Allocating Redundancy to Critical Information Technology Functions for Disaster Recovery

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1 IT isastr Rcovry Allocatig Rdudacy to ritical Iforatio Tchology Fuctios for isastr Rcovry Bja B.. Shao W. P. ary School of Busiss Arizoa Stat Uivrsity ABSTRAT I th prst twork cooy, busisss ar bcog icrasigly rliat o iforatio tchology (IT) to prfor thir opratios ad xchag iforatio with busiss partrs. This havy dpdc o IT, howvr, poss a pottial thrat for a orgaizatio. Wh atural or a-ad disastrs strik ad caus alfuctio to its coputig ad couicatig systs, it would b vulrabl to busiss discotiuity. Svr cosqucs rsultig fro such IT brakdow ay iclud th loss of sals, daags to rputatio ad cosur cofidc, palty icurrd by failur to fulfill th ordrs, ad so o. As a rsult, th issu of how to strgth IT capabilitis so that a copay ca prvt or quickly rcovr fro disastrs bcos a srious cocr. I this papr, w prst a discrt optizatio odl to allocat rdudacy to critical IT assts for disastr rcovry plaig. Th objctiv is to axiz th ovrall survivability of a orgaizatio s critical IT fuctios by slctig thir appropriat rdudacy lvls whil still satisfyig a budgtary rsourc costrait. A solutio procdur basd o probabilistic dyac prograg is proposd to solv th forulatd probl, ad two cocrt xapls ar discussd to illustrat its usag ad ffctivss. Kywords IT disastr rcovry, rdudacy allocatio, discrt optizatio, dcisio-akig, dyac prograg. INTROUTION odr orgaizatios hav bco icrasigly dpdt o iforatio tchology (IT) to facilitat thir busisss. Larg-scal databass hadld by high-spd coputrs rtriv, aalyz ad sythsiz data collctd fro diffrt sourcs. ouicatio tworks lik th Itrt xchag, shar, ad trast iforatio i ral ti btw supplirs, vdors ad buyrs i a idustry valu chai to carry out busiss trasactios. oputr-aidd dsig tchologis hlp th product dvlopt ta captur or custor rquirts ad dvlop bttr products to t thir spcific ds. Ths fw xapls dostrat that IT is big harssd as a ky ablr for a orgaizatio s opratios i th prst twork cooy. Th prowss of advacd IT rprsts urous busiss bfits for a fir, icludig hacd productivity, icrasd flxibility, bttr quality, ad rducd costs. Utilizd proprly ad crativly, IT ca provid coptitiv advatags for a fir to iprov its coptitiv positio by rovig coptitio barrirs basd o ti ad distac (Iyr ad Sarkis, 998). This icrasd rliac o IT, howvr, poss a pottial thrat for a orgaizatio. Wh th occurrc of catastrophic vts or disastrs affcts its IT opratios ad causs thir failurs, th orgaizatio ay suffr fro th itrruptio of thir supportd busiss fuctios. Svr cosqucs rsultig fro such IT brakdow ay iclud th loss of sals, daags to rputatio ad cosur cofidc, palty icurrd by failur to fulfill th ordrs, ad so o. As a cosquc, th issu of how to strgth IT capabilitis so that a copay ca prvt or quickly rcovr fro disastrs bcos a srious cocr. larly, a orgaizatio dpdig o IT to support its busiss procsss ad fuctios ds ffctiv IT scurity asurs to sur busiss cotiuity i th vt of disastr striks (Lwis, Watso, ad Pickr, 2003). ay kids of pottial disastrs ay iobiliz a orgaizatio s IT capabilitis (hgalur-sth, Blardo, ad Pazr, 999). Natural