We investigate the benefits of migrating from a call center, where all agents are pooled and customers

Transcription

1 MANAGEMENT SCIENCE Vol. 54, No. 2, February 2008, pp iss eiss iforms doi /msc INFORMS Aalysis of the Impact of Team-Based Orgaizatios i Call Ceter Maagemet Oualid Jouii, Yves Dallery Laboratoire Géie Idustriel, Ecole Cetrale Paris, Châteay-Malabry, Frace {walid.jouii@ecp.fr, yves.dallery@ecp.fr} Rabie Nait-Abdallah Gaz de Frace, Directio de la Recherche, Sait Deis la Plaie Cedex, Frace, rabie.ait@gazdefrace.com We ivestigate the beefits of migratig from a call ceter, where all agets are pooled ad customers are treated idifferetly by ay aget, toward a call ceter where customers are grouped ito clusters with dedicated teams of agets. Each cluster is referred to as a portfolio. Customers of the same portfolio are always served by a aget of the correspodig team. There is o specializatio ivolved i this orgaizatio i the sese that all customer portfolios as well as all aget teams have (statistically) idetical behaviors. The reaso for movig to this orgaizatio is that dealig with teams of limited size allows a much better workforce maagemet tha the situatio usually ecoutered i large call ceters. The purpose of this paper is to examie how the beefits of movig to this ew orgaizatio ca outweigh the drawbacks. The drawbacks come from the fact that there is less of a poolig effect i the ew orgaizatio tha i the origial oe. The beefits come from the better huma resource maagemet that results i a higher efficiecy of the agets, both i terms of speed ad quality of the aswers they provide to customers. Our aalysis is supported by the use of some simple queueig models ad provides some iterestig isights. I particular, it appears that for some reasoable rages of parameters, the ew orgaizatio ca outperform the origial orgaizatio. We the exted the aalysis to the case where, i additio to the idetified customer portfolios, there is a additioal flow of calls called out-portfolio flow. It is show that this feature makes the ew orgaizatio eve more efficiet. Key words: call ceter maagemet; quality of service; poolig; huma resource maagemet; customer portfolio maagemet; team-based orgaizatio; queueig models History: Accepted by Ger Koole, special issue editor; received November 9, This paper was with the authors 5 moths for 3 revisios. 1. Itroductio Recetly, the umber of call ceters has bee icreasig drastically. Call ceters are a meas of customer relatioship maagemet, ad their role is growig. A call ceter is a complicated service system, i which maagers must take ito accout the behavior of both customers ad agets (Gas et al. 2003). May issues are related to call ceters: a issue of corporate image, which is related to the quality of service perceived by customers; a fiacial issue from the cost of labor; ad fially a huma resource (HR) issue related to the social coditios of work. The purpose of this paper is to provide some isights ito the impact of the iteral orgaizatio of call ceters o their performaces. It is the result of a collaboratio with Bouygues Telecom, a Frech mobile phoe compay. The Bouygues Telecom call ceter hadles a average of 100,000 phoe calls daily. Some of the calls are treated by a automated operator. Agets, also called customer represetatives, deal with about 60% of these cotacts. There are also about 1 millio cotacts per year hadled by mail, , ad fax. Here, we ivestigate the adequacy of migratig from a call ceter where all agets are pooled ad customers are treated idifferetly toward a call ceter where customers are grouped ito clusters with dedicated agets. I our termiology, each cluster will be called a portfolio. The customers who do ot fit ito a precise portfolio geerate the so-called outportfolio flow ad must wait i a lower-priority outportfolio flow queue. Maagers of Bouygues Telecom believe that the challege is ot oly to aswer quickly but also to aswer customers correctly. I this sector (mobile telephoy), it is ot rare to see customers switchig from oe compay to aother as a cosequece of low-quality resposes by customer represetatives. Agets are the iterface betwee the compay ad the customers; hece, customer satisfactio is closely liked to agets performace. Maagers eed to motivate their employees so that the assistace they provide to customers is efficiet, 400

