Orgaizacija, Volume 42 Research papers Number 4, July-Augus 2009 OI: 10.2478/v10051-009-0010-5 Heurisic Approach o Iveory Corol wih Advace Capaciy Iformaio Marko Jakšič 1, 2, Boru Rusja 1 1 Uiversiy of jubljaa, Faculy of Ecoomics, jubljaa, Sloveia, Kardeljeva ploščad 17, jubljaa marko.jaksic@ef.ui-lj.si, boru.rusja@ef.ui-lj.si, 2 School of Idusrial Egieerig, Eidhove Uiversiy of Techology, The Neherlads There is a growig red of iformaio sharig wihi moder supply chais. This red is maily simulaed by rece developmes i iformaio echology ad he icreasig awareess ha accurae ad imely iformaio helps firms cope wih volaile ad ucerai busiess codiios. We model a periodic-review, sigle-iem, capaciaed sochasic iveory sysem, where a supply chai member has he abiliy o obai advace capaciy iformaio ( ACI ) abou fuure supply capaciy availabiliy. ACI is used o reduce he uceraiy of fuure supply ad hus eables he decisio-maker o make beer orderig decisios. We develop a easily applicable heurisic based o isighs gaied from a aalysis of he opimal policy. I a umerical sudy we quaify he beefis of ACI ad compare he performace of he proposed heurisic wih he opimal performace. We illusrae he codiios i which he procedure is workig well ad comme o is pracical applicabiliy. Keywords: Operaioal research, iveory, sochasic models, advace capaciy iformaio, heurisic 1 Iroducio I a realisic supply chai seig a commo modelig assumpio of sure deliveries of a exac quaiy ordered may o be appropriae. Several facors i a producio/iveory evirome, such as variaios i he workforce level (e.g. due o holiday leave), uexpeced machie breakdows ad maieace, chagig he supplier s capaciy allocaio o heir cusomers ec., affec he available supply capaciy ad correspodigly cause uceraiy i he supply process. Aicipaig possible fuure supply shorages allows a decisio-maker o make imely orderig decisios which resul i eiher buildig up sock o preve fuure sockous or reducig he sock whe fuure supply codiios migh be favorable. Thus, sysem coss ca be reduced by carryig less safey sock while sill achievig he same level of performace. These beefis should ecourage he supply chai paries o formalize heir cooperaio o eable he requisie iformaio exchage by eiher implemeig ecessary iformaio sharig coceps like he Elecroic aa Ierchage ( EI ) ad Eerprise Resource Plaig ( ERP ) or usig formal supply coracs. We may argue ha exra iformaio is always beeficial, bu furher hough has o be pu io ivesigaig i which siuaios he beefis of iformaio exchage are subsaial ad whe i is oly margially useful. I his paper, we explore he beefis of usig available advace capaciy iformaio ( ACI ) abou fuure ucerai supply capaciy o improve iveory corol mechaisms ad reduce releva iveory coss. The assumpio is ha a supplier has some isigh io ear fuure supply capaciy variaios (he exe of he capaciy ha hey ca delegae o a paricular reailer for isace), while for more disa fuure periods he capaciy dyamics are ucerai. Thus, he supplier ca commuicae his iformaio o he reailer ad help he reailer reduce supply uceraiy (Figure 1). However, he simulaeous reame of demad uceraiy ad supply uceraiy proves o be oo complex o esablish simple ad easily applicable iveory corol policies. Bush ad Cooper (1998) ad Buxey (1993) idicae ha firms facig hese codiios ed o have o formal plaig mechaism. Figure 1: Supply chai wih ACI sharig. The aim of his paper is o build a pracical ad reasoably accurae heurisic procedure ha capures he impora problem characerisics meioed. The heurisic is developed based o isighs gaied from a sudy of he opimal policy behavior by Jakšič e al. (2008). They show ha he opimal orderig policy is a base sock policy characerized by a sigle base sock level, which is a fucio of deermiisic ACI ha is available for a limied umber of fuure periods. 129
