hag on th it in tok.. Mathatial Foulation Lt u oni th lngth of hoizon H = n, wh n i an intg fo th nub of plnihnt to b a uing pio H, an i an intval of

3 Int. J Bui. Inf. h. Vol- No. Db 0 ti btwn plnihnt. h lvl of invntoy I(t) gaually a ainly to t an only. Hn, th vaiation of invntoy with pt to ti i givn by I ( t) t = t, 0 t = H/n () With bounay onition I() = 0 an I(o) = Q. Fo th o, w an obtain th ti intval that Q unit a plt to zo u to an only a = Q () h inquality Q < Q hol if an only if <. Sin th lngth of ti intval a all th a, w hav I(k + t) = ( t ), 0 k n, 0 t = H/n () o obtain total lvant ot in (o, H), w u th following t: (a) Cot of Plaing O n = k 0 S( k) S(n )) = (b) Cot of puhaing = n k0 = S(o) + S() + S() I( o) C( k) () Cot of aying invntoy = h n C( k) h I( k t) t (4) (5) k0 0 (6) W hav th following fou poibl a ba on th valu of, an, fo fining intt hag an an. Ca : 0 < < Sin < (i.. Q < Q ), th lay in paynt i not pitt in thi a. h uppli ut b pai fo th it a oon a th uto iv th. 76 Sin th intt hag fo all unol it tat at th initial ti, th intt payabl in (0, H) i givn by n I I ( ) ( ) C k I k t t k0 0 (7) hu, th total lvant ot in (0, H) i Z () = ot of plaing o + ot of puhaing + ot of aying invntoy + intt payabl. Ca : < ( h I ) (8) Sin <, w know that th i a piibl lay whih i gat than th plnihnt intval. In thi a, th i no intt hag, but th intt an in (0, H) i: I n P( k) t. t t ( ) k pi h total lvant ot in (0, H) i Z h pi t t (9) (0) Ca : Sin, th lay in paynt i pitt an th total lvant ot inlu both th intt hag an th intt an. h intt payabl in (0, H) i I n k0 C( k) I ( 6 I( k t) t h intt an in (0, H) i n I P( k) t. t t k0 0 ) pi () ()

4 77 Int. J Bui. Inf. h. Vol- No. Db 0 Hn, th total lvant ot in (0, H) i Ca 4: Sin, a 4 i iila to a. hfo, th total lvant ot in (0, H) i 4. hotial Rult In ality, inflation at i uually vy all. Uing aylo i xpanion fo th xponntial t, w hav + (5) Uing th abov appoxiation, th total lvant ot Z i (), i =,,, 4 an b wittn a ) ( 6 () = Z pi I h () ) ( 6 () = Z 4 pi I h (4) Z () I h ) ( (6) Z () pi h (7) Z () I h 6 (8) Z 4 () I h 6 (9) h fit o onition fo Z () in (6) i Z ()/ = 0, w gt ( ) ( ). 0 Z h I (0) h on o onition fo a, i ) ( Z = I h ) ( > 0 ()

5 Int. J Bui. Inf. h. Vol- No. Db 0 78 h optial (iniu) valu of = i obtain on olving Eqn. (0). At =, w gt th optial onoi o Q * ( ). Fo a, <. h fit o onition fo a i Z ()/ = 0, w gt Z ( ) h pi = = 0 () h on o onition fo a i Z ( ) h pi = > 0 () h optial (iniu) valu of = i obtain on olving Eqn. (). At =, w gt th optial onoi o Q * ( ) in thi a. Fo a, <. h fit o onition fo a i Z ()/ = 0, w gt Z ( ) h I 4 6 = = 0 (4) h on o onition fo a i Z( ) h I ( ) (5) h optial (iniu) valu of = i obtain on olving quation (4). At =, w gt th optial onoi o Q * ( ), in thi a. Fo a,. Bau th total lvant ot in a 4 i th a a that in a, th optial (iniu) valu of = 4 fo a 4 i obtain on olving quation (4). At = 4, th optial onoi o fo a 4 i Q * ( 4 ). Fo a 4, 4. Fo quation (0), () an (4), w hav 4 (h + I ) + 6 = 0 (6) (h + pi ) + ( pi ) 6 = 0 (7) an 4 (h + I ) + ( I ) (6 + I ) = 0 (8) Equation (6), (7) an (8) a ubi in. h quation an b olv by Nuial thniqu tho (lik bition tho, Rgula Fali tho o Nwton Raphon tho) o tial an o tho fo iffnt nuial valu of th paat.

