Amazon.com, Inc. started in 1995 as an Internet

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1 Vol. 36, No. 5, Sepember Ocober 2006, pp issn eissn X informs doi /ine INFORMS Improving Cusomer Service Operaions a Amazon.com Mahew F. Keblis Mays Business School, Texas A&M Universiy, College Saion, Texas 77843, keblis@amu.edu Maomao Chen Amazon.com, 605 5h Avenue Souh, Seale, Washingon 98104, mchen@amazon.com The success of he Inerne reailer Amazon.com depends on is providing high-qualiy cusomer service. Amazon.com s cusomer service operaions consis of inernally and exernally managed conac ceners. Amazon.com mus size is conac ceners appropriaely, deciding abou hiring and raining a inernally managed ceners, and he volume of voice calls and messages o allocae o exernal service providers. We developed an approach based on mahemaical programming ha Amazon.com uses in planning capaciy, reducing he average cos of handling a cusomer conac, and increasing he service level provided cusomers. Key words: organizaional sudies: manpower planning; programming: ineger. Hisory: This paper was refereed. Amazon.com, Inc. sared in 1995 as an Inerne reailer of books. Scarcely a year afer opening is virual doors, Amazon was rumored o have achieved annualized revenues of $17 million (Reid 1997, p. 50). Since is incepion, he firm has grown rapidly, and i is now a Forune 500 company wih sales in fiscal year 2004 of approximaely $7 billion (Amazon.com 2005, p. 25). In less han a decade, Amazon has evolved from jus an online booksore, admiedly wih Earh s bigges selecion (Amazon.com 2003, p. 1), o an Inerne reailer ha offers new, used, and refurbished iems in a number of caegories, including music, food, apparel, kichenware, and consumer elecronics. Making available such a broad array of producs reflecs Amazon s desire o be he place where cusomers can find and discover anyhing hey may wan o buy online (Amazon.com 2003, p. 1). The American Cusomer Saisfacion Index (ACSI) shows ha i has succeeded; in 2001, 2002, and 2003, i received he highes score ever recorded by he ACSI in any service indusry. Is success can be aribued parly o he srengh of Amazon s cusomer service operaions (CSO). As saed in a recen annual repor, We believe ha our abiliy o esablish and mainain long-erm relaionships wih cusomers and o encourage repea visis and purchases depends on he srengh of cusomer service operaions (Amazon.com 2003, p. 4). CSO provides service o cusomers via inernally and exernally managed conac ceners and feaures on he company Web sie. These feaures allow cusomers o perform various aciviies, including racking orders and shipmens, reviewing esimaed delivery daes, and cancelling unshipped iems. Cusomers who canno resolve heir inquiries using he Web sie feaures can call or cusomer service represenaives (CSRs) available in he conac ceners 24 hours a day. To handle growing sales and heir inheren seasonaliy (he radiional reail variey and ha due o Inerne usage, which generally declines during he summer), Amazon mus size appropriaely he capaciy of is conac ceners (processing nework). I mus make decisions abou hiring and raining a inernally managed ceners and abou he volume of voice calls and messages o allocae o exernal service providers (cosourcers). 433

2 Keblis and Chen: Improving Cusomer Service Operaions a Amazon.com 434 Inerfaces 36(5), pp , 2006 INFORMS Problem Seing and Previous Work Cusomers place orders and follow up on orders on he company Web sie. Cusomers who canno resolve issues using feaures on he Web sie can eiher call he company s 800 number or send messages o cusomer service. Cusomer calls and messages are fielded by CSRs locaed in inernally managed conac ceners or in ceners operaed by vendors wih which Amazon has cosourcing agreemens. The companymanaged conac ceners are locaed in Norh America (Tacoma, Washingon; Grand Forks, Norh Dakoa; Huningon, Wes Virginia), in Europe (Slough, he Unied Kingdom; Regensburg, Germany), and Asia (Sapporo, Japan). The cosourcers are spread hroughou he world. We focus here on sizing ha porion of he processing nework ha consiss of cosourcers and inernally managed conac ceners locaed in he Unied Saes. From an operaional perspecive, we can view hem as a single virual conac cener. The messages and voice calls (cusomer conacs) number in he millions annually wih he peak jus before and afer Chrismas and he nadir in midsummer (Figure 1). The handling ime for voice calls and exchanges depends on such conac aribues as produc ype, cusomer ype, and purchase ype. Amazon uses hese aribues o caegorize conacs. Mos are classified as primary, while he remainder fall ino seven specialiy caegories: hard lines (consumer elecronics, home improvemen, and Conac volume January March May July Ocober December Figure 1: The weekly volume of voice (solid line) and (broken line) cusomer conacs shows he ypical peak around Chrismas. Caegory Gif Specialy Helper Insiuional Wireless Digial Hardlines Primary Volume Figure 2: The voice (lower bar) and (upper bar) conac volume for he primary caegory ouweighs ha for he oher caegories on a ypical day. kichen sores), digial (downloads from he Web sie, such as sofware and e-books), wireless (cell phones), insiuional buying (corporae accouns), communiy helper (posing reviews, lismania, and so forh on he Web sie), communiy specialy (qualiy assurance vis-a-vis communiy-helper aciviies), and gif cerificaes (Figure 2). Amazon classified conacs ino caegories o reflec he skill ses needed o resolve differen issues. I creaed eigh planning groups (PGs) dedicaed o processing he conacs in he eigh caegories. CSRs a inernally managed conac ceners are assigned o specific PGs and rained o handle boh voice and conacs. All new represenaives begin wih several weeks of raining in he primary PG. Those hired ino he oher, specialy PGs ransfer from he primary PG and undergo addiional raining. The firm divides he CSRs in each PG ino eams, based on heir locaion (conac cener). The CSO s objecive is o handle conacs a arge service levels. For each of he eigh caegories, i ses service-level arges for boh ypes of conacs. For voice conacs, he objecive is ha a specific percenage of callers wai no more han a cerain amoun of ime before speaking wih a CSR. For conacs, he objecive is ha a specific percenage of all