Orgaizacija, Volume 42 Research papers Number 4, July-Augus 2009 However, hey sress ha he complexiy of he uderlyig opimal dyamic programmig procedure preves a aalysis of real-life siuaios. This problem will be addressed i his paper by cosiderig a approximae approach o deermie he parameers of he iveory policy. We ow briefly review he releva research lieraure. The pracical imporace of he effec of limied capaciy has geeraed cosiderable ieres i he research commuiy. Exedig he resuls of he classical ucapaciaed iveory corol, he capaciaed maufacurig/supply seig was firs addressed by Federgrue ad Zipki (1986). They proved he opimaliy of he modified base sock policy for a fixed capaciy cosrai ad saioary demad. Kapusciski ad Tayur (1998) assume sochasic seasoal demad where hey agai show he opimaliy of a modified base-sock policy. The aicipaio of fuure demad, due o is periodic aure, causes a correspodig icrease or decrease i he base sock level. A lie of research assumes sochasic capaciy (Ciarralo e al., 1994; Güllü e al., 1999; Iida, 2002), wihi which Ciarralo e al. (1994) show ha he opimal policy remais a base sock policy where he opimal base sock level is icreased o accou for possible capaciy shorfalls i fuure periods. They exed his work by iroducig he oio of exeded myopic policies ad show hese policies are opimal if he decisio-maker cosiders appropriaely defied review periods. The opimaliy or ear-opimaliy of myopic policies i a o-saioary demad evirome was explored by Moro ad Peico (1995) ad laer exeded wih he iclusio of fixed or sochasic capaciy by Bollapragada e al. (2004), Khag ad Fujiwara (2000), ad Meers (1998). Meers (1997) preses a heurisic cosruced uilizig a aalyical approximaio for opimal policy. I developig heurisics, researchers have geerally resored o a approximae aalysis of he opimal policies ad a close ispecio of he behavior of myopic policies. The remaider of he paper is orgaized as follows. I Secio 2 we prese a model icorporaig ACI ad is dyamic programmig formulaio as he basis for a opimal soluio. I Secio 3 we cosider a aleraive approach o solvig he preseed iveory problem by developig a heurisic procedure. Secio 4 provides he resuls of a umerical sudy i which we assess he accuracy of he proposed heurisic ad oulie releva maagerial isighs abou he seigs i which i should be applied. Fially, we summarize our fidigs i Secio 5. 2 Model formulaio I his secio, we describe i deail he ACI model developed i Jakšič e al. (2008). We iroduce he oaio ad prese he opimaliy equaios. The model uder cosideraio assumes periodic-review, sochasic demad, sochasic limied supply wih a fixed oegaive supply lead ime, fiie plaig horizo iveory corol sysem. However, he maager is able o obai ACI o he available supply capaciy for orders placed i he fuure ad use i o make beer orderig decisios. We iroduce parameer, which represes he legh of he ACI horizo, ha is, how far i advace he available supply capaciy iformaio is revealed. We assume 130 z + + ACI is revealed i each period for he supply capaciy ha will be realized i period +. The model assumes perfec ACI, meaig ha we kow he exac upper limi o supply capaciies limiig orders placed i he curre ad followig periods. Presumig ha ume demad is fully backlogged, he goal is o fid a opimal policy ha miimizes he releva coss, ha is iveory holdig coss ad backorder coss. Hece, we assume a zero fixed cos iveory sysem. The model preseed is quie geeral i he sese we do o make ay assumpios abou he aure of he demad ad supply process, wih boh beig assumed o be sochasic o-saioary ad wih kow disribuios i each ime period, however, idepede from period o period. The major oaio is summarized i Table 1 ad some oher oaio is iroduced