COST EVALUATION OF A TWO-ECHELON INVENTORY SYSTEM WITH LOST SALES AND NON-IDENTICAL RETAILERS

Transcription

1 Mehd SEIFBARGHY, PhD Emal : M.Sefbaghy@qazvnau.ac. Nma ESFANDIARI, PhD Canddate Emal: n.esfanda@yahoo.com Depatment of Industal and Mechancal Engneeng Qazvn Islamc Azad Unvesty Qazvn, Ian CST EVALUATIN F A TW-ECHELN INVENTRY SYSTEM WITH LST SALES AND NN-IDENTICAL RETAILERS Abstact. The nventoy system unde consdeaton conssts of one cental waehouse and an abtay numbe of non-dentcal etales contolled by contnuous evew polcy( R, Q ). It s assumed Independent Posson demands wth constant tanspotaton tmes fo the etales and constant lead tme fo eplenshng odes fom an extenal supple fo the waehouse. Unsatsfed demands ae assumed lost at the etales and unsatsfed etale odes ae backodeed at the waehouse. An appoxmate cost functon s developed to fnd optmal eode ponts fo gven batch szes n all nstallatons and the elated accuacy s assessed though smulaton. The poposed method s an extenson to the appoxmate assumpton of Posson demand on the waehouse pevously and adds moe appoxmatons to tackle etale s lead tme complexty. Keywods: Inventoy; Mult-echelon; Lost sales; Non-dentcal etales; Posson demand. JEL Classfcaton: M, C6, C63. Intoducton A two-echelon nventoy system conssts of one cental waehouse and an abtay numbe of non-dentcal etales, s consdeed. Retales demand fo a consumable tem at the waehouse. The nventoy contol polcy s assumed contnuous evew polcy (R,Q) n all nstallatons whch means that once the nventoy poston eaches a pedetemned value of R an ode of sze Q s placed. The demand pocesses s assumed ndependent Posson at the etales and unsatsfed demands ae lost. The tanspotaton tme of each ode placed by the etales s assumed constant. A constant lead tme fo eplenshng the waehouse odes fom an extenal supple s assumed and unsatsfed etales odes s backodeed at the waehouse and all backodeed odes ae flled accodng to a FIF-polcy. The eode pont and batch sze of the waehouse ae assumed ntege multples of the etales dentcal batch sze.

2 Mehd Sefbaghy, Nma Esfanda Revewng eseaches close to the aea of dvegent mult echelon nventoy systems whose stuctue typcally consstng of one cental waehouse (depot) and an abtay numbe of etales (bases), mples that mult-echelon nventoy systems lteatue s ch enough. Shebooke (986) s one of the ntal eseaches n ths aea. Assumng ( S, S) polces n a Depot-Base system fo a epaable tem, the aveage unt yeas of nventoy and stockout at the bases s estmated. Most of the eseaches n the 980s concentated on the epaable tems n a Depot-Base system. Gaves (985) detemned the stockng levels n such a system. Monzadeh and Lee (986) consdeed the ssue of detemnng the optmal ode batch sze and stockng levels at the stockng locatons usng a powe appoxmaton, Lee and Monzadeh (987) genealzed pevous models on multechelon epaable nventoy systems to cove the cases of batch odeng and batch shpment. n consumable tems, Deuemeye and Schwaz (98) poposed a smple appoxmaton fo a complex mult-echelon system (one waehouse and multple etales) assumng backodeng of unsatsfed demands n all nstallatons wth a batch odeng polcy.svoonos and Zpkn (988) poposed seveal efnements on the latte pape consdeng second-moment nfomaton (standad devaton as well as mean) n the appoxmatons. The lteatue on mult-echelon nventoy systems wth consumable tems contnued n the 990s. Axsäte (990) povded a smple ecusve pocedue fo detemnng the holdng and stockout costs of a system consstng of one cental waehouse and multple etales wth (S-, S) polcy, ndependent Posson demands at the etales,backodeed demand dung stockouts n all nstallatons and constant lead tmes. Axsäte (993) poposed exact and appoxmate methods fo evaluatng the pevous system fo the case of a geneal batch sze n all nstallatons but wth dentcal etales. Fo the case of non-dentcal etales and a geneal batch sze, Axsäte (998) poposed methods fo the exact evaluaton of two etales case and the appoxmate evaluaton fo the case of moe than two etales. Fosbeg (996) pesented a method fo exactly evaluatng the costs of the system wth one cental waehouse and a numbe of dffeent etales usng a dffeent appoach. Axsäte & Maklund (2008) consdeed the two-echelon nventoy system and deved a new polcy fo the waehouse odeng, whch was optmal n the boad class of poston-based polces elyng on complete nfomaton about the etale nventoy postons, tanspotaton tmes, cost stuctues and demand dstbutons at all facltes. The exact analyss of the new polcy ncluded a method fo detemnng the expected total nventoy holdng and backode costs fo the ente system. The common assumpton of the above papes s that demand dung stockout at the etales, ae backodeed. Howeve, on some condtons fo example n noncaptve makets demands may be lost. Andesson and Mechos (2002) poposed an appoxmate cost functon fo the stuctue of one cental waehouse and abtay numbe of dentcal etales assumng lost sales dung the stock out at the etales and ( S, S) contol polcy n all nstallatons. Unsatsfed etales, odes ae backodeed at the waehouse as the fome eseaches. Sefbaghy and Akba