3 Keblis and Chen: Improving Cusomer Service Operaions a Amazon.com Inerfaces 36(5), pp , 2006 INFORMS 435 messages receive a response wihin some ime. Achieving service-level objecives is a funcion of he processing nework s capaciy. Previous Planning Approach Amazon began by forecasing demand by produc line, for example, for apparel, music, or kichenware, by week over a ime horizon of a year. I hen ransformed his produc-line forecas ino a forecas of orders, using weekly ime buckes over a horizon of one year. I hen convered he poin forecass developed in his fashion ino weekly forecass of and voice conacs for he eigh caegories over he planning horizon. Afer he developmen of hese conac forecass, he capaciy-planning eam in CSO assessed he conac-handling capaciy of each PG for each week of he planning horizon. Beginning wih week one, i compued he capaciy of each specialiy PG for handling voice calls and compared i wih he corresponding voice forecas. The eam addressed capaciy shorfalls for specialiy PGs by planning o ransfer primary PG CSRs o he specialiy PGs. When he capaciy in a specialiy PG exceeded he forecas, i convered he excess capaciy, calculaed in erms of handling voice calls, ino capaciy for handling messages. I compared he value for each specialiy PG wih he corresponding forecas and addressed shorfalls by planning o ransfer primary PG CSRs o he specialy PG. Any capaciy no consumed in handling specialiy hen became capaciy available for handling primary conacs. Once planners had sized he specialy PGs, albei for only week one of he planning horizon, hey focused on primary voice conacs. Firs, hey allocaed some forecas voice conacs o cosourcers for handling. Then, hey compared he unallocaed volume remaining wih he capaciy in he primary PG for handling voice calls and planned o hire exernally o make up any shorfall or o conver excess voice capaciy ino capaciy for handling . They combined his capaciy in he primary PG for handling wih any excess capaciy in he specialiy PGs and compared he resul wih he forecas of primary conacs less some porion allocaed o cosourcers. If he capaciy was less han he forecas, hey planned o hire exernally. Afer planning for he firs week, hey repeaed he seps for he remaining weeks of he horizon o develop a complee capaciy plan. The company planned in his way every week of he year. Alhough planners used a spreadshee for he calculaions, close o a day was sill required o invesigae a single scenario. CSO managers recognized his shorcoming and he lack of rigor in evaluaing imporan rade-offs. They asked us o help hem srenghen he capaciy-planning process, specifying ha any new approach had o address hree imporan issues. Three Issues CSO managers hough ha hree imporan issues were no adequaely considered in he exising planning process: how hey added CSRs o eams, differences in conracs wih cosources, and saffing and service levels. CSO managers added CSRs o eams when hey brough on exernal hires or ransformed primary PG CSRs o specialy PGs. Tradiionally hey added or removed CSRs from eams o mainain he exising proporion of PG members on he various eams (a each conac cener); for example, if 20 percen of he CSRs of a PG were locaed a a paricular conac cener, hen he managers would hire and make ransfers for he enire PG so ha 20 percen of he CSRs of he PG would coninue o be locaed a ha cener. They ignored he fac ha average produciviy varied across eams wihin a PG and ha he average wage differed among ceners. Second, conrac erms differed across cosourcers. For some cosourcer conracs, Amazon incurred coss per conac handled. For oher cosourcer conracs, Amazon incurred a fixed charge if he volume allocaed o he cosourcer fell below a minimum hreshold; oherwise, i followed an all-unis discoun price schedule. Furhermore, some of hese conracs had ceilings on he volume of conacs. If he volume of conacs allocaed o he cosourcer exceeded some maximum amoun in a ime period, he minimum hreshold for fuure ime periods would rache upwards. Amazon allocaed conacs o cosourcers

4 Keblis and Chen: Improving Cusomer Service Operaions a Amazon.com 436 Inerfaces 36(5), pp , 2006 INFORMS wih such conracs o mee any minimum hresholds. For cosourcers wih conracs based on he number of conacs handled, Amazon allocaed conacs o ensure ha i resriced he percenage of primary conacs handled ouside of an inernally managed conac cener. I sough o minimize he risks of relying on cosourcers. Regarding saffing and service levels, Amazon esablished he capaciy for handling boh ypes of conacs a he minimum levels needed o mainain sysem sabiliy. I se he number of CSR hours available in a week for handling voice calls o a quaniy jus barely exceeding he expeced number of hours of voice-call-relaed work ha a PG would need o perform. I esablished capaciies for in a similar manner. Using his approach, i ignored he random behavior of conac arrival raes and handling imes. Even so, i achieved service-level objecives for boh ypes of conacs regularly. For messages, he company se response-ime arges ha allowed CSRs o pospone work. For voice calls, however, CSRs could no pospone responding. Alhough he spreadshee-based approach sized voice and capaciies independenly for a PG, he operaional realiy is ha CSRs handle boh voice and requess and inerrup heir processing of messages o handle voice calls as hey arrive. Because mos conacs are messages, he ceners regularly achieved voice arge service levels despie shorcomings in planning. Neverheless, he spreadshee-based approach