laer as required. Table 1: Summary of oaio T : umber of periods i he plaig horizo : cosa oegaive supply lead ime, where = 0, for zero lead ime case : advace supply iformaio parameer, 0 h : iveory holdig cos per ui per period b : backorder cos per ui per period x : iveory posiio a ime before orderig y : iveory posiio a ime afer orderig x ˆ : e iveory a he begiig of period z : order size a ime c : lack of capaciy i period a : aicipaory sock required i period : radom demad i period d : acual demad i period Z + : radom available supply capaciy a ime z + : acual available supply capaciy a ime, for which ACI was revealed a ime We assume he followig sequece of eves. (1) A he sar of he period, he maager reviews x ad ACI z + + for supply capaciy i period + is received, limiig order z + (Figure 2). (2) The orderig decisio z is made ad correspodigly he iveory posiio is raised o y = x + z. (3) The quaiy ordered i period is received. (4) A he ed of he period demad d is observed ad saisfied hrough o-had iveory; oherwise i is backordered. Iveory holdig/backorder coss are icurred based o he ed-of-period e iveory. ue o posiive supply lead ime, each order remais i he pipelie sock for periods. We ca herefore express he iveory posiio before orderig x as he sum of he e iveory ad pipelie sock. 1 = ˆ + s. (1) s= x x z
Orgaizacija, Volume 42 Research papers Number 4, July-Augus 2009 Figure 2: Advace capaciy iformaio updaig. Correspodigly, he iveory posiio afer orderig is y = x + z, (2) where 0 z z +, where z + represes he upper boud o he realizaio of he order z ha will be delivered periods laer i period +. Noe, ha due o perfec ACI, he iveory posiio y reflecs he acual quaiies ha will be delivered a all imes. Apar from x ad he curre supply capaciy z +, we eed o keep rack of ACI, + + + + z = [ z+ 1, z+ 2,, z+ ]. The ACI vecor cosiss of available supply capaciies poeially limiig he size of orders i fuure periods. The sae space is hus represeed by a + 2 -dimesioal vecor ad is updaed a he ed of period i he followig maer x + 1 = x + z d, z = [ z,, z, z ]. + + + + + 1 + 2 + + + 1 Goig from period o period + 1, order z is placed accordig o he available supply capaciy z + ad demad i period is realized. Before a ew order is placed i period + 1, ACI z + + + 1 for he order ha will be placed i period + + 1 is revealed ad he oldes daa poi z + is dropped ou of he ACI vecor ad ACI is updaed by he ew iformaio z + +. Observe ha i he case of = 0 he ACI affecig he curre order is revealed jus prior o he mome whe he order eeds o be placed. ue o a cosa o-zero lead ime he decisio-maker should proec he sysem agais lead ime + demad, = k = k, which is demad realized i ime ierval (, + ). Sice he curre order z affecs he e iveory a ime +, ad o laer order does so, i makes sese o reassig he correspodig iveory-backorder cos o period. Thus, he expeced iveory-backorder cos charged o period is based o he e iveory a he ed of he period +, xˆ + + 1 = y, ad we ca wrie i i he followig form of a sigle-period expeced cos fucio C ( y ) : (3) ( ) = ˆ C y α E C + ( y ), (4) where α is a discou facor. The expecaio is wih respec o lead ime demad ad he sigle-period cos fucio akes he followig form, ˆ ˆ ˆ + ˆ C + ( x + + 1) = h[ x + + 1] + b[ x + + 1]. The miimal expeced cos fucio, opimizig he cos over a fiie plaig horizo T from ime oward ad sarig i he iiial sae ( x, z + ), ca be wrie as: (5) where f ( ) 0 T + 1. The soluio o his dyamic programmig formulaio miimizes he cos of maagig he sysem for a fiie horizo problem wih T periods remaiig uil ermiaio. I was show i Jakšič e al. (2008) ha he opimal policy is he modified base sock policy, characerized by a sigle opimal base sock level yˆ ( z + ), which deermies he opimal level of he iveory posiio afer