3 Cost Evaluaton of a Two-Echelon Inventoy System wth Lost Sales and.. Joka (2006) consdeed the nventoy system wth one cental waehouse and many dentcal etales contolled by contnuous evew polcy. They assumed ndependent Posson demands wth constant tanspotaton tmes fo the etales and a constant lead tme fo eplenshng odes fom an extenal supple fo the waehouse. An appoxmaton cost functon to fnd optmal eode ponts fo gven batch szes n all nstallatons was poposed. Non-dentcal etales case wth lost sales dung stockout at the etales s addessed as an extenson by Sefbaghy and Akba Joka (2006). Ths s exactly what s consdeed n ths pape. Feld of nventoy management and systems has been exposed a lot of nteest by authos such as: Nta H. Shah and Chag J. Tved (2007) develop an ode level lot sze nventoy model fo exponentally deteoatng nventoy wth andom lead tme and suppoted t wth a numecal example. Cstna Fulga and Floentn Setban (2008) pesent a method to solve a deteoatng mult-tem nventoy model wth lmted stoage space and an assuance stock. The demand ate fo the tems s fnte, the tems deteoate at constant ates and ae eplenshed nstantaneously. The model s solved by a non-lnea pogammng method. Ntah H. Shah (2006) use an EQ model and a compason between exstng deteoatng tems models and effect of vaous paametes on the total cost of an nventoy system has been studed by hm. Nta H. Shah (2008) pesents nventoy polces fo deteoatng tems unde ncentves of pce dscount fo one tme only. It s qute a common pactce to offe specal dscount to motvate the buye to ode n lage than egula ode quanttes. Such specal sales ae avalable fo a lmted tme only. u pape wll be consdeed the nventoy management fom dffeent aspects. We now outlne the contents of ths pape. In Secton 2 the poblem fomulaton s gven. Secton 3 contans the evew of two specal sngle echelon poblems. Secton 4 explans poblem complextes. In Secton 5 the appoxmate total cost of the nventoy system s pesented. In Secton 6 a genetc algothm s poposed to optmze the total cost and fndng optmal eode ponts. In secton 7 some numecal poblems s gven to measue the accuacy of the appoxmaton and n Secton 8 some conclusons and futhe eseach s gven. 2. Poblem Fomulaton The common batch sze of the etales and the batch sze of the cental waehouse ae assumed pedetemned as many smla pevous woks such as Axsäte (993 and 998), Deuemeye and Schwaz (98) have done befoe to smplfy the poblem. The objectve s to fnd the optmal eode ponts though mnmzng the total holdng cost of the waehouse and etales and stockout costs of etales. The notaton s as follows: N : Numbe of etales : Demand ate at etale : Demand ate at the waehouse L : Tanspotaton tme fo delvees fom the waehouse to etale L : Lead tme of the waehouse odes