disastrs lik flood, arthquak, hurrica, torado, blizzard, tc. ar frqutly coutrd. isastrs ca also b a-ad, ithr ittioal or uittioal, such as trrorist attacks, coputr hackrs, virus attacks, uio striks, urliabl hardwar, ad faulty softwar. aagt has to b awar of th risks to which thir busiss opratios ar xposd ad rcogiz th thrats ad vts that ar likly to occur i th virot i which thir fir is opratd (Jkis, 2000). Furthr, firs i th twork cooy o logr suffr alo fro disastrs. Wh a disastr occurs, busiss partrs, both upstra ad dowstra i th idustry valu chai, ay too suffr fro th cocotat Procdigs of th Tth Aricas ofrc o Iforatio Systs, Nw York, Nw York, August

2 IT isastr Rcovry cosqucs. I othr words, th ffcts causd by a disastr ca grat to othr titis ovr ithr th virtual or physical twork. A thorough dcisio aalysis aids i idtifyig, valuatig, ad strgthig critical IT fuctios that ust b aitaid i cas of a disastr (Taura, Yaaoto, Toyaa, ad Hatoo, 2000). A disastr rcovry pla is dfid as a syst for itral cotrol ad scurity that focuss o quick rstoratio for critical orgaizatioal procsss wh thr ar opratioal failurs du to atural or a-ad disastr (Bryso, illar, Josph, ad oboluri, 2002). Th objctiv of a IT disastr rcovry pla is to sur that a orgaizatio s coputig ad couicatio systs oprat soothly ad uitrruptdly durig ad aftr th occurrc of a disastr. Oc quippd with a ffctiv IT disastr rcovry pla, a orgaizatio is bttr prpard ad ca iz pottial loss by idtifyig, prioritizig ad safguardig valuabl IT assts that d protctio. O th cotrary, a uprpard busiss without a IT disastr rcovry pla i plac is likly to suffr fro th loss of iforatio ad th iability to cotiu its opratios du to disastr. spit th uquivocal iportac of IT disastr rcovry plaig, littl rsarch has b do so far o th foral odlig of its dcisio-akig procss. It has b suggstd that ay of th issus coutrd i disastr rcovry plaig ca bfit fro th applicatio of quatitativ dcisio-akig tchiqus (Bryso, illar, Josph, ad oboluri, 2002). I this papr, a discrt optizatio odl is proposd to assist IT aagrs i allocatig appropriat rdudacy lvl for valuabl IT assts so that th ovrall risks agaist pottial disastrs ca b rducd. Our odl taks ito accout th criticality ad costs of various IT assts as wll as th rsourc litatio subjct to budgt availability. Th raidr of this papr is orgaizd as follows. Sctio 2 discusss th cocpt of usig rdudacy as a protctiv as to prpar for IT disastrs. Th athatical optizatio odl for rdudacy allocatio is prstd i Sctio 3. A solutio procdur basd o probabilistic dyac prograg is proposd i Sctio 4, alog with th illustratio of two spcific xapls. Fially, th coclusio ad so topics suggstd for futur rsarch ar giv i Sctio 5. REUNANY FOR IT ISASTER REOVERY Th us of rdudacy i prparatio for disastrs is of pottial advatag bcaus it ca siultaously addrss two aspcts of disastr prparatio proactiv prvtio ad ractiv rcovry. Bfor a disastr occurs, rdudat copots ca tigat th pottial risks by workig as backup facilitis ad thus prvtig th disastrous cosqucs i advac (Grabowski, rrick, Harrald, azzuchi, ad va orp, 2000). Aftr th occurrc of a disastr, orgaizatios ca quickly rstor busiss fuctios ad procsss