orderig. The opimal base sock level depeds o he fuure supply availabiliy, ha is supply capaciies give by he ACI vecor z +. Opimal policy isrucs ha we raise he base sock level if we aicipae a possible shorage i supply capaciy i he fuure. We hereby simulae he iveory build-up o avoid possible backorders which would be a probable cosequece of a capaciy shorage. O he corary, he base sock level is decreasig wih he higher supply availabiliy revealed by ACI. 3 Cosrucio of he heurisic However, he compuaioal effors relaed o esablishig he parameers of he opimal policy are cumbersome eve for simple problem isaces. Pracical applicabiliy is herefore severely resriced. This creaes a iceive o develop approximae procedures o ackle he problem. I his secio we prese a modificaio of exisig heurisics for a osaioary demad, fixed capaciy iveory sysem, kow 131
Orgaizacija, Volume 42 Research papers Number 4, July-Augus 2009 as he proporioal safey sock heurisic (Meers, 1997). We upgrade his heurisic cosiderably for he case of our ACI model by accouig for boh he effec of he variable capaciy ad he proposed ACI seig. To cosruc he heurisic i is firs useful o defie he myopic opimal soluio o he sigle-period ewsvedor problem: b Φ b + h M 1 yˆ =, where Φ ( d ) represes he cumulaive disribuio fucio of demad i period. For a sigle-period problem wih sochasic limied capaciy Ciarallo e al. (1994) show ha he variable capaciy does o affec he order policy. The myopic policy of he ewsvedor ype is opimal, meaig ha he decisio-maker has o iceive o ry o produce more ha is dicaed by he demad ad he coss, ad simply has o hope ha he capaciy is sufficie o produce he opimal amou. However, i muliple period siuaios oe ca respod o possible capaciy uavailabiliy by buildig up iveories i advace. We coiue by cosrucig he illusraive example preseed i Figure 3. Cosider he base sceario characerized by he followig parameers: T = 6, α = 0.99, h = 1, b = 20, discreized rucaed ormal demad ad supply capaciy followig a paer where expeced demad is give as 1..6 = (5,5,5,15,5,5) ad he expeced supply capaciy as Z + 1..6 = (10,10,10,10,10,10). The average capaciy uilizaio is 67%; however, here is a sigifica mismach bewee demad ad supply capaciy from period o period. I paricular, period 4 is problemaic sice he occurrece of a supply capaciy shorage is highly likely. Observe he differece bewee he opimal base sock levels y ˆ, deermied by solvig, ad he myopic opimal levels y ˆ M. The myopic opimal soluio y ˆ M oly opimizes a ucapaciaed sigle-period problem. Therefore, he correspodig base sock levels follow chages i mea demad, while he heigh depeds o he releva cos srucure, i our case he raio bewee he backorder ad iveory holdig cos, b h, hrough. Opimal base sock levels alig wih he (6) myopic oes oly i some periods, i our case, i periods 1, 5 ad 6, ad are close i he peak demad period 4; i he res of he periods, y ˆ lies above y ˆ M. This differece is due o he aicipaio of fuure capaciy shorages. The raioal reacio is o pre-build sock o prepare i advace. Based o his isigh, we ca sae he followig codiios whe a iveory buildup is eeded ad poeially brigs cosiderable beefis o he decisio-maker: whe here is a mismach bewee he demad ad supply capaciy, meaig ha here are ime periods whe he supply capaciy is highly uilized or eve over-uilized, bu here are also periods whe capaciy uilizaio is low; whe we ca aicipae a possible mismach i he fuure; ad whe we have eough ime ad excess capaciy o build up he iveory o a desired level o avoid backorder accumulaio durig a capaciy shorage. For a ucapaciaed sysem Veio (1965) shows ha he myopic policy represes ear-opimal upper boud o he opimal policy. Sice yˆ M is ear-opimal i he ucapaciaed case, he differece bewee y ˆ ad y ˆ M reflecs