possessed no lever ha allowed CSO managers o specify a service-level objecive and see is impac on saffing levels. Lieraure Managemen science analyss have only recenly considered he problem of deermining he capaciy required o serve cusomer classes differeniaed by response-ime requiremens, where cusomer arrival raes are ime dependen. Gans e al. (2003) provide a comprehensive summary of he sae of call-cener research peraining o capaciy managemen. Whi (1999) examined he deerminaion of capaciy in a seing wih wo cusomer classes, one requiring immediae response and he oher, response wihin a day. To deermine he capaciy required for he highes prioriy class, he employed an M/G/ model and normal approximaion wih a arge probabiliy ha a service reques will be delayed before service begins. For less-ime-sensiive cusomers, he used a normal approximaion alone wih anoher arge probabiliy ha all daily demand will be me. He showed ha he capaciy he service provider needs is he maximum of he wo previously defined requiremens. Armony and Maglaras (2004) considered a call cener in which cusomers, assuming ha heir calls are no answered immediaely, can choose o hold for service (class 1), indicae heir desire o be called back (class 2), or simply balk, making he choice afer being informed of he expeced delay. The auhors modeled he dynamics of his environmen as an M/M/N muliclass sysem and performed an asympoic analysis o choose he minimum number of agens o guaranee performance measures, such as a bound on he expeced waiing ime of class 1 cusomers and bounds on he probabiliy ha he waiing ime exceeds some hreshold. Chen and Henderson (2001) examined a call-cener seing wih wo or more classes where he objecive is ha, for each class, a class-specific percenage of calls are answered wihin a class-specific ime frame. For he highes prioriy class, he auhors leveraged ransform mehods o deermine he probabiliy ha a call will be delayed longer han a cerain period of ime (he ail probabiliy), while for oher classes hey used Markov s inequaliy o obain a bound on waiing-ime performance. To esablish he required saffing level, hey increased he number of agens unil he ail probabiliy was as small as desired and each Markov inequaliy was saisfied. Harrison and Zeevi (2005) considered ceners wih more han wo cusomer classes (and more han one pool of agens) where he objecive is o minimize he sum of saffing coss and expeced abandonmen penalies for he various classes. They assumed ime-dependen arrival raes ha can vary sochasically. They used sochasic fluid models o reduce he saffing problem o a mulidimensional newsvendor problem, which hey hen solved numerically wih a combinaion of linear-programming and simulaion mehods.

5 Keblis and Chen: Improving Cusomer Service Operaions a Amazon.com Inerfaces 36(5), pp , 2006 INFORMS 437 Gans and Zhou (2002) examined he problem of deermining he number of employees of differen speed or skill levels o saff, where workers gain in speed or skill and become capable of handling more classes of cusomers or kinds of work. They employed a Markov decision process model o deermine hiring and promoion policies ha minimize hiring, compensaion, and oher operaional coss. Gans and Zhou (2004) focused on a siuaion where here are wo classes of cusomers (high and low value), and he problem is o deermine he saffing level a an ousourcer handling he low-value cusomers. They examined and compared hree approaches for deermining he ousourcer s saffing levels. Like Whi (1999) and Chen and Henderson (2001), we show how o apply queuing-relaed conceps in seing saffing levels in conac ceners wih more han one cusomer class. However, whereas hey focused on deermining saffing levels o aain specific service-level objecives irrespecive of cos, we focused on meeing such objecives as inexpensively as possible given a global processing nework wih differing economics hroughou is pars. Such a perspecive migh have led us o consider call-rouing issues, like Armony and Maglaras (2004), Gans and Zhou (2004), and Harrison and Zeevi (2005), bu we chose no o invesigae such maers when we worked on our problem given he added complexiy of call rouing and our desire o quickly improve capaciy planning a Amazon. Gans and Zhou (2002) allowed sochasic urnover and considered ousourcing as we do; however, hey considered a firm operaing only a single inernal call cener. We applied exising mehods, wih some modificaion, o planning he capaciy of a firm wih muliple inernal conac ceners and muliple ousourcing opions where he objecive is o minimize oal coss subjec o service-level arges. Soluion Approach From he ouse, we hough ha we could represen mos of he essenial elemens of he capaciyplanning problem CSOs faced, wih one noable excepion, naurally wihin an opimizaion framework. The excepion was he hird issue concerning saffing and service levels; we hough we would need o apply some conceps from queueing heory. We developed a wo-sage soluion approach. In he firs sage, we adjused conac forecass previously generaed using conceps from queueing o ake ino accoun differen sources of uncerainy and service-level objecives. In he second sage, we solved an opimizaion model, using as inpu he adjused forecass and oher relevan daa, o deermine he bes allocaion of conacs across all ceners and he saffing levels a inernal ones. We began our opimizaion-based approach wih a collecion of conac forecass adjused o accoun for he randomness inheren in conac arrival raes and handling imes, and he exisence of service-level objecives. Our adjusmen procedure was shaped by our observaion ha for hose caegories wih a large volume of conacs, CSO s voice service levels regularly me argeed objecives. We ake ino accoun he forecas when generaing he corresponding adjused voice-call forecas. We will simplify our explanaion of he adjusmen procedure by focusing on an individual conac caegory and a single week of he planning