back to oral by substitutig rdudat copots for th priary but disabld parts whil thy ar big rpaird ad rstord. So far th practic of IT disastr rcovry plaig has b focusd o data rcovry ad progra rsuptio. ost orgaizatios owadays alrady hav daily backup procdurs for data ad progras, but ths procdurs alo ay ot b sufficit for rstorig busiss fuctios ad procsss back to oral proptly ough to sur busiss cotiuity (Iyr ad Sarkis, 998). Whil ths backup ad rcovry procdurs ar cssary for rsug th iforatio flow, thy ar sstially ractiv ad passiv i atur, litd i thir fuctioality. Thr ar ay othr vital IT fuctios that also d b actd. Such ractio-basd asurs thus ca b hacd by icorporatig rdudacy for vry critical IT asst. I a orgaizatio, th sa IT fuctio ca b ipltd by a ubr of IT assts. For xapl, th data backup procdur ca b prford usig ixpsiv agtic taps, odratly xpsiv -RW, xpsiv rdudat array of idpdt disks (RAI), or a cobiatio of ths tchologis togthr for rdudacy. Th IT assts cosidrd hr ar coprhsiv ad vary i scop. Thy ca iclud tagibl coputig hardwar, couicatio liks, IT prsol, ad othr ifrastructur that srv as th as by which data ar trasttd, procssd, or prstd for crtai IT fuctios. Altrativly, thy ca b itagibl assts lik databass cotaiig ssitiv custor iforatio or softwar progras dvlopd for data aipulatio. I trs of scop, ths IT assts ca b as sall as rdudat oduls for fault-tolrat softwar, or b as larg as a backup hot sit that has rplicatd alost vrythig for th whol IT dpartt. larly, IT assts diffr i thir pottial risks ad costs. As such, rdudacy at diffrt lvls also has diffrt cost ad bfit iplicatios. A rdudat odul i fault-tolrat softwar would likly cost oly a littl to dvlop but th risk tigatd by its prsc is probably sall as wll. O th othr had, a full-scal duplicatd hot sit rquirs a larg ivstt but ca provid a uch bttr protctio agaist a disastr; thus, it ay b a viabl optio for larg siz copais oly. Th objctiv is thus to slct aog ths coptig altrativs for rdudacy lvl ad rap th bst rturs subjct to rsourc litatios. A quatitativ aalytical odl ca provid th guidlis for allocatig th optial rdudacy lvl to critical IT fuctios that d th ost protctio i a cost-coscious ad ratioal way. Whil th tchiqu of itgr prograg has rctly b applid to th slctio of disastr scarios (Jki, 2000), ost studis hav ithr focusd o th ara of risk aalysis (Taura, Yaaoto, Toyaa, ad Hatoo, 2000) or b Procdigs of th Tth Aricas ofrc o Iforatio Systs, Nw York, Nw York, August

3 IT isastr Rcovry ractiv i atur by priarily dalig with th post-disastr opratioal activitis (Pidd, dsilva, ad Egls, 996). I aswr to th call for or rigorous quatitativ aalyss of th pr-disastr IT rcovry plaig (Bryso, illar, Josph, ad oboluri, 2002), w dvlop a discrt optizatio odl to hlp sur that IT disastr rcovry plas fuctio as xpctd wh put ito work. REUNANY ALLOATION OEL Suppos a fir is plaig for disastr rcovry by cosidrig icorporatig rdudacy lvl for its IT fuctios, ad th budgt is litd. Svral possibl disastrs hav b idtifid with th pottial to caus busiss discotiuity by affctig th supportig IT fuctios. Th qustio is how to allocat rdudacy to ths IT fuctios such that th ovrall survivability of ths IT