2 Jouii, Dallery, ad Nait-Abdallah: Team-Based Orgaizatios i Call Ceters Maagemet Sciece 54(2), pp , 2008 INFORMS 401 both i terms of speed ad quality of aswers. O the other had, employees eed to feel strogly supported by the compay so that the turover is as low as possible. I fact, turover meas traiig ew employees, ad it implies more costs. The aim of Bouygues Telecom i migratig ito customer portfolio maagemet is to better maage employees ad, as a cosequece, to satisfy customers more efficietly. This maagemet approach makes agets more resposible to their ow customers. Moreover, partitioig agets ito groups creates competitio, which icreases agets motivatio. These factors result i a overall improvemet i agets efficiecy, both quatitatively ad qualitatively. By quatitative efficiecy, we mea the speed (processig time) of providig assistace to the customers. By qualitative efficiecy, we mea the quality agets provide whe addressig the customers requests. I this paper, we argue that these advatages may outweigh the variability that results from the loss i ecoomy of scale origially associated with the pooled system. I additio, i the proposed orgaizatio, all portfolios, ad correspodig sets of dedicated agets are idetical (statistically). Therefore, issues such as traiig ad forecastig ca be doe i a homogeeous maer. Also, havig homogeeous teams yields more efficiet HR maagemet. I fact, it allows the call ceter maager to compare teams performaces, which results i a global competitio. Such a maagerial approach has bee widely ad successfully used i idustry ad is also likely to be of iterest i service activities such as call ceter operatios. It is, ideed, oe of the key success factors of the so-called world class maufacturig. For example, Schoberger (1986, pp ) refers to it as cellular maufacturig ad describes its beefits as follows: Cells create resposibility ceters where oe existed before. The cell leader ad the work group may be charged with makig improvemets i quality, cost, delays, etc. The remaider of this paper is structured as follows. I 2, we review two kids of literature close to our work. The first oe is o poolig, ad the secod is o itegratig huma factors i queueig systems, i particular i call ceters. I 3, we give a comprehesive presetatio of the problem we study i this paper. I 4, we develop a simple queueig model that is the used to address the issue of beefits versus costs of migratig from the pooled orgaizatio to the dedicated orgaizatio whe there is o outportfolio flow. We provide some iterestig isights o the trade-off betwee reductio of the poolig effect ad agets efficiecy improvemet, both quatitatively ad qualitatively. I 5, we exted this aalysis to the situatio where there is a out-portfolio flow. To do that, we first develop some approximate queueig models of the call ceter operatig with a mix of portfolio ad out-portfolio flows. Oe additioal isight is that the drawback of ot havig a totally pooled system is less importat i this cotext. Fially, we coclude ad propose some directios for future research. 2. Literature Review There is a extesive ad growig literature o call ceters, ad i geeral o cotact ceters. We refer the reader to Gas et al. (2003) ad Whitt (2002) for a overview. Our work is related to two streams of literature, oe dealig with poolig ad the other with huma factors i queueig systems. The literature dealig with poolig falls maily ito two categories: pool queues or pool servers (see Madelbaum ad Reima 1998). Kleirock (1976) is oe of the first researchers to give a depictio of these alterative poolig structures. He bega by cosiderig a collectio of m idetical G/G/1 queues, each of which has a sigle server with service rate ad faces a job stream at rate. Poolig oly queues would chage this collectio ito a G/G/m queue, which has m servers, each server with service rate ad a job stream at rate m. Poolig oly servers would chage the last G/G/m queue ito a G/G/1 queue with arrival rate m ad service rate m. I this paper we oly deal with queue-poolig issues. There are two importat aspects i the desig of call ceters. The first deals with the issue of skills: are all agets cross traied with all skills (fully-flexible call ceters), or are the agets oly traied for a subset of skills? I the latter case, what are the subsets of skills that will be cosidered, ad how may agets will have each subset of skills? A typical example of such multiskill call ceters is a iteratioal call ceter where icomig calls are i differet laguages (see Gas et al. 2003). Related studies iclude those by Garett ad Madelbaum (2001), Akşi ad Karaesme (2002), ad refereces therei. The secod aspect deals with the issue of the level of poolig i call ceters; i.e., are the agets all gathered ito a sigle large team, or are they partitioed ito a set of idepedet teams? This issue is ecoutered i geeral i multiskill call ceters but i particular i fully flexible call ceters, i.e., call ceters i which all agets have all skills (all agets are flexible eough to aswer all requiremets of service). Our cocer i this paper is a fully flexible call ceter. It is a plausible assumptio for may real cases, especially for uiligual call ceters where the complete flexibility is ot as difficult as i multiligual call ceters. Several papers discuss the effectiveess of poolig i multiserver queues (see, e.g., Teki et al. 2004). Beyod