6 Int. J Bui. Inf. h. Vol- No. Db 0 79 Invntoy Lvl Q 0 ().... (n-) (n-) n = H i Invntoy Lvl Ca. 0 < < Q 0 () ().... (n-) (n-) (n-) n = H i Invntoy Lvl Ca. < Q 0 () ().... (n-) (n-) (n-) n = H i Ca. Invntoy Lvl Q 0 () ().... (n-) (n-) (n-) n = H i Ca 4. Figu - Fou poibl invntoy yt.

7 Int. J Bui. Inf. h. Vol- No. Db Nuial xapl Exapl. Lt H = ya, = 500 unit, h = $ /unit/ya, I = 0.0/$/ya, I = 0.05/$/ya, = $50 p o an = $ 5 p unit. Subtituting th valu in Eqn. (6), w hav = 0 (9) Solving Eqn. (9), w gt optial = = 0.07 ya, an optial onoi o Q * ( ) = 4.8 unit, an Z * () = $ If Q = 5 unit, thn = ya, whih how that if Q * < Q, thn <, whih pov a I. Exapl. Lt H = ya, = 00 unit, h = $ /unit/ya, I = 0.08/$/ya, I = 0.05/$/ya, = 0.05 p unit, = $ 0 p unit, p = $ 40 p unit, = 90 ay = ya, = $ 50 p o. Subtituting th valu in Eqn. (7), w gt = 0 (0) Solving, w gt = = ya, an optial onoi o Q * ( ) = 7.7 unit, an Z * ( ) = $ 65.6 whih how that,, if Q * ( ) Q, thn, w gt, whih pov a. Exapl. Lt H = ya, = 00 unit, h = $ /unit/ya, I = 0.0/$/ya, = 90 ay = ya, = $ 0 p unit, = 0.05 p unit, an = $ 00 p o. Subtituting th valu in Eqn. (8), w gt = 0 () Solving Eqn. (), w gt = = ya, an optial onoi o Q * ( ) = 6.9 unit, an Z * ( ) = $ 7.0 whih how that,, if Q * () Q, thn, whih pov a., w gt Fo a 4, uing all paat in Ex., w gt 4, alo if Q * () Q, thn, w hav 4 ( 4 ), whih pov a Snitivity Analyi W hav pfo nitivity analyi by hanging,, h an an kping th aining paat at thi oiginal valu. h oponing vaiation i th yl ti, onoi o an total lvant ot a xhibit in abl (abl.a, abl.b, abl.) fo a, abl (abl.a, abl.b, abl., abl.) fo a an abl (abl.a, abl.b, abl., abl.) fo a ptivly. Ca - abl abl.a - Snitivity analyi on Rplnihnt yl ti (in ya) Eonoi o Q * ( ) abl.b - Snitivity analyi on Rplnihnt yl ti (in ya) Eonoi o Q * ( ) abl. - Snitivity analyi on h h Rplnihnt yl ti (in ya) Eonoi o Q * ( ) otal lvant ot Z * ( ) otal lvant ot Z * ( ) otal lvant ot Z * ( ) Ca - abl abl.a - Snitivity analyi on Rplnihnt yl ti (in ya) Eonoi o Q * ( ) otal lvant ot Z * ( )

8 Int. J Bui. Inf. h. Vol- No. Db abl.b - Snitivity analyi on Rplnihnt yl ti (in ya) Eonoi o Q * ( ) otal lvant ot Z * ( ) abl. - Snitivity analyi on h h Rplnihnt yl ti (in ya) Eonoi o Q * ( ) otal lvant ot Z * ( ) abl. - Snitivity analyi on h h Rplnihnt yl ti (in ya) Eonoi o Q * ( ) otal lvant ot Z * ( ) abl. - Snitivity analyi on (in ay) Rplnihnt yl ti (in ya) Eonoi o Q * ( ) otal lvant ot Z * ( ) abl. - Snitivity analyi on (in ay) Rplnihnt yl ti (in ya) Eonoi o Q * ( ) Ca - abl abl.a - Snitivity analyi on Rplnihnt yl ti (in ya) Eonoi o Q * ( ) abl.b - Snitivity analyi on Rplnihnt yl ti (in ya) Eonoi o Q * ( ) otal lvant ot Z * ( ) otal lvant ot Z * ( ) otal lvant ot Z * ( ) Fo th abov tabl th following ult hav bn obtain : a. h oputational ult a hown in abl., iniat that a high valu of oing ot ipli, high valu of plnihnt yl ti, o Q * ( ) an total lvant ot Z * ( ). b. h oputational ult a hown in abl.b, iniat that a high valu of unit puhaing ot ipli low valu of plnihnt yl ti, o Q * ( ) an total lvant ot Z * ( ).. h oputational ult a hown in abl., iniat that a high valu of holing ot h ipli low valu of plnihnt yl ti, o Q * ( ) an total lvant ot Z * ( ).. h oputational ult a hown in abl.a, iniat that a high valu of oing ot ipli, high valu of plnihnt yl ti, o Q * ( ) an total lvant ot Z * ( ).. h oputational ult a hown in abl.b, iniat that a high valu of unit puhaing ot ipli low valu of