4 Mehd Sefbaghy, Nma Esfanda Q : Common batch sze of a etale Q : Batch sze of the waehouse R : Reode pont of etale R : Reode pont of the waehouse (an ntege multple ofq ) h : Holdng cost pe unt pe unt tme at a etale h : Holdng cost pe unt pe unt tme at the waehouse π : Penalty cost pe unt of lost sale at a etale C : Cost pe unt tme of etale n steady state C : Cost pe unt tme of the waehouse n steady state TC : Total cost of the nventoy system pe unt tme n steady state 3. Revew of two specal cases 3.. Revew of exact soluton fo backodeng poblem wth Posson demand Consdeng a sngle echelon nventoy system wth contnuous evew contol polcy, eode pont of R and batch sze of Q, constant lead tme fo eplenshng odes, demand geneated by a Posson pocess and backodeed demand dung a stockout, Hadley and Whtn (963) developed fomulae fo the aveage stock level ( D ( Q, R) ), fo the aveage stockout level ( B ( Q, R) ) and fo the aveage numbe of backodes pe unt tme ( E ( Q, R) ). Assumng lnea unt costs of holdng and stockout, they obtaned the elated cost pe unt tme. The fomulae ae as follows: B( Q, R) = [ ( R) ( R Q)], () Q β β + Whee ( ) 2 ν ( ν + ) L β ( ν ) = P ( ν ; L ) ( L ) ν P ( ν ; L ) P ( ν+ ; L ) (2) ( Q+ ) D( Q, R) = + R L+ B( Q, R). 2 (3) E( Q, R) =. Pout = [ α( R) α( R+ Q) ], Q (4) whee α ( ν ) = L P( ν ; L) ν P( ν + ; L). (5) The paametes n the above fomulae ae as follows:

5 Cost Evaluaton of a Two-Echelon Inventoy System wth Lost Sales and.. Q : deng batch sze of contnuous evew polcy R : Reode pont of contnuous evew polcy : Demand ate (mean of Posson demand dstbuton) L : Constant lead tme P out : The pobablty that thee s no stock on hand and L ( L) P( x, L) = e x= 0,,2,3,... (6) = x! 3.2. Revew of exact soluton fo lost sale poblem wth Posson demand Consdeng the same system wth R< Q (we us ths assumpton to assue of not havng moe than one ode outstandng at a tme), Hadley and Wthn (963) developed fomulae fo the aveage stock level ( D) and fo the aveage numbe of lost sale ncued pe unt tme ( E ). Assumng lnea unt costs of holdng and stockout, they obtaned the elated annual cost. The fomulae and paametes ae as follows: E= Tˆ, Q+ Tˆ (7) Q( Q+ ) QR Q D= + QL + E, Q+ Tˆ 2 (8) Whee ˆ R T = LP( R; L) P( R+ ; L) 9 and Q+ Tˆ T =. 0 The paametes n the above fomulae ae as follows: Q : deng batch sze of contnuous evew polcy R : Reode pont of contnuous evew polcy : Demand ate (mean of Posson demand dstbuton) L : Constant lead tme T ˆ : The expected length of tme pe cycle that the system s out of stock T : Tme pe cycle and (6). 4. Complextes of the poblem 4.. Demand analyss n the waehouse As Sefbaghy and Akba Joka (2006) menton what makes the mult-echelon nventoy poblems dffcult to solve s how to exactly o appoxmately detemne ( ) ( )

6 Mehd Sefbaghy, Nma Esfanda the type of demand at hghe echelons and eal eplenshment tme of odes, fom downsteam echelons to hghe ones, because of possble stockouts n the hghe ones. In the unde study model, hghe echelon s the cental waehouse and downsteam echelon s the etales. n the type of demand at the cental waehouse, we extend the gven appoxmaton by Sefbaghy and Akba Joka (2206) fo the case of non-dentcal etales. They menton that demand at the waehouse could be well appoxmated by a Posson pocess wth mean ate whch s computed as (). N =, () Q +. Tˆ n tems of the dentcal batch sze of Q. N s the numbe of etales, s the demand ate at a etale (etales ae dentcal) and Tˆ s the expected length of tme pe cycle that a etale s out of stock. Such an appoxmaton wth a lttle dffeence had been suggested by Monzadeh and Lee (986), Muckstadt (977), Deuemeye and Schwaz (98), Albn (982), and Zpkn (986) fo the case of backodeng of unsatsfed demand at the etales. Consdeng the notaton defned n Secton 2, demand at the waehouse can be appoxmated by a Posson pocess wth mean ate whch s computed as (2). = n, (2) Q +. Tˆ = n tems of the dentcal batch sze of Q. Notng the Secton 3.2, Tˆ whch s the expected length of tme pe cycle that etale s out of stock, s computed as (3). ˆ R T = L P( R, L ) P( R +, L ) (3) 4.2. Appoxmatng the etales lead tme Retales at the fst echelon of the model expeence ndependent Posson demand pocesses. Demand dung a stockout s assumed lost. Each ode that s placed at the waehouse by each etale has a mnmum lead tme equal to the tanspotaton tme. Sefbaghy and Akba Joka (2006) expess that the effectve lead tme of each etale s ode conssts of two components: fst the tanspotaton tme of the odes fom the waehouse nto the etale; second an addtonal watng tme whch esults fom a stockout n the waehouse. Based on the appoxmaton of demand at the waehouse, the waehouse behaves just lke an nventoy system of type descbed n Secton 3.. Fom Lttle s fomula n queung theoy (as Andesson and Malchos [2] use t), they use the expesson fo the aveage stockout level gven by Fomula () and (2) to obtan the aveage watng tme of each etale ode as gven by Fomula (4).