he eed o pre-build iveory by raisig he base sock level i he capaciaed case. I our example, we see ha he pre-build phase for period 4 has sared back i period 2, where he heigheed y ˆ already reflecs he eed for iveory accumulaio. I he peak period, he aure of he problem is close o a sigleperiod problem hus yˆ M represes a good upper boud, bu oly if here are o aicipaed fuure capaciy shorages for a leas a few followig ime periods. Some aicipaio is already possible wihou kowledge of acual supply capaciy realizaios i fuure periods, as we have jus show. For his, kowig he demad ad supply capaciy disribuios is eough. However, we argue ha hrough he use of ACI we ca improve iveory corol furher due o beer iformaio abou he evoluio of he sysem i ear fuure periods. I Figure 4, we prese he same base seig i he case where we have a isigh io supply capaciy realizaios i he ex period, = 1. We see ha, if ACI wars us of a capaciy shorage (a low z + + 1 ), we will respod by icreasig he base sock level. This is also Figure 3: Opimal yˆ ad myopic opimal y ˆ M base sock levels. 132
Orgaizacija, Volume 42 Research papers Number 4, July-Augus 2009 Figure 4: Opimal y ˆ ad myopic opimal y ˆ M base sock levels for he ACI model he case i he peak period, where y ˆ ca exceed y ˆ M, whe shorages are aouced by ACI i he remaiig wo periods; alhough heir probabiliy is likely o be very small. A pracical ierpreaio of he above fidigs ca be made for a simple heurisic policy, which isrucs he followig: Se he base sock level a y ˆ M, uless you aicipae a capaciy shorage. I he case of a shorage he iveory eeds o be prebuild ad hus he base sock level eeds o be icreased above y ˆ M i he pre-build periods. The deermiaio of he amou of he pre-build iveory eeded is based o a evaluaio of fuure mismaches bewee available capaciies (give by ACI for ear fuure periods ad he parameers of capaciy disribuios for disa periods) ad he myopic opimal base sock levels. We sar by deermiig he mismach i supply capaciy c i period, where we disiguish wo possible cases. Firs, we look a a mismach i supply capaciy for he case whe ACI is already available for ha period. I his case, we kow he realizaio of capaciy ad herefore c ( z + ) is a fucio of he acual realizaio of supply capaciy z +. I he secod case, he supply capaciy is o ye revealed so he bes we ca do is o work wih he expeced supply capaciy, hus, c ( E( z + )). We formulae he mismach of supply capaciy c i period as: + + c ( z ) M M z yˆ ˆ y 1 E( 1) + = + + c ( E( z )) E( z ). (7) Observe ha c is deermied as he differece bewee he myopic base sock level y ˆ M ad he edig iveory M posiio y (deermied from, where x ˆ = y 1 E ( 1 ) ), give ha all of he supply capaciy z + available i period was used. A egaive c correspods o a excess of supply capaciy, ad a posiive o a lack of capaciy i period. Kowig he poeial lack or excess of supply capaciy i each period allows us o calculae he amou of iveory build-up required i a paricular period. Tha is he amou of iveory we have o build i advace i period o cover fuure supply capaciy/demad mismaches. We will deoe his iveory as aicipaory a, required i period : ( ) ( ) a, 0 max a 1, 0 c 1( E( z + = = + = + + + 1 )),0, if = 0, a, ( z +, ) = max a 1, ( z + 1, 1) + c 1( z + 1 ),0, if 0 + + + + > Observe ha a, ( z +, ) is a fucio of ACI, if ACI is available ( > 0 ). The aicipaory iveory is calculaed recursively from he ed of he plaig horizo dow o he firs period. Firs, he aicipaory iveory for = 0 case is deermied ad i is he used as he buildig block o deermie he aicipaory iveory for = 1 case. I he same maer we proceed by calculaig a, for higher, where a, is a fucio of all currely available ACI. Where excess supply capaciy is available, we ca use i o build up he aicipaory iveory. If he size of he excess supply capaciy accous for more ha he aicipaory iveory eeded, we oly use up o he amou eeded ad we herefore limi ourselves o posiive values of c, by imposig a max fucio i he above formulaio. If curre excess supply capaciy is o high eough some of he aicipaory iveory eeds o be pre-buil i earlier periods. Fially, he heurisic base sock level y ˆ H, is deermied by raisig i above he myopic opimal level y ˆ M, for he exe of aicipaory iveory a, : H M,,, (8) yˆ = yˆ + a ( z + ) (9) 133
