Procdns of th 43rd Hawa Intrnatonal Confrnc on Systm Scncs - 2010 Manan th Outsourcn of Two-Lvl Srvc Procsss: Ltratur Rvw and Intraton Edal Pnkr Unvrsty of Rochstr pnkr@smon.rochstr.du Robrt Shumsky Dartmouth Coll Robrt.A.Shumsky@dartmout h.du Hsao-Hu L Unvrsty of Rochstr Hsao- Hu.l@smon.rochstr.du Samr Hasja INSEAD samr.hasja@nsad.du Abstract Th outsourcn of srvc procsss prsnts svral complx manamnt challns. Srvcs typcally hav varablty n both th pattrn of customr arrvals and srvc tms, whch mak capacty plannn challnn. Workrs also hav dscrton ovr th workflow, and thrfor ach workr can affct th workload passd to othr parts of th systm. Whn a srvc procss s outsourcd, ths dscrton may b n th hands of a vndor who thn maks chocs that nflunc th customr xprnc. A frm must dcd upon th dsn of th procss, whch parts of th procss to outsourc, and how to contract wth th vndor to ovrcom ssus rlatd to nformaton asymmtry. Ths papr addrsss ths qustons wthn th contxt of a two-lvl srvc procss whr th frst lvl srvs as a atkpr for xprts n th scond lvl. W ntrat th rsults from svral paprs n th ltratur to v a comprhnsv prspctv on how to approach srvc outsourcn. 1. Introducton Thr ar many srvc procsss that ar oranzd n two lvls. Th frst lvl prforms tra to dtrmn whch cass may b tratd at th frst lvl, and whch rqur attnton at th scond lvl. Typcally th frst lvl s staffd by chapr, lowr-sklld workrs whl th scond lvl s staffd by mor xprt workrs who command hhr was. Exampls of such systms nclud tchncal support cntrs, mdcal srvcs, and th crdt applcaton dvsons of banks. In all of ths systms som customr cass can b succssfully handld at th frst lvl whl othrs cannot. W rfr to th frst-lvl workrs as atkprs bcaus thy control th flow of customr rqusts to workrs at th scond lvl, who w rfr to as xprts. In ths papr w wll dscuss th manamnt of such two-lvl srvc procsss. W choos to focus on such systms bcaus a) thy ar common n practc, b) thy ar smpl nouh to b amnabl to dtald analyss, and c) workr dcsons affct th flow of work. Thrfor wthn th contxt of such systms w can addrss opratonal qustons such as how th procss should b dsnd and staffd. W can also addrss conomc qustons, such as what ncntvs should b vn to th workrs and how th outsourcn of th procss can b manad va contract dsn. Our oal s to mprov our undrstandn of th ntrplay btwn ths dffrnt factors n th contxt of srvc procss outsourcn. To ths nd, w summarz and synthsz rsults from a varty of paprs. Each partcular papr n ths ara dscrbs som varant of ths srvc systms. On papr analyss on-lvl systms, whl othrs analyz two-lvl systms. Som xamn cntrally controlld systms, whl othrs xamn outsourcn and contractn dcsons. On papr dscrbs a dtrmnstc modl whl othrs nclud stochastc quun phnomna. In ths papr w athr tothr ths rsults and ntrat thr answrs to nral qustons,.., whn should on or two-lvl systms b usd? If th on-lvl or two-lvl systm s outsourcd, dos an optmal contract xst, and what form mht t tak? Fur 1: Schmatc of Workflow Customr ntrs Gatkpr Danoss 1-k Exprt Tratmnt 1-F(k) Customr xts k Gatkpr Tratmnt k-f(k) F(k) Customr xts Dspt th wd varty of potntal applcatons, throuhout ths papr w wll us lanua drvd from th halth car sttn. W wll rfr to th ntal assssmnt by th atkpr as a danoss, th 978-0-7695-3869-3/10 $26.00 2010 IEEE 1
Procdns of th 43rd Hawa Intrnatonal Confrnc on Systm Scncs - 2010 rsoluton of th customr's problm as a tratmnt, and a atkpr's unsuccssful attmpt at rsoluton as a mstratmnt. Fur 1 provds a schmatc of th systm. It shows that all customrs ar ntally danosd by th atkpr, wth a fracton k rcvn tratmnt from th atkpr as wll. Of thos rcvn tratmnt from th atkpr, a fracton F(k) ar succssfully tratd and thus lav th systm mmdatly wthout sn an xprt. A fracton 1-k of th customrs ar drctly rfrrd to th xprts aftr danoss by th atkpr, whl a fracton k-f(k) ar mstratd by th atkpr and ultmatly nd up at th xprt. To smplfy our analyss, w assum that xprts can rsolv all customr rqusts. A manar of such a systm has a numbr of dcsons to mak. A vry fundamntal dcson s: should ths procss b opratd as a two-lvl procss at all? It s possbl that a on-lvl systm staffd only wth xprts s mor ffcnt. For both on and two-lvl systms th manar must dcd how many workrs to staff. For a two-lvl systm th manar must also dcd whch cass should b tratd by th atkpr and whch ons should b drctly rfrrd to th xprts. A hhr-lvl dcson rlats to outsourcn. Should th manar outsourc all or som part of th procss? Fnally, from th manar s prspctv thr ar potntally two knds of ants n ths systm: th workrs, and th vndor to whch