7 Cost Evaluaton of a Two-Echelon Inventoy System wth Lost Sales and.. B( Q Q, R Q) W =, (4) Whee W s the aveage watng tme of each etale ode and B Q Q, R Q s the aveage stockout level at the waehouse (Fomula ()). ( ) The batch sze and eode pont of the waehouse ( Q and R ) ae assumed ntege multples of the dentcal batch sze of the etales( Q ). W s added to the tanspotaton tme of each etale to make the appoxmate constant lead tme fo the odes and t can be used fo evaluatng the etale costs (Sefbaghy and Akba Joka (2206)). In the appoxmaton poposed n ths pape fo the case of non-dentcal etales, the etales costs ae not computed based on an effectve lead tme. In the othe hand, C s composed of two pats. The fst pat s fo the odes that do not ncu stockout at the waehouse fo whch the waehouse feghts once ecevng the ode and the eal lead tme s the tanspotaton tme. The second pat s fo the odes ncung stockout at the waehouse. Snce s the demand ate at the waehouse and P s the pobablty that the waehouse to be n stockout, the out numbe of such odes pe unt tme s. P ode whch ncus stockout (W ), s gven by (5). out. The aveage watng of each etale (, ) B Q Q R Q W =. P out (5) Notng Fomula (4) and consdeng that the batch sze and eode pont of the waehouse ( Q and R ) ae assumed ntege multples of the dentcal batch sze of the etales( Q ), W can be computed as (, ) (, ) B Q Q R Q W = E Q Q R Q, (6) whee B( Q / Q, R / Q ) [ ( R / Q ) ( R / Q Q / Q )], Q / Q β β (7) E( Q / Q, R / Q ) = [ α ( R / Q ) α ( R / Q + Q / Q )]. Q / Q (8) The functons α and β ae as n (2) and (5). The lead tme fo the odes whch ncu stockout at the waehouse ( y ) can be well appoxmated wth a unfom dstbuton wth the lowe and uppe bounds of

8 Mehd Sefbaghy, Nma Esfanda L and L + 2W. It s clea that the pobablty dstbuton functon of the lead tme s 2W and the expected value of the lead tme s L + W. The cost pe unt tme of etale n steady state ( C ) s computed as L+ 2W = out π + + out π L + C ( P ).(. E h. D ) P. (. E h. D ). dy, (9) 2W whee E( Q / Q, R / Q ) Pout =, (20) E ˆ = T, Q + Tˆ (2) Q ( Q + ) Q R Q D = ˆ + Q L + E Q 2 + T and Tˆ s obtaned fom (3). (22) eplacng y wth L. E and D ae obtanable as E and (22) D n (2) and 5. Appoxmate total cost The total cost of the nventoy system (TC ) conssts of the etales nventoy holdng and stockout costs and the waehouse nventoy holdng cost and s computed as n = + = TC C C The waehouse nventoy holdng cost s as n (24): Q. ( R C, = h D ). Q 24 Q Q ( 23) In the above fomula Q ( R D, ) s the aveage stock level n the Q Q waehouse and s as n (25), usng Fomula (3) n Secton 3. and notng that Q should be an ntege multple of Q. ( Q / Q + ) D( Q / Q, R / Q ) = + R / Q L + B( Q / Q, R / Q ). (25) 2 In the above fomula, s obtaned fom (2) consdeng (3) and B( Q / Q, R / Q ) s obtaned fom (7). C s as n (9) consdeng Fomulae (20), (2), (22) and (3). ( )