Orgaizacija, Volume 42 Research papers Number 4, July-Augus 2009 While wih he myopic base sock level we oly accou for uceraiies i demad, by addig he aicipaory sock we ow also accou for fuure capaciy shorages. Wih his he variabiliy i fuure supply capaciy is also ake io cosideraio. Give he acual supply capaciy realizaio i he curre period he edig iveory posiio may o be raised o he heurisic base sock level y ˆ H,. I his case, all of he available capaciy is used. I geeral he heurisic policy behaves i he same way as he opimal policy, where he opimal base sock level y ˆ is replaced by is heurisic couerpar. 4 The value of ACI ad heurisic performace I his secio we prese a umerical sudy o assess he value of ACI ad he heurisic performace. The resuls are give i Table 2. Usig he same base seig as i he previous secio, we ow look a he ifluece of he cos srucure ad he variabiliy of boh he demad ad supply capaciy o heurisic performace. We vary: he coefficie of he variaio of demad CV = (0,0.25,0.5,0.7) ad supply capaciy CV Z = (0,0.25,0.5,0.7), where boh CVs do o chage hrough ime; ad he cos srucure, by chagig he backorder cos b = (5, 20) ad keepig he iveory holdig cos cosa a h = 1, hus chagig he cos raio b h. We give he followig maagerial isighs abou he siuaios i which ACI cosiderably improves he iveory cos. The value of ACI is defied as he reducio i cos for he case where ACI is available > 0, relaive o he base case wih o ACI, = 0. ookig a he resuls preseed i Table 1, we see ha cos reducios of 5-15% ca be expeced ad i cerai siuaios hey ca exceed 20%. Several facors affec he value of ACI ad we formulae he followig codiios i which iveory coss ca be effecively decreased: (1) whe here is a mismach bewee demad ad supply capaciy, which ca be aicipaed hrough ACI, ad here is a opporuiy o pre-build iveory i a adequae maer; (2) whe uceraiy i fuure supply capaciy is high ad ACI is used o lower i effecively; ad (3) i he case of high backorder coss, which furher emphasizes he imporace of avoidig sockous. I hese circumsaces, maagers should recogize he imporace of esurig he ecessary iformaio exchage wih heir suppliers. Such relaios may brig cosiderable operaioal cos savigs. We proceed by esablishig he performace of he proposed heurisic. To do his, we give wo accuracy measures: he Absolue error ad he Relaive error. Boh are deermied based o a compariso of oal iveory coss bewee he heurisic case ad he opimal case, where he firs oe gives he absolue cos differece ad he laer he relaive oe. Observe ha i geeral he heurisic performace is wihi or close o 1% of he opimal. However, we ca also see ha here are some variaios for differe selecios of he parameer seigs we have esed. I a compleely deermiisic sceario (Exp. No. 1), he heurisic maages o reproduce he opimal resuls. For sochasic scearios, where cos reducio hrough ACI is possible, we see ha he relaive error decreases whe we exed he ACI horizo. This is i lie wih he iuiio which suggess ha he heurisic will perform beer if he geeral uceraiy is lower, ad he uceraiy i his case is effecively reduced hrough ACI. This suggess ha he proposed heurisic should be applied i he ACI seig i paricular. While his ca be observed i mos of he cases where b = 20, i does o hold for some