work s outsourcd. Both ants may hav nformaton about thr actons and capablts that ar dffcult for th manar to obsrv. Ths nformaton asymmtry crats an ancy problm that must b manad as wll. Thrfor th manar must construct an ncntv systm to nsur that th ants ar actn n hs ntrsts. As part of our analyss w wll also nvstat how ths dcsons ar nfluncd by th prsnc of stochastcty n th systm. Srvc procsss oftn nvolv lar amounts of uncrtanty that s drvn by th customr s rol n th procss. Bcaus srvcs rqur co-producton btwn a frm and ts customrs, randomnss n th arrval procss of customr rqusts cannot b manad throuh th us of nvntory. Furthr, customr nvolvmnt maks ach provson of th srvc a somwhat customzd actvty, whch ntroducs uncrtanty nto th srvc tm. Our oal s to provd a st of contractn udlns for manars who ar outsourcn two-lvl srvc procsss, by ntratn rsults of studs of varous aspcts of srvc procss manamnt and outsourcn. W ntnd our analyss to also contrbut mor broadly to th undrstandn of what factors manars of nral srvc procsss nd to consdr whn outsourcn, as wll as to th undrstandn of th tools avalabl for analyzn such systms. W draw upon svral strams of rsarch whch w summarz n Scton 2. In Scton 3 w dscrb a dtrmnstc modl of th two-lvl systm manad ntrnally, whch forms th bass of th papr. In Scton 4 w consdr th stochastc vrson of th systm and llustrat th nw ssus rasd whn conston and quun bcom factors n th analyss. In Scton 5 w dscrb modls for outsourcn of both dtrmnstc and stochastc systms and prsnt optmal contractn schms. In Scton 6 w prsnt rsults on outsourcn wth nformaton asymmtry about ant and vndor capablts. W conclud n Scton 7. 2. Summary of Rlatd Ltratur To addrss th ssus rasd abov w draw upon svral dffrnt strams of rsarch: busnss procss rnnrn and dsn, prncpal-ant modls, modls of stochastc srvc systms, and outsourcn. On of th most common busnss procss rnnrn (BPR) tchnqus s to rplac a procss n whch functonal spcalsts prform squntal tasks wth a systm that tras (ffcntly routs) customrs amon workrs. In a typcal tran systm, customrs frst ntract wth a nralst who dtrmns f th customr rqurs th attnton of a spcalst. Cas studs dscrbd n [14] ndcat that ths approach can hav normous ffcncy bnfts. In a srs of paprs usn quun analyss, [28], [29], and [30] nvstat th factors that nflunc th bnfts of tran. [5] also uss quun modls to nvstat th condtons undr whch varous rnnrn strats, such as th us of paralll casworkrs rathr than sral procssn, mprov procss prformanc. All of ths paprs focus on how structural chocs affct systm prformanc. Ths stram of rsarch, howvr, dos not xamn th ntractons btwn th ncntvs and th bhavors of ndvdual workrs. Mor prcsly, n all of ths paprs, for a vn systm confuraton th rat at whch work s routd amon work statons s dtrmnd xonously. W blv that th ultmat succss of any attmpt to rnnr a systm hns on th dr to whch th mploys adhr to th procss oals and protocols. In our tran systm, th atkprs dcsons rardn whn to rfr a cas to an xprt ar crtcal to th procss prformanc. As n th classc prncpalant modl, th atkpr s prfrncs may dffr from th prncpal s, and thr may b nformaton asymmtry btwn th prncpal and th ant (n our cas th atkpr but not th frm may s th 2
Procdns of th 43rd Hawa Intrnatonal Confrnc on Systm Scncs - 2010 dtals of ach customr s problm and th sutablty of th atkpr s sklls for that customr). Thr s a rch ltratur n conomcs on stuatons charactrzd by such nformaton asymmtry: th rsarch on th prncpal-ant modl as wll as rlatd work on contract (or, mor nrally, mchansm) dsn. Ths stram of rsarch ncluds th dynamc prncpal-ant modl n [17], and th multtask prncpal-ant modls n [18] and [20]. Ths paprs usually bn wth xtrmly nral modls of th rlatonshp btwn workr actons and output. A standard modl s dscrbd n [17], n whch th workr (ant) chooss an acton p, and th mpact of that acton s fully dscrbd by ts affct on th probablts of outcoms θ 1, θ N. In ths papr, howvr, w focus on modls that dscrb th opratonal dtals of actons and outcoms. Thrfor, our modls ar lss nral thy only apply to atkpr systms but thy provd dpr nshts nto th challns of manan thos systms, as wll as clarr rcommndatons for opratn dcsons (staffn, routn) and conomc dcsons (contract dsn). In partcular, th sttn hr s dstnushd from prvous work n both ancy thory and prsonnl conomcs n that accountn for how an ant allocats hr tm s mportant. For xampl, f a atkpr dcds to trat a partcular customr to obtan a rward, thn th atkpr s sacrfcn th ablty to trat any othr customr durn that prod of tm (.., tm s mony ). [31] hav dvlopd a modl that taks ths