9 Cost Evaluaton of a Two-Echelon Inventoy System wth Lost Sales and.. It s clea that the optmal eode ponts n all nstallatons should be found though optmzng the total nventoy system cost (TC ). Snce TC belongs to Nonlnea Intege Pogammng (NIP) poblems, a GA based heustc s poposed to evolve optmal o nea to optmal values of the eode ponts R and R fo =,..., N. 6. Computatonal Pocedue Genetc Algothm (GA) s a class of evolutonay algothms and s based on a populaton of solutons. GA s a genec optmzaton method whch can be appled to almost evey poblem. The feasble solutons of the poblem ae usually epesented as stngs of bnay o eal numbes called chomosomes. Each chomosome has a ftness value that coesponds to the objectve functon value of the assocated soluton. Intally thee s a populaton of chomosomes andomly geneated. Then, a numbe of chomosomes ae selected as paents fo matng n ode to poduce new chomosomes (solutons) called offspng. The matng of paents s done applyng the GA opeatos, such as cossove and mutaton. The selecton of paents and poducng offspng ae epeated untl the stoppng ule (fo example a cetan numbe of teatons) s satsfed. Befoe gvng a geneal outlne of the poposed genetc algothm, some addtonal notaton s defned as follows: Populaton_sze: Sze of the populaton of solutons that emans constant dung the algothm pefomance. Max_teaton: Numbe of geneatons whch should be poduced untl the algothm stops. p c : Cossove ate (whch s the pobablty of selectng a chomosome n each geneaton fo pefomng cossove) p m : Mutaton ate (whch s the pobablty of selectng a gene o bt nsde a chomosome fo mutatng) Ftness_functon: Ftness value o the objectve functon value The geneal outlne of the poposed GA s as follows: Step 0: Intalze Populaton_sze, Max_teaton, pc and p m. Step : Randomly geneate the ntal populaton. Step 2: Repeat untl the Max_teaton: Step 2.: Pefom the epoducton opeato accodng to the oulette wheel ule and make a newe populaton. Step 2.2: Select the paent chomosomes fom the populaton wth pobablty p. c Step 2.3: cossove: a. Detemne the pas of paents among the paent chomosomes. b. Apply the cossove opeato to poduce two offspng fo each pa. c. Replace each offspng n the populaton nstead of the paents.

10 Mehd Sefbaghy, Nma Esfanda Step 2.4: Apply the mutaton opeato on the populaton wth pobablty p m. Step 2.5: Calculate the Ftness_functon fo each chomosome and save the best value n bv (best value). Step 3: Pnt bv. In the poposed GA, each chomosome s epesented by an N+ dmensonal vecto as [ R R R2... R N] whch N s the numbe of etales and the values ae eode ponts of the waehouse and N etales espectvely. The Populaton_sze, p and p ae assumed 00, 0.8 and 0.0 espectvely. Max_teaton s assumed c m equal to It s necessay to state that the eode pont of a etale s bounded by 0 and whch means 0 R p Q, snce hee should not be moe than one ode outstandng n each etale at any tme and ths constant satsfes ths condton fo a contnuous evew nventoy system wth lost sales (Hadley and Whtn (963)). Snce thee ae N etales n the model and none of them can have moe than one ode outstandng, R has a lowe bound equal to ( N Q ). 7. Numecal Results In ode to detemne the powe of ou appoxmaton we have desgned a set of 24 numecal poblems. We also smulated each numecal poblem 0 tmes (havng 0 uns), fo the optmal eode ponts obtaned fom the appoxmate model, usng GPSS/H smulaton softwae. The smulaton tme length of each un s 0,000 unt tmes wth 0,000 unt tmes as a un n peod. Dffeent statng andom numbe seeds wee employed fo each poblem. All of the esults show that ths length of tme s suffcent fo the system to each a steady state. Ths s also clea fom the standad devaton of the total system cost. The numecal poblems ae as n Table and Table 2. In Table, the etales ae consdeed wth dffeent demand ates whch ae andomly geneated among 0.5,,.5 and 2 but wth equal tanspotaton tmes whch s assumed one tme unt, L =, fo =, 2,3,4. In Table 2 the etales ae consdeed wth dffeent tanspotaton tmes whch ae andomly geneated among 0.5,,.5 and 2 but wth equal demand ates whch s assumed one pe tme unt, =, fo =, 2,3, 4. Thee ae dffeent stockout costs to assess the accuacy of the appoxmatons fo the vaous sevce levels. The numbe of etales s fou. The holdng costs of the waehouse and etales pe unt pe unt tme ae assumed to be, h = h =, and the lead tme of the waehouse s assumed to be, L =.TI. Q C