fuctios agaist disastrs is axizd ad th cost rais udr budgt. Blow ar th paratr otatios ad thir dfiitios usd i th odl. : ubr of pottial disastrs + (th last o for o disastr occurrig); p d d = p d : probability of disastr d occurrig, p d (0, ) ad = ; : ubr of IT fuctios th orgaizatio ds to prfor; w = w : iportac wight (or frqucy of usag) of IT fuctio, w (0, ) ad = ; : ubr of solutios (assts) availabl for IT fuctio to slct fro; : if solutio i (=,, ) is slctd for IT fuctio, or 0 othrwis; : cost of slctig solutio i for IT fuctio ; S d : survivability of solutio i for IT fuctio agaist disastr d; d : failur probability of solutio i for IT fuctio agaist disastr d, d = S d ; B: availabl budgt. Th followig odl is forulatd to axiz th ovrall survivability of th idpdt IT fuctios: (RAP) * ax S = pd w d = = subjct to =, =, K, = 0 or, B d for =,..., ad i =,..., It is assud th occurrig probability p d of a crtai disastr d is kow or ca b stiatd. Th paratr is qual to th ubr of pottial disastrs plus o. Th last additioal o corrspods to th cas wh o disastr actually occurs (i.., p = p d ). orovr, th IT fuctios ar rgardd as sparat ad idpdt. Th criticality of a crtai IT d = fuctio is asurd by its frqucy of usag. Th ratioal is that th or frqutly a IT fuctio is usd to support busiss opratios, th or iportac it carris for th orgaizatio. Thr xists a pool of cadidat IT assts (solutios) to slct fro for IT fuctio. Wh a crtai IT asst i is slctd for IT fuctio, its corrspodig dcisio variabl is st to, or 0 othrwis. () (2) (3) Procdigs of th Tth Aricas ofrc o Iforatio Systs, Nw York, Nw York, August

4 IT isastr Rcovry I (RAP), th objctiv fuctio tris to axiz th ovrall survivability of all IT fuctios agaist all pottial disastrs. It rflcts th fact that a IT fuctio fails agaist a crtai disastr d oly wh all of its slctd solutios fail at th sa ti. I othr words, as log as o of th slctd solutios survivs th disastr, IT fuctio would still b opratioal, thus d. ostrait () surs that at last o IT solutio b slctd ad allocatd to ach IT fuctio. This, howvr, iplis that it is possibl for so IT fuctios to hav oly o solutio allocatd without rdudacy. I cas w ust hav at last so stadby solutio for vry IT fuctio, w d to oly chag th costat o th right had sid of costrait () fro to 2. ostrait (2) guarats that th total costs of rdudacy allocatio ot xcd th budgt litatio. To provid a systatic viw o th probl, Figur illustrats th scario that (RAP) attpts to rsolv. IT fuctio IT fuctio 2 IT fuctio : IT solutio : Allocatio : isastr : isastr ffct Figur. Rdudacy Allocatio Scario for isastr Rcovry Plaig SOLUTION PROEURE AN EAPLES Th proposd odl of (RAP) is a 0- itgr prograg probl with a oliar objctiv fuctio. For sall probl istacs, total uratio or athatical softwar packags ca b usd to solv (RAP). Howvr, for rlativly larg probls, such approachs ar likly ipractical. Furthr, owig to th o-liarity of th objctiv fuctio, Lagragia rlaxatio caot b ployd to hlp tackl this discrt optizatio probl. As such, a partial uratio solutio procdur basd o probabilistic dyac prograg (Wisto, 987) is prstd to hlp th solutio of (RAP). W first ca rforulat (RAP) as a izatio probl by rwritig th objctiv fuctio as follows: Procdigs of th Tth Aricas ofrc o Iforatio Systs, Nw York, Nw York, August