scearios where b = 5. We aribue his o he fac ha he heurisic geerally pus a sress o assurig eough iveory build-up, which ca be subopimal i he case of a low b h. I a pracical applicaio his migh o pose a big problem sice oe rarely comes across such a low b h raio. Also observe also ha he heurisic performs well i he case where demad uceraiy, CV, is high relaive o he capaciy uceraiy, CV Z +, or i he case where boh demad ad capaciy uceraiy are similar. This is due o he heurisic beig highly sesiive o demad uceraiy hrough he use of myopic opimal base sock levels as he simple lower bouds. However, he effec of chagig CV ad CV Z + is heerogeeous ad by iself i does o exhibi ay obvious moooic properies. The heurisic performace is wors for he specific seig of high capaciy uceraiy ad low ACI availabiliy, paricularly he case of = 0, which is due o he fac ha he proposed heurisic does o fully accou for capaciy variabiliy. However, because of he complexiy of he uderlyig model i should be oed here ha, for he base case of osaioary demad ad capaciy uceraiy, o easily applicable approximaio echiques are proposed i he lieraure apar from more complex ad ime-cosumig algorihms ivolvig simulaio ad search mehods. 5 Coclusios I his paper, we propose a heurisic o evaluae he cos of he ACI iveory model ad deermie he value of ACI. The heurisic developme was moivaed by he fac ha he opimal aalysis of he problem is very edious, eve impossible for larger, real-life problems. Based o he isighs gaied from aalyzig he opimal policy, we firs give he releva maagerial isighs by showig whe ACI ca brig cosiderable iveory cos reducios ad describe he impora characerisics ha had o be addressed whe formulaig he heurisic. This, i iself, is a valuable resul sice i helps wih buildig up decisio-makers iuiio ad helps hem address he problem beer i a realisic siuaio. We ca coclude ha he performace aalysis of he proposed heurisic shows ha he heurisic works reasoably well i he ACI seig. Especially i he case where ACI is available ad he commo backorder o iveory holdig cos raio is assumed, he heurisic performace is wihi 1% of he opimal. We foresee ha effors o esablish a superior heurisic may be seriously hampered by he complexiy of he uderlyig problem. For a iveory corol policy o be applicable ad effecive i a pracical siuaio, a cerai degree of simplificaio is eeded ad fidig a good heurisic is a compromise bewee remai- 134
Orgaizacija, Volume 42 Research papers Number 4, July-Augus 2009 Table 2: The value of ACI ad heurisic performace ig pracical ad improvig accuracy by icreasig he complexiy. The proposed heurisic could also be esed for oher, more specific demad/capaciy siuaios such as where we are dealig wih wo-poi capaciy disribuio (eiher zero or full capaciy availabiliy). ieraure Bollapragada, S. & Moro, T. E. (1999). Myopic heurisics for he radom yield problem. Operaios Research. 47, 713-722. Bush, C. & Cooper W. (1988). Iveory level decisio suppor. Producio ad Iveory Maageme Joural. 29(1), 16-20. Buxey, G. (1993). Producio plaig ad schedulig for seasoal demad. Ieraioal Joural of Operaios ad Producio Maageme. 13(7), 4-21. OI: 10.1108/01443579310038769 Ciarallo, F. W., Akella R. & Moro T. E. (1994). A periodic review, producio plaig model wih ucerai capaciy ad ucerai demad opimaliy of exeded myopic policies. Maageme Sciece. 40, 320 332. OI: 10.1287/msc.40.3.320. Federgrue, A. & Zipki P. H. (1986). A iveory model wih limied producio capaciy ad ucerai demads i. he average-cos crierio. Mahemaics of Operaios Research. 11, 193 207. OI: 10.1287/moor.11.2.193. Güllü, R., Öol E. & Erkip N. (1997). Aalysis of a deermiisic demad producio/ iveory sysem uder osaioary sup- 135