horizon. The ask hus becomes, for he week of ineres, o produce a pair of adjused forecass, one for and one for voice. The informaion we have o work wih in compuing hese numbers includes hourly forecass of and voice conacs for he week concerned, an average CSR handling ime for each ype of conac, and service-level objecives for boh conac ypes. We denoe he forecas of (voice) in hour h of he week as e h ( v h ). We denoe he average rae a which CSRs handle (voice) conacs per hour as e ( v ). Finally, service-level objecives are of he elephone-service-facor variey, ha is, a leas x percen of conacs answered wihin y ime unis. Adjusmen Procedure The adjusmen procedure consiss of five seps. Sep 1 We deermine he minimum number of CSRs needed o preven he number of unprocessed conacs from growing o infiniy. We perform his calculaion for boh ypes of conacs for each hour of he week, and i amouns o dividing each hourly forecas by he relevan service rae. In he case of , he resuling

6 Keblis and Chen: Improving Cusomer Service Operaions a Amazon.com 438 Inerfaces 36(5), pp , 2006 INFORMS value e h / e for each hour h of he week is denoed as e h. Similarly for voice, v h = v h / v. We perform he calculaions in he firs sep wihou regard o service-level objecives. Sep 2 We deermine he minimum number of CSRs needed o achieve he specified service-level objecive for voice conacs using he Erlang C formula o perform he calculaion for each hour of he week, using as inpus v h, v, and he specified arge service level. For each hour h of he week, we denoe he resuling value as v h. Sep 3 Because our opimizaion model requires weekly forecass and he daa ha we are working wih is hourly, we aggregae his hourly informaion. We perform an aggregaion for each day of he week for each of he above collecions of daa, producing hree values for each day d of he week: d which is a summaion of v h for a given day, d which is a summaion of e h for a given day, and d which is a summaion of v h for a given day. Sep 4 We esablish he weekly forecas for voice conacs o use in he opimizaion model. We arrive a his weekly value by firs assessing he capaciy needed for each day of he week. We do his by evaluaing he following inequaliy for each day d of he week: d + d > d. When his inequaliy is rue, he forecas amoun of posponable work for he day (given in erms of CSRs by d ) is sufficien o buffer agains voice-conac-relaed variabiliy. We se he voice-conac forecas for he day equal o d v, which we denoe as d. If he inequaliy evaluaes o false, hen he volume is no sufficien o buffer agains voice-conac-relaed variabiliy and d is se equal o d v. By summing over d for a week, we produce he weekly forecas for voice conacs, which we denoe as V k, where k indicaes he conac caegory and he week of ineres. Sep 5 We esablish he weekly forecas for conacs, which we denoe as E k, where k indicaes he conac caegory and he week of ineres. We arrive a i by summing over d e for he week, which complees our ask of producing an adjused forecas for and an adjused forecas for voice for he week concerned. We hen apply he adjusmen procedure o he voice and conac forecass for all he remaining caegories and weeks of he planning horizon. This collecion of adjused forecass becomes inpu o he opimizaion model. This adjusmen procedure will generae aggregae CSR requiremens and ulimaely forecass ha are idenical for differen call-volume scenarios; for example, a scenario where he call-volume paern dicaes he need for 10 CSRs per hour over a 10-hour day will generae he same aggregae requiremen as a scenario where he need is for 100 CSRs in one hour and none in any oher ime period. Noneheless, he adjusmen procedure recurrenly generaes oupu ha is meaningful for wo reasons: (1) While he call-volume paern Amazon faces over a workday is cerainly no saionary, i is also no anywhere near as lumpy as depiced in he laer, second scenario. (2) Alhough we can expec he call volume o be much higher in some hours han i is in ohers, Amazon does no necessarily have o increase saffing a is inernal conac ceners a such imes because he cosourcing agreemens i has allow i o look o cosourcers o provide capaciy when i provides enough advance noice. Pu anoher way, he flexibiliy afforded by he cosourcing agreemens allows Amazon o plan o handle a baseline load inernally and o push o cosourcers any excess volume. Aksin e al. (2004) discuss he economic raionale for his ype of agreemen. Opimizaion Model The opimizaion model we developed is a mixedineger program (appendix). The program oupus a minimum-cos capaciy plan for processing he conacs forecas for a given finie planning horizon, deailing for each week decisions regarding hiring and raining CSRs and he volume of conacs o allocae o each cosourcer. Objecive Funcion The erms of he objecive (cos) funcion fall ino wo caegories: hose perinen o inernally managed conac ceners, and hose relaed o cosourcers. We idenified four cos drivers as relevan for each week and

7 Keblis and Chen: Improving Cusomer Service Operaions a Amazon.com Inerfaces 36(5), pp , 2006 INFORMS 439 each eam i j, where i denoes he PG and j he conac-cener locaion: he number of normal-ime hours (n ij ) CSRs work, he number of overime hours (o ij ) CSRs work, he number of new CSRs hired (h ij ), and he number of CSRs ransferred (s ij ) from he primary PG a a conac cener o one of he specialiy PGs a ha cener. In our mahemaical program, we model he coss associaed wih hese drivers using linear expressions (appendix). For he firs wo drivers (variables), he coefficiens are normal and overime hourly wages, respecively, while for he hird and fourh variables, he coefficiens capure raining and hiring/or ransfer expenses in addiion o wages paid during he raining period. Because many CSRs are conrac employees, coss for decreasing he size of he workforce are minimal and hence ignored. The remaining erms of he objecive funcion concern he cos