9 Int. J Bui. Inf. h. Vol- No. Db 0 plnihnt yl ti, o Q * ( ) an total lvant ot Z * ( ). f. h oputational ult a hown in abl., iniat that a high valu of holing ot h ipli high valu of plnihnt yl ti, o Q * ( ) an total lvant ot Z * ( ). g. h oputational ult a hown in abl., iniat that a high valu of it pio ipli high valu of plnihnt yl ti, o Q * ( ) an total lvant ot Z * ( ). h. h oputational ult a hown in abl.a, iniat that a high valu of oing ot ipli, high valu of plnihnt yl ti, o Q * ( ) an total lvant ot Z * ( ). i. h oputational ult a hown in abl.b, iniat that a high valu of unit puhaing ot ipli low valu of plnihnt yl ti, o Q * ( ) an total lvant ot Z * ( ). j. h oputational ult a hown in abl., iniat that a high valu of holing ot h ipli low valu of plnihnt yl ti, o Q * ( ) an total lvant ot Z * ( ). k. h oputational ult a hown in abl., iniat that a high valu of it pio ipli high valu of plnihnt yl ti, o Q * ( ) an total lvant ot Z * ( ). 7. Conluion W vlop an EOQ ol un inflation fo non-tioating it an ti-pnnt an at to tin th optial oing poliy whn th uppli povi a piibl lay in paynt link to o. W u aylo i appoxiation to obtain th xpliit olution of th optial plnihnt yl ti an total lvant ot. Finally, nuial xapl a tui to illutat th popo ol. h a o anagial phnona () Fo a (a), a high valu of oing o ot au high valu of plnihnt yl ti, o Q * ( ) an total lvant ot Z * ( ) (b) a high valu of unit puhaing ot au low valu of plnihnt yl ti, o Q * ( ) an high valu of total lvant ot Z * ( ), () a high valu of holing ot au low valu of plnihnt 8 yl ti, o Q * ( ) an high valu of total lvant ot Z * ( ). Fo a (a) a high valu of oing ot au high valu of plnihnt yl ti, o Q * ( ) an total lvant ot Z * ( ), (b) a high valu of unit puhaing ot au low valu of plnihnt yl ti, o Q * ( ) an high valu of total lvant ot Z * ( ), () a high valu of holing ot au low valu of plnihnt yl ti, o Q * ( ) an high valu of total lvant ot Z * ( ), () a high valu of it pio ipli high valu of plnihnt yl ti, o Q * ( ) an low valu of total lvant ot Z * ( ). Fo a, (a) a high valu of oing ot ipli high valu of plnihnt yl ti, o Q * ( ) an total lvant ot Z * ( ), (b) a high valu of unit puhaing ot ipli low valu of plnihnt yl ti, o Q * ( ) an high valu of total lvant ot Z * ( ), () a high valu of holing ot h ipli low valu of plnihnt yl ti, o Q * ( ) an high valu of total lvant ot Z * ( ), () a high valu of it pio ipli high valu of plnihnt yl ti, o Q * ( ) an appoxiatly ontant valu of total lvant ot Z * ( ). h popo ol an b xtn in val way. Fo intan, w ay xtn th an at to a quaati ti pnnt an at. W oul alo oni th an a a funtion of, lling pi, pout an oth. Finally, w oul gnaliz th ol to allow fo hotag, iount an ti-pnnt tioation at, t. Rfn [] Aggawal, S.P., Jaggi, C.K.(995). Oing polii of tioating it un piibl lay in paynt. Jounal of th Opational Rah Soity,46, [] Bhahbhatt, A.C. (98). Eonoi o quality un vaiabl at of inflation an akup pi. Poutivity,, 7-0. [] Bian, H., hoa, J. (977). Invntoy iion un inflationay onition. Diion Sin, 8, [4] Buzaott, J.A. (975). Eonoi o quantiti with inflation. Opational Rah Quatly, 6, [5] Chana, J.M., Bahn, M.L.(988). h fft of inflation an th valu of ony o o