5 IT isastr Rcovry S * = = pd w d = pd w pd w d = = d = = d = = d = p d d = p d = To axiz S * is quivalt to izig F * w = d = d p d = = w d = p d = d w d d, which is th su of failur probabilitis of ay IT fuctio du to ay disastr. Nxt, w dfi a stat of syst T as th budgt availabl, ad stag to rprst IT fuctio for =,,. Lt F (T) b th failur rat of th syst coposd of IT fuctios, +,,, giv that T is th raiig budgt for IT fuctios,,. Th rcursiv forula for F (T) wh < is: F ( ) = + T w pd d F+ ( B ) (4) d = whr th variabls ar rstrictd to thos that satisfy ad T For stag (IT fuctio), stat (budgt) T caot xcd th total availabl budgt B us th iu costs to b allocatd for th raiig stags,,, ad it ust b at last qual to th cost of th last xpsiv solutio i th currt stag to guarat at last o solutio for IT fuctio. Thus, F (T) should b valuatd for all T valus i th rag: = { },, T K B,..., r= {,..., r For stats ot i th spcifid rag, F (T) ca b dfid as so it would ot bco th iu chos by Eq. (4) for stags,,. Th solutio procdur is basd o probabilistic dyac prograg bcaus, ulik dtristic dyac prograg, F (T) of Eq. (4) dals with th ucrtaity of disastr occurrig ad ivolvs th calculatio of xpctd failur rat of IT fuctio basd o th raiig budgt T. Th solutio procdur solvs (RAP) by workig backwards with th iitial stag = ad F whr agai th variabls i satisfy w i = pd d = id ri } i ( T) (6) i ad i i T Fially, th optial objctiv fuctio valu F * is obtaid as F (B) ad rprsts th iu ovrall failur rat of th whol syst coposd of idpdt IT fuctios with a budgt of B. That is, th origial axiu ovrall survivability S * of (RAP) is qual to F (B). (5) Procdigs of th Tth Aricas ofrc o Iforatio Systs, Nw York, Nw York, August

6 IT isastr Rcovry Exapl To dostrat th ffctivss of th proposd odl ad solutio procdur, w cosidr a hypothtical xapl i which a copay prfors two IT fuctios ( = 2) for its busiss opratios. IT fuctio is usd 30% of th ti (w = 0.30) ad IT fuctio 2 is usd 70% of th ti (w 2 = 0.70). Th copay is suscptibl to a floodig disastr that occurs with a liklihood of 0.05 (p = 0.05 ad p 2 = 0.95 for o disastr). Th copay is ow cosidrig icorporatig rdudacy for th two IT fuctios with a budgt B = 4. For IT fuctio, four solutios ar availabl ( = 4), with associatd costs of = 8, 2 = 3, 3 = 7, ad 4 = 5. Thir survival rats agaist th floodig ar S = 0.0, S 2 = 0.05, S 3 = 0.08, ad S 4 = 0.2 (i.., = 0.90, 2 = 0.95, 3 = 0.92, ad 4 = 0.88). Thir rliabilitis wh o disastr occurs ar S 2 = 0.95, S 22 = 0.88, S 32 = 0.92, ad S 42 = 0.85 (i.., 2 = 0.05, 22 = 0.2, 32 = 0.08, ad 42 = 0.5). For IT fuctio 2, thr solutios ar availabl ( 2 = 3), with associatd costs of 2 = 4, 22 = 6, ad 23 = 3. Thir survival rats agaist th floodig ar S 2 = 0.06, S 22 = 0.0, ad S 23 = 0.20 (i.., 2 = 0.94, 22 = 0.90, ad 23 = 0.80). Thir rliabilitis wh o disastr occurs ar S 22 = 0.92, S 222 = 0.78, ad S 232 = 0.84 (i.., 22 = 0.08, 222 = 0.22, ad 232 = 0.6). Th origial axizatio probl for this xapl is forulatd: ax S * subjct to = [ 0.30 ( ) ( )] [ 0.30 ( ) ( )] = 0 or, for all, i To apply th solutio