of conracing wih cosourcers o handle some primary voice and conacs. Amazon employs wo kinds of agreemens wih is cosourcers: a ake-or-pay conrac wih an all-unis discoun price schedule, and a per-conac conrac. Under a ake-or-pay conrac, Amazon guaranees a cosourcer a conrac-specific minimum weekly paymen regardless of he volume of conacs i allocaes o he cosourcer (Figure 3). The fifh erm of he Paymen F U 1 U 2 U 3 B 1 B 2 B 3 U 4 Volume Figure 3: In a ake-or-pay conrac, when he volume allocaed is less han or equal o B 1, he minimum hreshold, he volume pushed o he cosourcer falls wihin he firs range of he price schedule and he cosourcer receives a minimum paymen F. The fee per conac in he firs range, U 1, is equal o he slope of he paymen funcion in ha range. When he volume allocaed is beween B 1 and B 2, he volume pushed o he cosourcer falls ino he second range of he price schedule, wih a fee per conac of U 2, and so forh. objecive funcion indicaes ha every week Amazon makes a paymen of F i o each cosourcer i. The maer of a minimum paymen becomes irrelevan, however, if he volume of conacs allocaed exceeds a conrac-specific minimum hreshold, a which poin he paymen made becomes a funcion of he number of conacs he cosourcer handles: Amazon hen pays only a fee per conac handled, wih he fee depending on he acual volume allocaed and becoming progressively lower as he volume allocaed rises. In our objecive funcion, he sixh and sevenh erms adjus he paymen made when conac volumes exceed he minimum hreshold. The sixh erm offses, when he volume allocaed exceeds he minimum hreshold, he minimum paymen made o a cosourcer per he fifh erm. We accomplish his by seing he negaive of F i as he coefficien of he binary variable y i k, which akes he value 1 when he volume of conacs allocaed o cosourcer i in week falls ino range k. Because we seek an offseing effec only when he volume allocaed exceeds he minimum hreshold, we include such a erm in he objecive funcion only when he subscrip k of he variable y i k is greaer han one. The sevenh and las erm capures per-conac handling charges. I conains he variable x i k, which indicaes he number of conacs handled by cosourcer i in week if he oal volume processed falls ino range k of he price schedule. For a given week and cosourcer i, one such variable exiss for each range in he price schedule of he cosourcer. Of his collecion of x i k, only one will ever be greaer han zero in a given week for cosourcer i, and ha variable will correspond o he same range of he price schedule as he y i k ha akes he value 1. Because he coefficien of each x i k is he relevan fee per conac (U i k ), i capures he paymen due o handling charges for each week and cosourcer i. A per-conac conrac is jus a special case of akeor-pay. In a per-conac conrac, Amazon does no guaranee a minimum weekly paymen; hence he value of F i is equal o zero for each cosourcer i under a per-conac conrac for every week. Tha makes he fifh and sixh erms of he objecive funcion irrelevan under a per-conac conrac; he only meaningful erm herefore is he las involving he variable x i k. Wih a per-conac conrac, he fee per conac

8 Keblis and Chen: Improving Cusomer Service Operaions a Amazon.com 440 Inerfaces 36(5), pp , 2006 INFORMS does no vary wih he volume of conacs allocaed; hence he price schedule has only a single range. Consrains We can divide he consrains largely ino wo caegories, hose for inernally managed conac ceners, and hose for cosourcers. The firs wo consrains we discuss, however, represen a poin of inersecion. Defining v ij k as he number of caegory k (k equal o 1 denoes primary) voice conacs allocaed o eam i j (i denoes he PG and j he conac cener locaion) and c i as he number of primary conacs allocaed o cosourcer i, consrain 1 indicaes ha he sum of primary voice conacs allocaed over all eams and over all cosourcers ha handle voice conacs mus be a leas as large as V 1, he voice-call forecas. Defining e ij k as he number of caegory k conacs allocaed o eam i j, he second consrain indicaes ha he sum of primary conacs allocaed over all eams and over all cosourcers ha handle conacs mus be a leas as large as E 1, he forecas. Consrain 3 resembles consrain (1); for each caegory k of voice conacs (wih he excepion of primary), i esablishes ha Amazon mus allocae conacs o each eam i j, given by v ij k, when summed over all eams, a leas as large as V k he voice-call forecas. Unlike he firs consrain, he hird conains no cosourcer-relaed erm. The fourh consrain resembles he second. The remaining consrains follow from he firs four in some manner. Consrain 5 requires ha he number of normal (n ij ) and overime (o ij ) hours each eam i j works (adjused by a shrinkage facor ha capures ha no all hours a CSR spends a work are spen producively) mus be a leas as many as he number of hours eam i j allocaes o handling conacs. We arrive a his laer amoun by adding he number of hours allocaed by eam i j o handling voice conacs o he number of hours eam i j allocaes o handling . We find he number of hours eam i j allocaes o handling voice by muliplying v ij k (each PG handles only is own voice calls so he value of k is equal o he value of i) by he average handling ime of a voice call by eam i j. Each eam will handle is own , and specialiy PGs may also handle primary . Hence, we find he number of hours eam i j allocaes o handling , by muliplying e ij k by he average handling ime of a caegory k (k equal o i) message by eam i j and adding ha o e ij 1 muliplied by he average handling ime of a primary message by eam i j. Consrain 6 specifies ha he number of overime hours (o ij ) ha each eam i j can work is bounded by a percenage of he normal hours (n ij ) each eam i j works, while he number of normal hours (n ij ) each eam i j works is by consrain 7 bounded by w ij, he number of CSRs on eam i j, muliplied by he number of normal hours in a sandard work week. Two