factors nto account to drv nshts about th lmts of compnsaton schms that ar td to tm-ntnsv nvstmnts by th ants. Wthn th conomcs ltratur, both [10] and [25] do dal xplctly wth atkprs and rfrral procsss. Aan, th modln of tm n [31] s a dstnushn fatur of th work. Th modl n [10] dscrbs how low-sklld and hh-sklld ants may dsn contracts to shar an ncom-producn opportunty obtand by th low-sklld ant. [25] dscrbs a srvc systm n whch a atkpr must dcd whthr to mak a rfrral that s costly to th frm, but th atkpr dos not hav th opton to offr any tratmnt hrslf. Thy focus on th nffcncs cratd whn a atkpr s allocatd a budt that xprs aftr a fxd tm prod. Th dstncton btwn [31] and ths othr studs, n trms of how th ant s tm s modld, s an mportant on. In [31] th dcsons mad by th atkpr hav mplcatons for how thy spnd thr tm, whch affcts utlzaton, whch thn affcts staffn dcsons. Th staffn dcson tslf bcoms vn mor mportant whn on consdrs a stochastc modl, whr th manar must balanc staffn costs and th mplct costs of customr watn tm. Thr has bn som rlatd work on ncntvs n stochastc srvc sttns. [11] us a prncpal-ant framwork to compar a srvc ntwork wth a common quu to a srvc ntwork wth sparat quus. In thr modl, a cntral, coordnatn ancy maks routn dcsons. In our cas w ar ntrstd n how th ants thmslvs mak routn dcsons. [22] also formulat a modl n whch ants drct customrs to srvc cntrs. In thr modl, th ants (or atkprs) do not hav th opton to trat th customr, and ach ant sks to mnmz hr customrs xpctd watn tms at th srvc cntrs. [12] xamn how ncntvs n a call cntr can affct th quantty of srvc offrd to dffrnt classs of customrs, focusn on how ncntvs ntract wth th cost of conston and th customr smntaton dcson. [23] s closly rlatd to [31] n that th prncpal dsns ncntvs to nduc ant ffort that affcts workflow. [23], howvr, s basd on a manufacturn sttn n whch dfctv jobs may b routd back to th workr who causd th dfct, to a rwork spcalst, or to anothr workr who may b workn on nw jobs. Thrfor, n [23], on workr s actons may nflunc both th flow of jobs as wll as th contnt of jobs sn by othr workrs. Whl not xplctly modln a prncpal-ant sttn and ncntvs [19] also consdr stuatons n whch workrs hav dscrton about how thy allocat thr tm n wht-collar work. [15] and [21] xtnd th dtrmnstc modl of [31] to a stochastc sttn. Wth stochastc customr arrvals and srvc tms t s ncssary to modl th systm as a quun systm and to tak nto account customr watn costs and staffn lvls. Ths works mak us of asymptotc quun approxmatons dvlopd n [13] and th squar root staffn ruls dvlopd n [4]. Thy show that ssntally th sam atkpr ncntvs dvlopd for th dtrmnstc atkpr systm modld n [31] can b appld ffctvly n th stochastc sttn. Ths rsults v a foundaton upon whch to consdr outsourcn all or part of th srvc procss. Whl consdrabl attnton has bn vn to outsourcn contracts n manufacturn supply chans (s [6] and th rfrncs thrn), th ltratur on outsourcn contracts for srvc supply chans s mor lmtd. Th work n ths ara has focusd on callcntr outsourcn bcaus that nvronmnt s most amnabl to analyss usn tools from quun thory. In addton, call cntrs hav wll-dfnd prformanc mtrcs. S [8] for a survy of call-cntr rsarch. [9] and [1] consdr a clnt who can outsourc som fracton of srvc calls to a vndor. [9] study th 3
Procdns of th 43rd Hawa Intrnatonal Confrnc on Systm Scncs - 2010 cntralzd capacty dcson and quun control problm. [1] compar th qulbrum prformanc of srvc systms n whch th clnt thr outsourcs a stady stram of calls or outsourcs pak dmand. Ths studs vw outsourcn as a mchansm for handln varablty n srvc dmand. Essntally thy ar askn whch porton of th workload should b don n-hous vrsus outsourcd. Our attnton hr s on whch porton of th procss should b outsourcd. W ar also ntrstd n dtrmnn th ncntv contract that wll mak th arranmnt work bst. [2] study rtalrs who ar lockd n prc and watn-tm comptton and hav th opton to outsourc call cntr srvc to a common vndor. Thy prsnt condtons undr whch outsourcn s proftabl for th clnts. A porton of thr analyss dscrbs th ffcts of volum-basd contracts on srvc supply chan coordnaton; w wll also consdr smlar contracts. [26] study a srvc supply chan consstn of a snl clnt and a snl vndor, and also consdr contracts that nduc th vndor to choos supply chan optmal staffn lvls. Thy assum that vndor productvty s common knowld and focus on th vndor s lvl of ffort, whr hhr ffort ncrass th probablty that a call arns rvnu for th clnt. In thr analyss, thy us a flud modl that ssntally nors quun ffcts. [16] also modl a clnt that outsourcs a call-cntr to a vndor, and