procdur to this probl istac, w start with stag = 2. Sic th last xpsiv solutio for IT fuctio 2 has cost 23 = 3 ad th last xpsiv solutio for th oly raiig IT fuctio also has cost 2 = 3, th valid rag for T is 3 T (= 4 3). Eq. (6) th calculats F 2 (T) for T = 3,,. For istac, F 2 (7) is calculatd as: {(0.70)[ (0.05)(0.94) (0.90) (0.80) (0.95)(0.08) (0.22) (0.6) ] } 23 F ( 7) = + 2 whr th variabls 2i satisfy ad Thr ar four sts of 2i qualifid for F 2 (7), ad thy ar ( 2, 22, 23 ) = (0, 0, ), (0,, 0), (, 0, 0), ad (, 0, ). Th iu F 2 (7) = is foud associatd with ( 2, 22, 23 ) = (, 0, ). Th coplt rsults for F 2 (T) ar show i Tabl. T Solutio F 2 (T) 3 2 = 0, 22 = 0, 23 = =, 22 = 0, 23 = =, 22 = 0, 23 = =, 22 = 0, 23 = =, 22 = 0, 23 = =, 22 = 0, 23 = =, 22 = 0, 23 = =, 22 = 0, 23 = =, 22 = 0, 23 = Tabl. Stat T, Solutio, ad F 2 (T) for Stag 2 with B = 4 Procdigs of th Tth Aricas ofrc o Iforatio Systs, Nw York, Nw York, August

7 IT isastr Rcovry Nxt, w procd to fid th optial solutio F (4) i th xt stag = : F (4) = {(0.30)[(0.05)(0.90) + (0.95)(0.05) (0.2) 2 (0.95) (0.08) 2 3 (0.92) (0.5) 3 4 (0.88) ] + F 2 4 (4 whr th variabls i satisfy ad Thr ar sv sts of i qualifid for F (4), ad thy ar (, 2, 3, 4 ) = (, 0, 0, 0), (0,, 0, 0), (0, 0,, 0), (0, 0, 0, ), (,, 0, 0), (0,,, 0), ad (0,, 0, ). Th iu F (4) is foud associatd with (, 2, 3, 4 ) = (0, 0,, 0) with F * = F (4) = usig F 2 (7) = Thrfor, th axiu ovrall survivability S * agaist floodig is F * = = by slctig solutio 3 for IT fuctio ( 3 = ) as wll as solutios ad 3 for IT fuctio 2 ( 2 = 23 = ). Exapl 2 Lt us xa th ffct of havig or budgtary rsourcs for rdudacy allocatio. Suppos all th data ar th sa as i Exapl. Th oly xcptio is that th copay ow has a gratr budgt B = 6. Startig with stag = 2, th valid rag for T bcos 3 T 3 (= 6 3). Th valus of F 2 (T) for T = 3,, ar th sa as i Tabl. W thus oly d to coput F 2 (T) for T = 2 ad 3. Th rsults ar show i Tabl 2. 4 i i )} T Solutio F 2 (T) 3,, Sa as i Tabl 2 2 =, 22 = 0, 23 = =, 22 =, 23 = Tabl 2. Stat T, Solutio, ad F 2 (T) for Stag 2 with B = 6 W xt fid th optial solutio F (6) i th xt stag = : F (6) = {(0.30)[(0.05)(0.90) + (0.95)(0.05) (0.2) 2 (0.95) (0.08) 2 3 (0.92) (0.5) 3 4 (0.88) ] + F (6 whr th variabls i satisfy ad Thr ar i sts of i qualifid for F (6), ad thy ar (, 2, 3, 4 ) = (, 0, 0, 0), (0,, 0, 0), (0, 0,, 0), (0, 0, 0, ), (,, 0, 0), (, 0, 0, ), (0,,, 0), (0,, 0, ), ad (0, 0,, ). Th iu F (6) is foud associatd with (, 2, 3, 4 ) = (0,, 0, ) with F * = F (6) = usig F 2 (8) = Thus, th axiu ovrall survivability S * agaist floodig has b icrasd to F * = = by slctig solutios 2 ad 4 for IT fuctio ( 2 = 4 =) as wll as solutios ad 3 for IT fuctio 2 ( 2 = 23 = ). I this arragt, ach IT fuctio ow has at last o rdudat copot for disastr rcovry. OEL APPLIATIONS IN ORGANIZATIONS Th applicatio of th proposd rdudacy allocatio odl to ral-world risk aalysis of disastrs for odr orgaizatios ca b hacd by ay tchiqus that hav b dvlopd ad ployd by copais ad istitutios i th isurac idustry. For xapl, th liklihood of pottial disastrs assud i th odl ca b stiatd to a crtai dgr by historical data ad sophisticatd forcastig tools. I