consrains capure he number of CSRs on a eam. For a eam ha is par of he primary PG, consrain 8 ses w ij, he number of CSRs on eam i j in week, equal o he number available he previous week (w ij 1 ) (adjused by an ariion rae reflecing occasional volunary deparures), less any involunary separaions (d ij ), less he planned ransfer of CSRs o any specialiy PG (s ij ; he superscrip denoing he desinaion eam), bu augmened by any new ouside hires (h ij ). For each eam ha is a member of a specialiy PG, consrain (9) performs a similar funcion, capuring planned in-bound ransfers, ha is, from he primary PG, he only way of increasing he number of CSRs in a specialiy PG; here are no ouside hires. Consrains 10 hrough 15 concern risk miigaion. The firs wo concern eams in inernally managed conac ceners. Consrain 10 indicaes ha for each caegory k of voice conacs, he number allocaed o each eam i j, given by v ij k, mus be less han some percenage of V k, he voice-call forecas. Consrain 11 holds similarly for . Consrains 12 hrough 15 concern managing cosourcer-relaed risk. Consrain 12 indicaes ha he number of primary voice conacs allocaed o each cosourcer mus be less han some percenage of he voice-call forecas, while consrain 14 limis he number of primary voice conacs allocaed o all cosourcers combined o less han some percenage of he number of voice calls forecas. Consrains 13 and 15 are equivalen consrains for . The remaining consrains, excep hose ha indicae wheher a variable is coninuous or ineger, concern cosourcers and fall ino wo caegories: conrac cos and conrac smoohing. We use he

9 Keblis and Chen: Improving Cusomer Service Operaions a Amazon.com Inerfaces 36(5), pp , 2006 INFORMS 441 conrac-cos consrains (16 hrough 19) o ensure ha Amazon obains he mos aracive prices of he ake-or-pay conrac only when hey mee he required volume minimums. We use he conracsmoohing consrains (20 hrough 25) o consrain variaion in he number of conacs allocaed week o week o each cosourcer. We do his by esablishing hresholds. If Amazon pushes more volume o a cosourcer han a hreshold (moniored by 20 and 21) or less (moniored by 22 and 23), hen new hresholds become esablished and he volume pushed o ha cosourcer henceforh is no allowed o cross he newly esablished hresholds for a fixed amoun of ime (enforced by 24 and 25). Resuls Each week, he capaciy-planning eam in CSO employs our soluion approach. When he planning horizon is 52 weeks, as i is a he beginning of a calendar year, he opimizaion model consiss of approximaely 134,000 consrains and almos 16,000 variables, where a lile over 1,000 of hese are boh binary and ineger. The model is encoded as an AMPL program and is solved using CPLEX on an HP 9000 Superdome server wih a 1.1 GHz processor. Each run of he model requires slighly less han five minues of compuing ime. A planner can invesigae a single scenario (inpus adjused, model execued, and oupu analyzed) in less han an hour, a process ha formerly consumed an enire day. Now he capaciy-planning eam can examine a larger number of scenarios and consider uncerainy by performing sensiiviy analysis on he inpus o he planning process. Afer analyzing he oupu for a se of scenarios, he planners pass on informaion for he ime horizon of ineres o hree groups. They inform Amazon Human Resources of he number of new CSRs Amazon will need o hire, CSO managers of he ransfers needed ino and ou of heir PGs, and cosourcers of fuure conac volumes. The new approach saves ime and herefore enables addiional scenario analysis and, mos imporan, brings opimizaion o bear direcly on he planning process. Planners previously considered cos rade-offs by analyzing he oupus of he spreadshee model. Our opimizaion model capures hese rade-offs explicily and grealy increases annual operaional cos savings. Managers hough ha hree imporan issues did no receive due consideraion wih spreadshee-based planning: Firs was adding new CSRs o PGs wihou regard o produciviy and wage differences. The model revealed ha Amazon should sop processing a one inernally managed cener or change is process or provide furher raining o CSRs. Second was allocaing conacs o cosourcers. The model revealed ha some cosourcers were more expensive for processing voice calls han some inernally managed ceners. We discovered his by forcing he model o allocae conacs according o exising pracice and hen allowing i o allocae conacs as i deemed opimal. We found ha Amazon could save over one million dollars by handling more calls inernally. We aribued he savings largely o smoohing consrains in he cosourcers conracs ha esablished new long-lasing hresholds when an exising hreshold was exceeded. Third was a lack of consideraion beween service objecives and saffing coss. Wih he forecas adjusmen procedure we incorporaed ino our approach, planners can evaluae he cos effecs of changing service parameers, such as arge response imes or limis on cusomers waiing imes (Figure 4). Kim Rachmeler, Amazon.com s vice presiden of worldwide cusomer service, said These advancemens in planning our capaciy and opimizing our conac allocaion plans have significanly improved our abiliy boh o respond o cusomers quickly, which improves cusomer experience, and also o lower our coss, which increases corporae flexibiliy (personal communicaion, 2003). Alhough we developed our approach wih he weekly planning process in mind, he benefis exend o conrac negoiaions wih cosourcers. Periodically, Amazon revisis he erms of is exising agreemens wih each of is cosourcers. Previously, he ools available for invesigaing cosourcer relaionships were limied and ime consuming. Our opimizaion model yielded insighs concerning he coss o Amazon of he parameers (volume hresholds, and he lengh of ime ha volume allocaed o a cosourcer is required o remain beween a pair of newly esablished hresholds afer he breaching of previously esablished ones) of he conrac-smoohing pieces of conracs.