us a stochastc modl that prsrvs quun ffcts. Thy consdr both th cas n whch th frm knows th srvc rat of th vndor and th cas n whch t dos not. Wth full nformaton, th clnt must dsn a contract that wll ncoura th vndor to staff suffcntly. Wth unknown srvc rats th frm must structur th contract to both ncoura th vndor to work as fast as h can and to staff appropratly. Studyn qualty, byond watn tm, n srvc outsourcn s challnn bcaus prformanc masurmnts ar poorly dfnd. An xcpton s [3] who xamn coordnaton of th qualty-of-srvc dcsons mad by vndors. Thy study ovrnanc systms whr th clnt actvly partcpats n th manaral procss of montorn and controlln th vndor s ants to nsur a dsrd qualty lvl. Thy fnd that whn th outsourcd srvc procss s complx, so that th cost of masurn output qualty s hh, thn th clnts can ncras th ffcncy and scop of outsourcn by combnn th ffcncy of th prc mchansm (markt control) wth manaral control. Thy also show that for a low-complxty procss, thr s no snfcant advanta for th clnt to xrt manaral control ovr th vndor s ants. 3. Dtrmnstc Modl In ths Scton w summarz th analyss of th dtrmnstc atkpr modl from [31]. Ths modl s th basc buldn block of th analyss n subsqunt sctons. W assum that ach atkpr can rankordr customr jobs n trms of ncrasn complxty. Lt k [0,1] b a fractl of call volum, rankd by tratmnt complxty, that s, k dnots a poston n th rankn of calls such that k 100% of calls ar lss complx. W dfn th atkpr s tratmnt functon as dnotn th probablty that th atkpr can succssfully trat th problm durn a tratmnt tm wth xpctd duraton t, vn that th customr s problm s at th kth fractl of dffculty (assumn, of cours, that th atkpr maks an ffort to provd tratmnt to th customr). In our modl, th complxty ordrn of tasks may vary from atkpr to atkpr (.., at a tchncal support dsk, modm ltchs may prsnt dffcults for on atkpr whl problms wth -mal may b dffcult for anothr). Howvr, hr w assum that th skll lvl for ach lvl of complxty, dfnd by s th sam for all atkprs. W also assum to smplfy th analyss that th xpctd tratmnt tm t dos not vary wth call complxty k. From th dfnton of k, t follows that 0 k 1, 0 1, and < 0 (th last nqualty stms from th ordrn of calls by tratmnt dffculty). Lt F(k) b th xpctd fracton of all calls that ar succssfully tratd by th atkpr, vn that th atkpr chooss to trat all calls up to and ncludn th kth fractl, so that and 0 F(k) k. W dfn th follown cost paramtrs: C =atkpr was ($/tm prod). C = xprt was ($/tm prod). C m = xpctd cost of ncorrct tratmnt by a atkpr ($/customr). Ths ncluds any oodwll cost as wll as th xpctd cost of customr rntry. W ar assumn hr that t s dffcult for a manar to obsrv th dffculty of ach cas handld by a atkpr and thrfor know th atkpr s lklhood of succssfully tratn th cas. Wthout known ths lklhood th manar cannot say f th cas should b tratd by th atkpr or rfrrd drctly to an xprt. Ths nformaton asymmtry btwn th atkpr and th manar mans that th manar would lk to construct an ncntv systm that compls th atkpr to rfr n a systm-optmal way. W assum that customrs arrv accordn to a dtrmnstc procss and that th danoss and tratmnt tms ar dtrmnstc. Th atkpr s paramtrs ar: d for atkpr danoss tm, t for atkpr tratmnt tm and t for xprt tratmnt tm. Th frm s problm s to mnmz th labor and mstratmnt costs pr cas. Staffn lvls ar fully 4
Procdns of th 43rd Hawa Intrnatonal Confrnc on Systm Scncs - 2010 dtrmnd by th atkpr tratmnt dcson. Staffn any lss would lad to an ovrloadd systm and staffn mor would not add any valu. Fur 2: Tratmnt Functon a hh-sklld 1 atkpr f(k) a low-sklld atkpr 0 0 k (cas dffculty) Th frm s objctv functon s: 1 (1) Ths ylds th optmal tratmnt thrshold, k C + C t * 1 = m f Cm + Ct (2) Furthr, f k* cannot b prscrbd by manars (.., f th srvc s outsourcd and th rfrral rat cannot b obsrvd), thn [31] fnd that th frm can lct th optmal rfrral bhavor from th atkprs by offrn thm a paymnt pr danoss and a bonus for ach succssfully tratd cas. In ths dtrmnstc systm, dcdn f a on-lvl procss s prfrabl rqurs a smpl comparson of th pr-cas labor costs. Wth only xprts th cost would b t C pr call whl wth atkprs th cost s vn by th objctv functon n (1) wth k = k* as n quaton (2). 