10 Int. J Bui. Inf. h. Vol- No. Db 0 invntoy yt. Intnational Jounal of Poution Eonoi, 4(4), [6] Chang, C.. (004). An EOQ ol with tioating it un inflation whn uppli it link to o. Intnational Jounal of Poution Eonoi, 88, [7] Chang, C.., Ouyang, L.Y., ng, J.. (00). An EOQ ol of tioating it un uppli it link to oing. Appli Mathatial Molling, 7, [8] Chang, H.J., Dy, C.Y.(00). An invntoy ol fo tioating it with patial baklogging an piibl lay in paynt. Intnational Jounal of Syt Sin,, [9] Chapan, C.B., Wa, S.C., Coop, D.F., Pag, M.J., 985. Cit poliy an invntoy ontol. Jounal of Opational Rah Soity 5, [0] Chung, K.H., 989. Invntoy ontol an ta it viit. Jounal of Opational Rah Soity,40, [] Chung, K.J., Goyal, S.K., Huang, Y.F. (005). h optial invntoy polii un piibl lay in paynt pning on th oing. Intnational Jounal of Poution Eonoi, 95, 0-. [] Chung, K.J., Liao, J.J. (006). h optial poliy in a iount ah-flow analyi fo tioating it whn ta it pn on th o. Intnational Jounal of Poution Eonoi, 00, 6-0. [] Covt, R.B., Philip, G.S. (97). An EOQ ol with Wibull itibution tioation. AIIE anation, 5, -6. [4] Dallnbah, H.G.(986). Invntoy ontol an ta it. Jounal of th Opational Rah Soity, 7, [5] Datta,.K., Pal, A.K. (99). Efft of inflation an ti valu of ony on an invntoy ol with lina ti-pnnt an at an hotag. Euopan Jounal of Opation Rah, 5, -8. [6] Dav, U. (985). On onoi o un onition of piibl lay in paynt by Goyal. Jounal of th Opational Rah Soity, 6, 069. [7] Elay, E.A. an i, C. (98). Analyi of invntoy yt with tioating it. Intnational Jounal of Poution Rah,, [8] Gha, P.M., Sha, G.P.(96). A ol fo an xponntially aying invntoy. Jounal of Inutial Engining,4, [9] Hou, K.L., Lin, L.C.(008). An oing poliy with a ot iniization pou fo tioating it un ta it an ti iounting. Apt. Jounal of Statiti an Managnt Syt. [0] Hwang, H., Shinn, W. (997). Rtail piing fo xponntially tioating pout un th onition of piibl lay in paynt. Coput an Opation Rah,4, [] Jaal, A.M.M., Saka, B.R., Wang, S. (997). An oing poliy fo tioating it with allowabl hotag an piibl lay in paynt. Jounal of th Opational Rah Soity, 48, [] J, R.R., Mita, A., Cox, J.F.(98). EOQ foula: I it vali un inflationay onition? Diion Sin, 4, [] Kingan, B.G. (98). h fft of paynt ul on oing an toking in puha. Jounal of Opation Rah Soity 4, [4] Liao, H.C., ai, C.H., Su, C.. (000). An invntoy ol with tioating it un inflation whn a lay in paynt i piibl. Intnational Jounal of Poution Eonoi 6, [5] Mia, R.B. (975). A tuy of inflationay fft on invntoy yt. Logit. Sptu 9, [6] Ouyang, L.Y., Wu, K.S. an Yang, C..(006). A tuy on an invntoy ol fo nonintantanou tioating it with piibl lay in paynt. Coput In. Eng. 5, [7] Ray, J., Chauhui, K.S. (997). An EOQ ol with tok-pnnt an, hotag, inflation an ti-iounting. Intnational Jounal of Poution Eonoi, 5, [8] Su, C.., nj, L.., Liao, H.C.(996). An invntoy ol un inflation fo tok pnnt onuption at an xponntial ay. Opah, 7-8. [9] ng, J.. (00). On th onoi o un onition of piibl lay in paynt. Jounal of th Opational Rah Soity 5,

ESCI 341 Atmospheric Thermodynamics Lesson 16 Pseudoadiabatic Processes Dr. DeCaria

ESCI 341 Atmospheric Thermodynamics Lesson 16 Pseudoadiabatic Processes Dr. DeCaria ESCI 34 Atmohi hmoynami on 6 Puoaiabati Po D DCaia fn: Man, A an FE obitaill, 97: A omaion of th uialnt otntial tmatu an th tati ngy, J Atmo Si, 7, 37-39 Btt, AK, 974: Futh ommnt on A omaion of th uialnt