10 Keblis and Chen: Improving Cusomer Service Operaions a Amazon.com 442 Inerfaces 36(5), pp , 2006 INFORMS Voice call cos (per 20,000 conacs) 85.0% 87.5% 90.0% 92.5% 95.0% 97.5% 99.9% Percenage of voice calls answered wihin y seconds Figure 4: In he fla range of he curve i is possible o aain successively higher voice service levels wihou incurring addiional cos because he number of handlers is sufficienly large and each of hese CSRs can swich o processing voice calls wihou any operaional delay. Beyond he fla range, he combined number of and voice-call handlers is smaller han ha required o achieve he desired service levels, making i necessary o add resources essenially dedicaed o processing voice calls, which causes he curve o rise wih a rajecory ha depends on he mix of cosourcers and inernal hires employed. CSO managers are now able o undersand when conrac-smoohing parameers are acually consraining operaional flexibiliy in he Amazon processing nework (and hence raising is cos of operaion) versus when hey appear o be, bu acually are no. This is informaion CSO managers find useful when negoiaing new conracs wih cosourcers as hey assess wheher o make specific concessions. Appendix Parameers = 1 C is he se of conac caegories where 1 denoes primary and 2 hrough C he specialiy caegories. L = 1 L is he se of conac-cener locaions. = 1 P is he se of planning groups (PGs), where 1 denoes he primary PG and 2 hrough P, he specialiy PGs. = i j i = 1 P j = 1 L is he se of eams. = 1 Q is he se of cosourcers. v = subse of ha handles voice calls. e = subse of ha handles . T = number of weeks in he planning horizon. = number of caegory k voice conacs forecas for week. = number of caegory k conacs forecas for week. = average handling ime (in hours) of a caegory k voice conac by eam i j. = average handling ime (in hours) of a caegory k conac by eam i j. = normal ime wage for a CSR on eam i j in week. V k E k 1 ij k 1 ij k N ij O ij = overime wage for a CSR on eam i j in week. H ij = cos o hire and rain a new CSR for eam i j in week. S ij = coss relaed o swiching a CSR o eam i j in week. W ij = number of normal hours in he work week of a CSR on eam i j. ij = upper bound (expressed as a proporion of normal hours) on number of overime hours ha may be worked in week by eam i j. ij = shrinkage facor (proporion of a CSR s ime on eam i j los o hings like breaks, abseneeism, and ongoing raining). i = ariion facor (proporion of CSRs on eam i j ha volunarily leave he firm). = number of weeks before a newly hired CSR becomes a producive worker. = number of weeks before a CSR ha ransfers from he primary PG o a specialiy PG becomes producive as a specialis. ij = upper bound (expressed as a proporion of forecas voice conacs) on number of voice conacs ha may be handled by eam i j in week. ij = upper bound (expressed as a proporion of forecas conacs) on number of conacs ha may be handled by eam i j in week. i = upper bound (expressed as a proporion of forecas voice or conacs) on number of conacs ha may be handled by cosourcer i in week. ˆ v = upper bound (expressed as a proporion of forecas voice conacs) on number of voice conacs ha may be handled by all cosourcers combined in week.

11 Keblis and Chen: Improving Cusomer Service Operaions a Amazon.com Inerfaces 36(5), pp , 2006 INFORMS 443 ˆ e = upper bound (expressed as a proporion of forecas conacs) on number of conacs ha may be handled by all cosourcers combined in week. A i = number of break poins in he price schedule of cosourcer i; equals 0 (zero) when he price schedule does no involve quaniy discouns. B i = B1 i Bi A i is he se of volume break poins in he price schedule of cosourcer i, where 0 < B1 i <Bi 2 <Bi 3 R i = number of disinc ranges in he price schedule of cosourcer i, where assuming B i he firs range is 0 B1 i ; noe ha Ri = A i + 1. F i = fixed paymen made o cosourcer i unless he oal volume of conacs processed by he cosourcer in week exceeds a specific hreshold. = per-conac handling fee a cosourcer i in week when he oal volume of conacs processed falls ino range k. i = hreshold expressed as a proporion of he number of conacs pushed o cosourcer i. i = number of weeks he volume pushed o cosourcer i mus remain wihin newly esablished limis (upper and lower hresholds) afer crossing (exceeding or falling below) a previously exising hreshold. M = a very large number. U i k Variables v ij k = number of caegory k voice conacs handled by eam i j in week. e ij k = number of caegory k conacs handled by eam i j in week. c i = number of primary conacs handled by cosourcer i in week. n ij = number of planned normal hours for eam i j in week. o ij = number of planned overime hours for eam i j