11 Cost Evaluaton of a Two-Echelon Inventoy System wth Lost Sales and.. Table LE IN PRESS Numecal examples wth dffeent demand ates but equal tanspotaton tmes. No π Qo Q Table 2 Numecal examples wth dffeent tanspotaton tmes but equal demand ates No π Qo Q L L2 L3 L The total cost esults ae as n Tables 3 and Table 4. As can be seen fom the tables the eos n the appoxmate total cost ae small n compason wth the smulated values. The mean eo s 2.73.

12 Mehd Sefbaghy, Nma Esfanda Table 3. Appoxmated and smulated total cost esults fo the numecal poblems n Table. No R R2 R3 R4 R Appoxm ate TC Smulated TC Eo % Mean Eo St dev Table 4 Appoxmated and smulated total cost esults fo the numecal poblems n Table 2. No R R2 R3 R4 R Appoxm ate TC Smulated TC Eo % Mean Eo St dev

13 Cost Evaluaton of a Two-Echelon Inventoy System wth Lost Sales and.. 8. Conclusons and futhe eseach An appoxmate cost functon fo a two-echelon nventoy system consstng of one waehouse and an abtay numbe of non-dentcal etales whee unsatsfed demand at the etales s lost and the contol polcy s contnuous evew has been developed. The man assumptons of ths eseach ae havng non-dentcal etales n the model and lost sales dung a stockout at the etales. Demand dstbuton has been appoxmated as Posson at the waehouse and the etales costs ae not computed based on an effectve lead tme. In the othe hand, t s composed of two pats. The fst pat s fo the odes that do not ncu stockout at the waehouse fo whch the waehouse feghts once ecevng the ode and the eal lead tme s the tanspotaton tme. The second pat s fo the odes ncung stockout at the waehouse. The numecal esults show that the appoxmaton s good enough and the mean eo s aound 2.73 %. Futue eseach s to use a sevce level objectve fo detemnng the optmal contol polcy. The nventoy contol polces could be changed and some paametes such as tanspotaton tme the odes fom the cental waehouse to the etales and the waehouse lead tme could be assumed stochastc. REFERENCES [] Albn, S.(982), n Posson Appoxmaton fo Supeposton Aval Pocesses n Queues. Management Scence ; 28: 26 37; [2] Andesson, J. Melchos, P.(200), A Two Echelon Inventoy Model wth Lost Sales. Intenatonal Jounal of Poducton Economcs ; 69: ; [3]Axsäte, S.(990), Smple Soluton Pocedues fo a Class of Two-echelon Inventoy Poblems. peatons Reseach ; 38: 64 69; [4]Axsäte, S. (993), Exact and Appoxmate Evaluaton of Batch deng Polces fo Two-level Inventoy Systems. peatons Reseach; 4: ; [5]Axsäte, S.(998), Evaluaton of Installaton Stock Based (R,Q)- Polces fo Two-level Inventoy Systems wth Posson Demand. peatons Reseach; 46: 35 45; [6]Axsäte, S, Maklund, J.(2008), ptmal Poston-based Waehouse deng n Dvegent Two-echelon Inventoy Systems. peatons Reseach ; 56:975-99; [7]Deuemeye, B., Schwaz, L.B. (98), A Model fo the Analyss of System Sevce Level n Waehouse/Retale Dstbuton System: The Identcal Retale Case. In: Schwaz, L. (Ed.), Multlevel Poducton/Inventoy Contol Systems (TIMS Studes n Management Scence 6). Elseve, New Yok (Chapte 3); [8]Fosbeg, R. (996), Exact Evaluaton of (R, Q)-Polces fo Two Level Inventoy Systems wth Posson Demand. Euopean Jounal of peatonal Reseach ; 96: 30 38;

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