additio, th survivability of IT assts to b slctd fro th pool for ach critical IT fuctio ca b furthr guaratd by ithr th cotracts with vdors or th warrat offrd for IT assts. Whil th odlig dtails ay b too coplicatd for aagrs to fully coprhd, this should ot pos ay difficulty for its usrs. For xapl, th odl ca b dsigd as a dcisio support syst with a usr-fridly itrfac to shild aagrs fro such tchical itricacis. aagrs thus ca prfor ssitivity aalysis asily o IT disastr rcovry plaig by usig th dcisio support syst that icorporats th proposd rdudacy allocatio odl i i )} Procdigs of th Tth Aricas ofrc o Iforatio Systs, Nw York, Nw York, August

8 IT isastr Rcovry ONLUSIONS Th cotiud rapid advac i coputr ad couicatio tchologis abls thir widsprad us of supportig busiss procsss ad fuctios. orovr, xtsiv chags i busiss procss autoatio ad rdsig hav b ad possibl by IT as wll. Th ability of IT to facilitat couicatio ad iforatio xchag i ral ti has rsultd i urous bfits for a busiss opratig i th prst twork cooy. With th icrasd iportac of IT for th opratios of odr orgaizatios, w ca aticipat a v gratr IT adoptio by or idustris for a wid varity of applicatios i th ar futur. Howvr, coputr ad couicatio systs that srv as th backbo of today s busiss fuctios also rprst pottial vulrabilitis to disastrs. Wh a disastr striks ad causs disruptio to a fir s IT fuctios ad thus thir supportd opratios, th vt ay asily thrat th survival of a busiss. aagrs ust prfor a busiss ipact aalysis to both valuat th dgr to which thir IT opratios ar suscptibl to disastrs ad asur th pottial losss causd by such disastrs. Th thy ust tak cssary actios to strgth ths IT fuctios accordig to thir criticality. Th discrt optizatio odl proposd i th papr ca fulfill th d for a structurd dcisio aalysis of IT disastr rcovry plaig. Th odl attpts to axiz th ovrall survivability of IT fuctios agaist pottial disastrs by allocatig appropriat rdudacy lvls whil takig ito accout th tradoff btw survival rats ad costs of IT solutios slctd. Th fasibl us of athatical optizatio is dostratd as a ffctiv dcisio support tool for bttr rsourc allocatio of rdudacy to cop with disastr rcovry. Th ai purpos is to sur IT capabilitis ar uitrruptd ad thir supportd busiss procsss oprat cotiuously by usig rdudat solutios as backup as to wathr pottial disastrs. It is otd that th proposd odl is a gralizatio of th rliability optizatio odls for softwar ad hardwar (Ashrafi ad Bra, 992). Wh o disastr is cosidrd possibl (i.., = i our odl), (RAP) is rducd to a rliability probl dalig with fault tolrac (Kuo ad Prasad, 2000). I othr words, th odl proposd i th papr is abl to hadl such spcial cass of softwar ad hardwar rliability as wll. I additio, (RAP) is rlatd to th gral discrt rsourc allocatio probls (Ibaraki ad Katoh, 988; Shao ad Rao, 200), but it cosidrs a varity of IT rsourc typs for supportig spcific IT fuctios, istad of gral rsourcs that ca b allocatd to ay activity or agt. So topics ar suggstd for futur rsarch. Th IT fuctios cosidrd by our odl ar tratd as sparat ad idpdt, which as thr is o physical or logical lik btw ay two IT fuctios. This assuptio ay hav a ffct o th graularity of IT