4. Stochastc Modls In a systm wth stochastc arrvals and srvc tms, nw dynamcs ntr th analyss. Frst, stochastc srvc systms (quus) hav conston and thus w ar concrnd wth customr watn. Scond, staffn dcsons bcom mportant bcaus of th nhrnt trad-off btwn staffn and watn costs. Thrd, from a procss dsn prspctv, multpl lvls ntroduc addtonal dlays thus chann th calculus of th dcson to hav on or two lvls. Fourth, conoms of scal can b mportant n stochastc systms bcaus thy nabl th pooln of varablty. Ths wll also nflunc th choc of on or two-lvl systms and how work s dvdd btwn th two lvls. For th stochastc systm w dfn th follown addtonal notaton: µ th srvc rat at th atkpr lvl (a functon of k µ th srvc rat of th xprt.. 1 λ customr arrval rat to th systm λ arrval rat to th xprts (a functon of k) n, n th staffn at th atkpr and xprt lvls, rspctvly W, W th xpctd watn tm at th atkpr and xprt lvls, rspctvly C w cost of watn, pr unt tm 4.1. Cntralzd Systm For a frm that has complt control ovr th staffn and tratmnt thrshold th objctv functon s, Mn C n + C n + C [ W λ + W λ ( k) ] n, n, k + C ( k F( k)) λ. m (3) Not that th watn tms at th atkprs and xprts ar dpndnt upon th tratmnt thrshold k and th staffn lvls. As shown n Fur 1, vn k* at th atkpr lvl, th srvc rat of th atkpr s dtrmnd, and th rat of flow from atkprs to xprts s also dtrmnd. To drv xprssons for th watn tm at ach lvl that wll nabl us to dtrmn optmal staffn lvls, w mak a fw smplfyn approxmatons. Frst w assum, as n standard n such modls, that th customr arrval procss to th atkprs s Posson. Scond, w assum that th srvc procsss at both th atkpr and xprt lvls ar xponntal. Th atkprs srvc rat s whl th xprts s. For th atkprs ths approxmaton s mor snfcant bcaus thr srvc tms ar a mxtur of danoss and tratmnts. Our fnal approxmaton s that th arrval procss to th xprt quu s Posson as wll. Th abov approxmatons mply that for a fxd thrshold k th two sub-systms (atkpr and xprt) can b analyzd ndpndntly as M/M/N quun systms for th purpos of dtrmnn th staffn lvls that optmally balanc watn and staffn costs. In partcular, t mans that f w assum w ar opratn n th QED rm of [13] w can us squar-root staffn ruls as n [4] to dtrmn optmal staffn. In addton, n th QED rm thr xst closd-form xprssons for xpctd wats. Thrfor, w hav mad two sts of approxmatons: that ach quu s an M/M/N systm, and that ach oprats n th QED rm. Exprmnts n [4], [13], [15], and [21] show that both of ths approxmatons ar xtrmly accurat. For xampl, xprmnts n [21] dmonstrat that ovr a wd varty of paramtrs, th man rror for th total tm n systm s lss than 1%, and for lar systms (ovr 250 srvrs), th maxmum rror s 3.5% or lss. w 5
Procdns of th 43rd Hawa Intrnatonal Confrnc on Systm Scncs - 2010 In addton, th larst rrors ar not causd drctly by th approxmatons, but rathr by th roundn of staffn lvls (th QED approxmaton and squarroot staffn rul lad to a contnuous staffn lvl, whl th tst smulaton n [21] rqurs ntr staffn lvls). Lkws, xprmnts n [15] show that th rror n th total cost of th systm du to th approxmaton s consstntly lss than 1% and that staffn dcsons mad undr th approxmaton ar consstntly dntcal to, or wthn 1 srvr, of th xact optmal soluton. 4.2. Squar-Root Staffn Approxmaton Th squar root staffn rul follows [4]. Consdr a snl-quu systm n th QED rm wth an arrval rat of λ a srvc rat of µ and n srvrs. Th optmal staffn lvl s: n = ρ + β ρ, (4) whr β can b sn as th standard xcss capacty n ordr to mana th systm varablty and ρ = λ /µ. W can always fnd a β that mts th dsrd srvc rqurmnt. In ths papr, w quantfy th srvc rqurmnt by th watn tm, and th oal s to mnmz th xpctd total cost C n + C w W, n whch C w s th watn cost pr unt tm, C s th unt cost pr staff n systm, and W s th man watn tm n systm. For an M/M/N quu, th xpctd watn tm W can b rprsntd as a functon of β, λ and µ ([13]):, (5) n whch Φ / and Φ and ar th CDF and PDF of a standard normal dstrbuton. Thrfor β can b wrttn as: β = ar mn Cˆ ( β ) β (6) Cˆ ( β ) = Cβ + Cwα ( β ) For a cntralzd dcson makr usn squar root staffn ruls optmally manan th two-lvl srvc systm s rducd to a on varabl problm: choosn th atkpr tratmnt thrshold k. 4.3. Optmal Tratmnt Thrshold Th optmal tratmnt thrshold s dffcult to calculat for a stochastc systm. Howvr [15] hav found that for a lnar tratmnt functon th dtrmnstc tratmnt thrshold s vry clos to optmal. Th cass n whch t s snfcantly dffrs from th optmal ar thos cass n whch t s optmal to oprat a on-lvl systm of xprts anyway. [21] show that for a lar class of tratmnt functons th optmal tratmnt thrshold asymptotcally approachs th dtrmnstc on for lar systms. In partcular th optmal thrshold s dscrbd by: * ( 1+ Θ ) ( k, Cw) * ( 1+ Θ (, ) k Cw = C + 1 m Ct f C + ) m Ct * k. (7) Thrfor, k* s calculatd rcursvly, and bcaus f s contnuous, from th fxd-pont thorm w know that a soluton k* xsts. W also fnd that functons Θ and Θ asymptotcally approach 0 as th systm sz ncrass. Takn tothr ths rsults sust that uncrtanty n arrval and srvc procsss ar not mportant for dtrmnn th optmal tratmnt thrshold for a twolvl srvc procss and thus th udlns n [31] ar robust. It also mans that th ncntv schm of pay pr danoss and pr solvd cas (s Scton 5.3) can b usd n a varty of nvronmnts and can b drvd just usn nformaton about avra srvc tms, tratmnt functons, and pay rats for xprts and atkprs. 