in week. w ij = number of CSRs needed on eam i j in week. h ij = number of planned ouside hires for eam i j in week. s ij = number of planned CSR ransfers o specialiy eam i j from he colocaed primary eam in week. d ij = number of involunary deparures from eam i j in week. = number of conacs handled by cosourcer i in week if he oal volume processed falls ino range k of is price schedule; 0 oherwise. = 1 if he number of conacs handled by cosourcer i in week falls ino range k of is price schedule; 0 oherwise. z i = 1 if he proporional increase in he number of conacs pushed o cosourcer i in week is greaer han i, when compared o he week prior; 0 oherwise. ẑ i = 1 if he proporional decrease in he number of conacs pushed o cosourcer i in week is greaer han i, when compared o he week prior; 0 oherwise. x i k y i k Formulaion min s.. T =1 i j + T ( ij N n ij + O ij o ij ) T + =1 i j i 1 F i =1 i k=2 S ij s ij + =1 i j i=1 T =1 i T R i T yi k + R i i j i j i j i=k i j i=k 1 ij i vij i F i U i k xi k =1 i k=1 H ij h ij v ij 1 + c i V 1 = 1 T (1) i v e ij 1 + c i E1 = 1 T (2) i e v ij k e ij k + k V k k k 1 = 1 T (3) E k k k 1 = 1 T (4) 1 ij k eij k 1 ij ( n ij + o ij ) i j = 1 T (5) o ij ij n ij i j = 1 T (6) W ij w ij n ij i j = 1 T (7)

12 Keblis and Chen: Improving Cusomer Service Operaions a Amazon.com 444 Inerfaces 36(5), pp , 2006 INFORMS w 1j 1 1 1j d 1j i i 1 w ij 1 1 ij d ij + s ij = wij v ij k e ij k ij k V k ij k E k s ij + h 1j = w 1j j L = 1 T (8) i j i 1 = 1 T (9) i j k = 1 T (10) i j k = 1 T (11) c i i V 1 i v = 1 T (12) c i i E1 i e = 1 T (13) c i ˆ v V 1 = 1 T (14) i v c i ˆ e E1 = 1 T (15) i e x i k Bi k yi k 0 i k= 1 R i 1 = 1 T (16) x i k Bi k yi k 0 i k= 2 R i = 1 T (17) Ri c i = x i k i = 1 T (18) k=1 R i y i k k=1 = 1 i = 1 T (19) M 1 z i 1 + i c i 1 ci i = 1 T (20) Mz i ci 1+ i c i 1 i =1 T (21) M 1 ẑ i ci 1 i c i 1 i = 1 T (22) Mẑ i 1 i c i 1 ci i =1 T (23) M 1 z i ci i c i i = i +1 T =1 i (24) M 1 ẑ i ci + 1 i c i i = i +1 T =1 i (25) n ij o ij w ij h ij d ij 0 i j = 1 T (26) s ij 0 i j i 1 = 1 T (27) v ij k e ij k 0 i j k = 1 T (28) c i 0 i = 1 T (29) x i k 0 i k=1 Ri =1 T (30) y i k = 0or1 i k= 1 R i = 1 T (31) z i ẑi = 0or1 i = 1 T (32) where w ij 0 is given i j, hij is given i j, i = 1, = + 1 0, s ij is given i j, i 1, = + 1 0, c i is given i, = i + 1 0, z i is given i, = i + 1 0, and ẑ i is given i, = i Acknowledgmens We hank he anonymous reviewers for heir suggesions ha helped us improve he paper. The firs auhor also hanks Bill Sein for his many useful commens. References Aksin, O. Z., F. Vericour, F. Karaesmen Call cener ousourcing conrac design and choice. Working paper, Fuqua School of Business, Duke Universiy, Durham, NC. Amazon.com Annual Repor. Amazon.com, Seale, WA. Amazon.com Annual Repor. Amazon.com, Seale, WA. American Cusomer Saisfacion Index, The. Armony, M., C. Maglaras On cusomer conac ceners wih a call-back opion: Cusomer decisions, rouing rules, and sysem design. Oper. Res. 52(2) Chen, Ber P. K., S. G. Henderson Two issues in seing call cenre saffing levels. Ann. Oper. Res. 108(1 4) Gans, N., Y-P. Zhou Managing learning and urnover in employee saffing. Oper. Res. 50(6) Gans, N., Y-P. Zhou Overflow rouing for call-cener ousourcing. Working paper, The Wharon School, Universiy of Pennsylvania, Philadelphia, PA. Gans, N., G. Koole, A. Mandelbaum Telephone call ceners: A uorial and lieraure review. Manufacuring Service Oper. Managemen 5(2) Harrison, J. M., A. Zeevi A mehod for saffing large call ceners based on sochasic fluid models. Manufacuring Service Oper. Managemen 7(1) Reid, R. H Archiecs of he Web. John Wiley and Sons, New York. Whi, W Using differen response-ime requiremens o smooh ime-varying demand for service. Oper. Res. Le. 24(1 2) 1 10.

13 Keblis and Chen: Improving Cusomer Service Operaions a Amazon.com Inerfaces 36(5), pp , 2006 INFORMS 445 Raghu Sehuraman, Manager of Worldwide Cusomer Service Nework, Amazon.com Inc., 605 5h Ave. S, Seale, WA 98104, wries: I am wriing his leer o confirm ha he planning and opimizaion model presened in his paper has been implemened a Amazon.com. The model has enabled us o opimize saffing and conac allocaion across all global sies and media ypes o ensure worldclass imely experience for our cusomers. Furhermore I can ell you ha, afer implemenaion, i recenly passed is oughes es wih flying colors: our company s holiday season and high service level goals. The model allows more flexibiliy for business rules and wha-if sensiiviy analysis, helping us make high-level sraegic decisions o opimize our global cusomer service nework. In summary, he model has remendously improved our planning process and is now one of our key decision suppor ools.