assts big rlativly larg sic fir-graid IT assts typically ca srv ultipl purposs. For xapl, a workstatio ay b usd siultaously as wb srvr, databas srvr, ad ail srvr to support IT fuctios of -corc trasactios, data storag, ad iforatio couicatio, rspctivly. I futur study, th proposd odl ca b xtdd to addrss itrrlatd IT fuctios by odifyig th objctiv fuctio. Th approach of probabilistic dyac prograg would still b applicabl for solvig this xtdd probl (Bra ad Ashrafi, 993). orovr, w ca catgoriz IT assts as hardwar, softwar, hua capitals, ad othr typs to xa th ipacts of spcific charactristics of ach IT asst typ o th rdudacy allocatio dcisios for disastr rcovry plaig. For xapl, tagibl hardwar caot b duplicatd without purchasig two quipts, but softwar with propr licss ca b asily dployd to ay IT assts. Thir costs iplicatios thus ar xpctd to b diffrt. Aothr prosig avu would b to look at rdudacy allocatios at th idustry valu chai lvl ad aalyz disastr rcovry plaig across busiss partrs i a coordiatd ad collaborativ ar. REFERENES. N. Ashrafi ad O. Bra. Optizatio odls for Slctio of Progras, osidrig ost & Rliability. IEEE Trasactios o Rliability, vol. 4, o. 2, pp , Ju O. Bra ad N. Ashrafi. Optizatio odls for Rliability of odular Softwar Systs. IEEE Trasactios o Softwar Egirig, vol. 9, o., pp. 9-23, Nov K. Bryso, H. illar, A. Josph, ad A. oboluri. Usig Foral S/OR odlig to Support isastr Rcovry Plaig. Europa Joural of Opratioal Rsarch, vol. 4, pp , I. hgalur-sth, S. Blardo, ad H. Pazr. Adoptig a isastr-aagt-basd otigcy odl to th Probl of Ad Hoc Forcastig: Toward Iforatio Tchology-Basd Stratgis. IEEE Trasactios o Egirig aagt, vol. 46, o. 2, pp , ay 999. Procdigs of th Tth Aricas ofrc o Iforatio Systs, Nw York, Nw York, August

9 IT isastr Rcovry 5.. Grabowski, J. R. W. rrick, J. R. Harrald, T. A. azzuchi, ad J. R. va orp. Risk odlig i istributd, Larg-Scal Systs. IEEE Trasactios o Systs, a, ad ybrtics-part A, vol. 30, o. 6, pp , Novbr T. Ibaraki ad N. Katoh. Rsourc Allocatio Probls. IT Prss, A, R. K. Iyr ad J. Sarkis. isastr Rcovry Plaig i a Autoatd aufacturig Evirot. IEEE Trasactios o Egirig aagt, vol. 45, o. 2, pp , ay L. Jkis. Slctig Scarios for Evirotal isastr Plaig. Europa Joural of Opratioal Rsarch, vol. 2, pp , W. Kuo ad V. R. Prasad. A Aotatd Ovrviw of Syst-Rliability Optizatio. IEEE Trasactios o Rliability, vol. 49, o. 2, pp , Ju W. Lwis, Jr., R. T. Watso, ad A. Pickr. A Epirical Asssst of IT isastr Risk. ouicatios of th A, vol. 49, o. 9, pp , Spt Pidd, F. dsilva, ad R. Egls. A siulatio study for rgcy vacuatio. Europa Joural of Opratioal Rsarch, vol. 90, pp , B. B.. Shao ad H. R. Rao. A oparativ Aalysis of Iforatio Acquisitio chaiss for iscrt Rsourc Allocatio. IEEE Trasactios o Systs, a, ad ybrtics-part A, vol. 3, o. 3, pp , ay H. Taura, K. Yaaoto, S. Toyaa, ad I. Hatoo. odlig ad Aalysis of cisio akig Probl for itigatig Natural isastr Risks. Europa Joural of Opratioal Rsarch, vol. 22, pp , W. L. Wisto. Opratios Rsarch: Applicatio ad Algoriths. PWS Publishrs, Bosto, A, 987. Procdigs of th Tth Aricas ofrc o Iforatio Systs, Nw York, Nw York, August

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