4.4. On-Lvl vs. Two-Lvl Systms Analyss and numrcal xprmnts n [15] and [21] dscrb th nvronmnts n whch on-lvl or two-lvl systms ar prfrrd. In th halth car sttn, a two-lvl systm s somtms calld a drct accss systm bcaus patnts bypass atkprs such as nurss or prmary car physcans and nstad mov drctly to spcalsts. Patnts oftn prfr such systms, so t s mportant to dtrmn how drct accss systms compar wth atkpr systms n trms of ovrall cost. It s not surprsn that w fnd that on-lvl systms tnd to b prfrrd whn xprt staffn costs (C ) and atkpr productvty (µ ) ar low. Lkws, on-lvl systms ar favord whn atkpr staffn costs (C ), mstratmnt costs (C m) and xprt productvty (µ ) ar hh. Anothr mportant drvr of th systm prfrnc s th skll lvl of th atkprs. Whn th functon f(k) s rlatvly hh (clos to 1) ovr a wd ran of k, th two-lvl systm s prfrrd. Whl th ffcts of ths paramtrs on th systm choc ar strahtforward, th mpact of th cost of watn, C w, s mor subtl. W dntfy nstancs n whch a two-lvl systm s prfrrd whn watn costs ar low, and whr a on-lvl systm bcoms mor appaln as watn costs rs. Th transton from a two-lvl to a on-lvl systm as watn costs rs s du to th quun conoms of scal and lowr watn tms that may b achvd n a on-lvl systm. Howvr, w also fnd combnatons of paramtrs for whch rsn watn costs do not lad to th suprorty of a on-lvl systm. In partcular, f th atkprs hav suffcntly hh sklls (f(k) suffcntly hh), thn as 6
Procdns of th 43rd Hawa Intrnatonal Confrnc on Systm Scncs - 2010 C w rss, th optmal tratmnt thrshold rss, and a on-lvl systm s nvr prfrrd. In that cas, th conoms of scal ar achvd at th atkpr lvl, rathr than n an all-xprt systm. Fnally, not that ths rsults comparn onlvl and two-lvl systms apply whthr or not th systm s outsourcd. 5. Outsourcn th Srvc Systm Whn outsourcn a srvc procss a frm facs challns that ar dffrnt than whn outsourcn a manufacturn procss. Fur 3a dpcts a schmatc of tradtonal manufacturn outsourcn n whch a clnt frm contracts wth a vndor to provd som ntrmdat producton nput. In ths sttn th customr pays th frm and ntracts drctly wth th frm. Th frm pays th vndor and can prform qualty control bfor any product rachs th customr. From th customr s prspctv th vndor s nvsbl. In th srvc sttn (s Fur 3b) th stuaton s qut dffrnt. Consdr th cas of a computr makr who outsourcs tchncal support. In ths cas th customr pays th clnt frm but ntracts drctly wth th vndor whn rcvn tchncal support. Th frm wants th customr-srvc xprnc to mt som standard but dos not hav drct control ovr t. Also, montorn th vndor s staffn, procdurs, and ntractons wth customrs can b vry costly. Vndor Clnt Customrs Fur 3a: Manufacturn $ $ $ Clnt Vndor Customrs 3b: Srvc 5.1. Outsourcn a Dtrmnstc Systm If th frm outsourcs th procss to a vndor t has thr optons: outsourc both lvls (or a on-lvl systm f that s optmal), outsourc th xprt, or outsourc th atkpr. W fnd that for a dtrmnstc systm, n all thr cass t s strahtforward to dsn an optmal (frst-bst) contract. If th frm outsourcs both lvls thn t may appar as f th frm loss vsblty about th atkpr s tratmnt dcsons, and thrfor cannot nforc a contract that dmands optmal rfrral rats. Howvr, n a dtrmnstc systm, a partcular tratmnt thrshold unquly dtrmns th avra total systm tm of a customr rqust. Thrfor th $ clnt frm can contract on th systm tm. If th frm outsourcs th xprt only, thn t can pay th vndor for ts staffn costs, th vndor dos not mak any dcson bsds staffn lvls and t s asly obsrvabl f th vndor has suffcnt staff. If th frm outsourcs th atkpr thn t can pay th vndor th sam as f thy wr payn ts own workrs to mak th corrct rfrral dcsons. 