Orgaizacija, Volume 42 Research papers Number 4, July-Augus 2009 ply uceraiy. IIE Trasacios. 29, 703-709. OI: 10.1080/0 7408179708966380. Iida, T. (2002). A o-saioary periodic review producio-iveory model wih ucerai producio capaciy ad ucerai demad. Europea Joural of Operaioal Research. 140, 670-683. OI: 10.1016/S0377-2217(01)00218-1. Jakšič, M., Frasoo J.C., Ta T., de Kok A. G. & Rusja B. (2008). Iveory maageme wih advace capaciy iformaio. Bea publicaie. wp 249, Bea Research School for Operaios Maageme ad ogisics, Eidhove Uiversiy of Techology, The Neherlads. Kapusciski, R. & Tayur S. (1998). A capaciaed producio-iveory model wih periodic demad. Operaios Research. 46, 899-911. OI: 899-911 10.1287/opre.46.6.899. Khag,. B. & Fujiwara O. (2000). Opimaliy of myopic orderig policies for iveory model wih sochasic supply. Europea Joural of Operaioal Research. 48, 181-184. OI: 10.1287/ opre.48.1.181.12442. Meers, R. (1997). Producio plaig wih sochasic seasoal demad ad capaciaed producio. IIE Trasacios. 29, 1017-1029. OI: 10.1080/07408179708966420. Meers, R. (1998). Geeral rules for producio plaig wih seasoal demad. Ieraioal Joural of Producio Research. 36, 1387 1399. OI: 10.1080/002075498193381. Moro, T. E. & Peico. W. (1995). The fiie horizo osaioary sochasic iveory problem: ear-myopic bouds, heurisics, esig. Maageme Sciece. 41, 334-343. OI: 10.1287/msc.41.2.334. Veio, A. (1965). Opimal policy for a muli-produc, dyamic, o-saioary iveory problem. Maageme Sciece. 12, 206-222. OI: 10.1287/msc.12.3.206. Marko Jakšič currely holds a posiio of a Teachig Assisa a he Faculy of Ecoomics Uiversiy of jubljaa. His area of experise is Operaios Maageme ad especially Supply Chai Maageme, which are he opics he is lecurig o a he bachelor ad he maser level sudies. He has aaied his Ph.. i cooperaio wih Techische Uiversiei Eidhove, The Neherlads, as a docoral sude a Faculy of Ecoomics ad a sude a Bea School for Operaios Maageme ad ogisics. His research work is focused o quaiaive aalysis of iveory maageme sraegies i supply chais ad as a resul he has published several papers i domesic ad foreig jourals ad cofereces. Boru Rusja aaied his Ph.. a he Faculy of Ecoomics Uiversiy of jubljaa i 1998. He is currely employed as a Associae Professor i he eparme of Maageme ad Orgaizaio, primarily lecurig i he field of Operaios ad Qualiy maageme. He has published a series of papers i domesic ad ieraioal jourals ad cofereces, where his mai research ieres lies i sraegic view of operaios maageme, qualiy maageme ad busiess excellece. Hevrisiče prisop k uravavaju zalog z iformacijo o razpoložljivosi oskrbe V sodobih oskrbih verigah je v zadjih dveh deselejih močo prisoe red izmejave iformacij, ki omogočajo izboljšaje poslovaja posamezih podjeij, ko udi celoe oskrbe verige. S pomočjo aačih i pravočasih iformacij, kaerih preos je z edavim razvojem iformacijskih ehologij močo olajša, se podjeja uspešo spopadajo s spremeljivimi i egoovimi pogoji poslovaja. V člaku predsavimo model uravavaja zalog s periodičim spremljajem zalog v pogojih eeakomerega sohasičega povpraševaja z omejeo zmogljivosjo oskrbe, kjer ima čle oskrbe verige dosop do iformacije o razpoložljivosi oskrbe. Iformacija o razpoložljivosi oskrbe zmajša egoovos prihodje oskrbe i omogoči maagerju učikoviejše aročaje. Na podlagi glavih vpogledov pridobljeih z aalizo opimale poliike aročaja razvijemo prakičo uporabo hevrisičo meodo. Z umeričo aalizo določimo vredos iformacije o razpoložljivosi oskrbe i prepozamo scearije, kjer je a ajvečja. Ob em a podlagi primerjave med rezulai opimale poliike aročaja i predlagae hevrisike izmerimo aačos le-e i podamo pogoje, ki morajo bii izpoljei, da hevrisika doseže želeo aačos. Ključe besede: Operacijske raziskave, uravavaje zalog, sohasiči modeli, iformacija o razpoložljivosi oskrbe, hevrisika 136