5.2. Outsourcn th Exprts or a On-Lvl Stochastc Systm Whn outsourcn only th xprt lvl th frm s objctv functon s, Mn C n + C [ W λ + W λ ( k) ] n, k, T w + Cm( k F( k)) λ + T, (8) whr T s th paymnt rcvd by th vndor undr th outsourcn armnt. T, of cours, may dpnd upon systm prformanc, and th spcfc structur of T wll b dscussd blow. Not that bcaus th frm oprats th atkpr lvl t controls th flow of customrs to th vndor. If th frm knows th srvc rat of th vndor s xprts thn ths stuaton s quvalnt to th stuaton analyzd n [16], and th sam contracts can b usd to achv th frst-bst outcom. An xampl contract structur dscrbd n [16] would pay th vndor pr call handld and xtract a pnalty on th avra tm customrs spnd n th systm. To nforc such a contract th frm would only hav to montor whn customr rqusts arrvd to th vndor and whn thy lft, wthout obsrvn th nnr workns of th vndor s opratons. As w hav dscussd arlr, n som cass t may b mor ffcnt to oprat th systm as a on-lvl procss n whch all th workrs ar xprts. In ths cas thr s only on dcson for a vndor to mak, choosn th numbr of staff. Outsourcn ths systm s structurally quvalnt to outsourcn only th xprts. Thrfor th sam contract structur s optmal for th frm. 5.3. Outsourcn th Gatkpr n a Stochastc Systm Whn outsourcn only th atkpr lvl th frm s objctv functon s, Mn C n + C [ W λ + W λ ( k) ] T, n + C w ( k F( k)) λ + T m (9) whr T s th paymnt rcvd by th vndor undr th outsourcn armnt. T, may dpnd upon systm prformanc, such as th rat of srvc and th, 7
Procdns of th 43rd Hawa Intrnatonal Confrnc on Systm Scncs - 2010 Tabl 1: Optmal outsourcn contracts, assumn no nformaton asymmtry Typ of Outsourcn On-Lvl Procss or Exprt Only Gatkpr Only Both Gatkpr and Exprt To On Vndor rat of succssful tratmnt. In ths cas th vndor chooss how many atkprs to staff, n, as wll as th tratmnt thrshold, k. As a rsult th vndor wll not only dtrmn th customr watn tm at th atkpr lvl but also both th flow of customrs to th xprt lvl and th mstratmnt rat. Th clnt frm nds to construct an ncntv schm (nratn T ) that wll nduc th vndor to choos th systm-optmal staffn lvl and tratmnt thrshold. In othr words, th clnt frm s ntrstd n both th capacty nvstmnt of th vndor and how t dos ts work. [21] show that t s possbl to construct a systmoptmal contract that only rqurs obsrvn how many customrs ntr th atkpr lvl, how much tm thy spnd at th atkpr lvl, and whthr th customr s problm has bn solvd whn th customr lavs th atkprs. Th contract schm draws upon th rsults of [31] and [16]. Th analyss n [21] dscrbs a spcfc contract that pays pr customr, pays pr succssful tratmnt, and lvs a systm tm pnalty. Ths contract trms ncntvz th vndor to choos both th corrct tratmnt thrshold and th corrct staffn lvl. 5.4. Outsourcn Both Lvls n a Stochastc Systm Whn th frm outsourcs th ntr procss to on vndor, ts objctv functon s, Mn C [ W λ + W λ k) ] + C ( k F( k)) λ + T, TB w Vndor s ntrnal dcsons Exprt staffn Gatkpr staffn, tratmnt thrshold Gatkpr and xprt staffn, tratmnt thrshold Trms of ach optmal contract Dtrmnstc Stochastc Systm Systm Pay-prsrvc, Pay-prsrvc systmtm pnalty Pay-prsrvc, Pay-prsuccssful tratmnt Pay-prsrvc, paymnt contnnt on Systm Tm ( m b Pay-prsrvc, Pay-prsuccssful tratmnt, systmtm pnalty No optmal contract (10) whr T b s th paymnt rcvd by th vndor undr th outsourcn armnt. In ths cas th frm s ncurrn all th costs rlatd to th srvc xprnc.. th watn and mstratmnt costs, whl not drctly controlln any of th opratonal dcsons that dtrmn thm. Wthout any spcal ffort, th frm can only obsrv th numbr of customrs that ntr and xt th procss, and thr total systm tm. [21] show that t s mpossbl to construct a contract, usn just ths nformaton, whch wll lad to a systm optmal outcom. By outsourcn th ntr procss th frm loss knowld about th nnr workns of how th procss s prformd. It has thus turnd th procss nto a black box and ths crats contractn nffcncy. Not, howvr, that f th clnt outsourcs th atkprs to on vndor, outsourcs th xprts to anothr vndor, and obsrvs th flow of jobs btwn thn, thn th analyss dscrbd n Sctons 5.2 and 5.3 apply, and optmal contracts ar possbl. W summarz our analyss of outsourcn n Tabl 1. 6. Outsourcn wth Informaton Asymmtry on Capablts Most srvc cntrs hav a snfcant amount of varablty n th capablts of customr srvc ants (for on xampl, s th study of th rfrral rats of prmary car physcans by [7]). In th sttn of ths papr thr ar two knds of capablts that workrs/vndors hav that may b mprcsly known to th clnt frm. Frst th clnt may not know what srvc rat th vndor s workrs ar capabl of. Ths mpls that th vndor may not ncssarly hav an ncntv to work as fast or as ffcntly as possbl. Scond, wth rard to atkprs, th clnt frm may not know th tratmnt ablts of th vndor s workrs. Ths mpls that th frm may not know what th corrct tratmnt thrshold s for a st of atkprs. Th conomcs ltratur can v us udanc on how to mana n such stuatons wth nformaton asymmtry. Th standard approach s to vw ths as a scrnn problm, s, for xampl, [27] and [24]. Th uncrtanty n workr or vndor capablts can b ntrprtd ths way: thr s a spctrum of vndor typs, and th frm nds to scrn th vndors by ncouran th bst possbl prformanc from all typs. A possbl mchansm s to offr a varty, or mnu, of contracts that lad vndors to slf-slct and thrby rval thr typs. W us ths approach for our problm as wll, and w show that by offrn varatons on pay-pr-cas, pay-pr-tm, pay-pr-solv and SLA contracts, th clnt can ovrcom th 8
Procdns of th 43rd Hawa Intrnatonal Confrnc on Systm Scncs - 2010 vndor s rlatv nformaton advanta and achv optmal rsults. 6.1. Srvc rat scrnn [16] analyz how to structur contracts whn th frm dos not know th srvc rat capablts of th vndor and s outsourcn a on-lvl procss. Thy hav shown that whn th vndor s srvc rat s known, thn th clnt can ncntvz th vndor to staff corrctly by offrn a contract wth a combnaton of pay-pr-cas (PPC) and watn tm pnalts, or a combnaton of pay-pr-tm (PPT) and watn-tm pnalts. Smlarly, rplacn th watn tm pnalts wth a srvc lvl armnt (SLA) also works wll. Whn th vndor s srvc rat s unknown, for xampl f th vndor s thr fast (hh rat) or slow (low rat), th clnt would lk th offrd contract to push th vndor to staff corrctly, to b suffcnt for a slow vndor to partcpat, and yt nduc a fast vndor to work as fast as thy can and not slow down. It can b shown that offrn a choc btwn a PPC-basd contract and a PPT-basd contract wll achv just that. Slow vndors wll slct th PPT contract whl staffn n a systmoptmal way, and th fast vndors wll choos th PPC contract and also staff n a systm-optmal way. 6.2. Gatkpr tratmnt skll scrnn If th frm dd not know th sklls of th atkpr t would b quvalnt to not known what th tratmnt functon lookd lk. As a rsult th frm would not know what tratmnt thrshold to slct and what ncntvs to offr th atkpr or vndor to achv that thrshold. Aan scrnn contracts can b of us n ths stuaton. [31] consdr th cas n whch th pool of atkprs s mad up of low and hh skll workrs. Th tratmnt functon of th hh skll atkprs s ratr than or qual to that of th low skll for vry complxty lvl. Thy fnd that thr xsts a combnaton of paymnt for danoss and paymnt for solvd cas that wll nduc scrnn. That s ach typ of atkpr wll fnd t optmal to choos th tratmnt thrshold k that th clnt frm would want thm to us vn thr ablts. It rmans an opn quston, for futur rsarch, as to how to prform scrnn whn both srvc rat and tratmnt skll nformaton asymmtry xst n an outsourcn sttn. Gvn that a hrarchcal approach to manan such a systm,.. sttn th tratmnt thrshold and thn usn squar-root staffn ruls to st staffn lvls, work wll; t sms lkly that th constructon of scrnn contracts can b smlarly dcomposd. 7. Conclusons Typcally frms outsourc bcaus thy want to rduc costs. Thy want to tak advanta of th fact that som vndors hav lowr labor costs and thus can dlvr th srvc mor ffcntly. Thr ar clarly costs to outsourcn and vndors rqur a proft marn. If, takn ths nto account, th frm can stll rduc ts costs t may b a vabl opton. On of th potntal costs of outsourcn s contractn nffcncy. Our analyss n ths papr shows that for a twolvl procss contractn nffcncy should not b a concrn f th frm s only outsourcn a snl part of th procss, or a on-lvl vrson of th procss, to a partcular vndor. In ths cass, f th vndor has lowr labor costs th frm can construct that contracts that ncntvz th vndor to bhav n a systm optmal way. How th costs of opratn th systm ar shard by th clnt and vndor bcoms prmarly a functon of th notatn strnth of ach party. Whn th clnt outsourcs th ntr two-lvl procss to a snl vndor, t s not possbl to contract ffcntly. Howvr, t may stll b worthwhl to outsourc anyway f th cost advantas offrd by th vndor ar suffcnt. Quantfyn th contractn nffcncy cost s an ara for futur rsarch. W hav basd our analyss on a two-lvl atkpr procss bcaus t occurs oftn n practc and bcaus t rqurs dcsons about procss dsn as wll as nvolvs workr dscrton on workflow. Anothr ara for furthr rsarch s to xplor th applcablty of our analyss to othr mor nral procss structurs. 8. Rfrncs [1] Z. Aksn,, F. d Vércourt, and F. Karasmn, Call Cntr Outsourcn Contract Analyss and Choc. Manamnt Scnc. 54(2) 2008, pp. 354-368. [2] G. Allon, and A. Fdrrun, Outsourcn srvc procsss to a common srvc provdr undr prc and tm comptton. Workn papr, Kllo School of Manamnt, Northwstrn Unvrsty, Evanston, IL. 2006. [3] R. Aron, and R., Y. Lu, Dtrmnants of opratonal rsk n lobal sourcn of fnancal srvcs: Evdnc from fld rsarch. S. M. Collns, L. Branard, ds. Brookns Trad Forum 2005: Offshorn Wht-Collar Work. Brookns Insttuton Prss, Washnton, D.C., 2005 pp. 373 398. [4] S. Borst, A. Mandlbaum, and M.I. Rman, Dmnsonn lar call cntrs. Opratons Rsarch, 52(1), 2004, pp. 17-34. 9
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