3 Jouii, Dallery, ad Nait-Abdallah: Team-Based Orgaizatios i Call Ceters 402 Maagemet Sciece 54(2), pp , 2008 INFORMS service systems, poolig-effect problems arise i various applicatios, such as maufacturig ad computer etwork systems. The stadard argumet for combiig queues is because of the ecoomies of scale, which absorb stochastic variability (Borst et al. 2004). Although it is easy to see that pooled systems are more effective tha idepedet oes, this ituitio was for a log time based o experiece ad umerical data rather tha o rigorous mathematical proof. Smith ad Whitt (1981) were the first to formally prove this result, whe they combied systems with idetical service time distributios. They applied aalytic methods for the M/M/s/s loss systems (Erlag-B, o waitig room) ad the M/M/s delay systems (Erlag-C, ifiite waitig room). By usig sample path methods, they also showed that efficiecy icreases by combiig queues i systems with geeral arrival processes ad geeral service time distributios. Bejaafar (1995) exteded theses results by providig performace bouds o the effectiveess of several poolig scearios. Whe we allow service rates i separate systems to become differet, combiig queues ca be couterproductive (Smith ad Whitt 1981, Bejaafar 1995). Va Dijk ad va der Sluis (2006) preset a case study simulatio supportig this outcome. Usig approximatios for M/G/s performace measures, Whitt (1999) explored the trade-off betwee ecoomies of scale associated with larger systems ad the beefit of havig customers with shorter service times separated from customers with loger service times. All of the above results i o way take ito accout the huma elemet. This takes us to the secod area of literature close to our work. The huma elemet is the mai characteristic of call ceters ad cotact ceters. Both customers ad agets are people. Eve though it is atural to focus o uderstadig huma behavior, few papers itegrate this aspect i aalyzig call ceters or, i geeral, queueig systems. We refer the reader to the survey of Gas et al. (2003), where we fid some refereces examiig queueig models of call ceters that icorporate customers behaviors, such as abadomets ad retrials. Some other models iclude the lik betwee agets ad customers experieces. I 1987, two papers lauched discussios about huma factors i queueig systems. The first is Larso s (1987) paper, which goes beyod the classical iterest o delays ad poits out the psychological experieces of people i queues. He argues the importace of perceptios of fairess ad shows how the violatio of the first-come, firstserved order may cotribute to customers dissatisfactio. The secod is Rothkopf ad Rech s (1987) paper, which deals with the questio of combiig queues. They discuss the trade-off betwee pooled ad separated systems by icludig customers reactios ad jockeyig betwee separate queues (a customer ca chage to oe queue while waitig i aother). Moreover, they show how separate systems may lead to servers that are more resposible toward their ow customers. It may also allow for a faster service because of the degree of specializatio gaied through experiece. To our kowledge, they were the first to emphasize this issue. Fischer et al. (1999) coclude that call ceter maagemet requires a mix of disciplies that are ot typically foud i orgaizatios. The review of Boudreau et al. (2003) follows through this ew area. They propose a framework that is a fertile source of research opportuities. They justify by usig real examples that operatios maagemet itself without HR maagemet caot aalyze systems such as those we are dealig with very well. I others words, there is a mutual impact betwee the two fields, ad takig this fact ito accout yields more realistic ad precise isights. I particular, Boudreau et al. (2003) cosider that more realistic operatios maagemet models eed to itegrate huma factors such as turover, motivatio, ad team structure. I fact, a team settig allows for better commuicatio, ad may allow for more resposible ad motivated agets. I a more recet paper, Boudreau (2004) uderlies oce agai the sigificat opportuities for fruitful research at the boudaries betwee the traditioal topics of operatios maagemet ad HR maagemet. I this paper, we address this issue i a call ceter cotext. We explore how maagig agets by creatig separate pools might lead to the agets performig more efficietly. 3. ProblemSettig Cosider a compay operatig a fairly large call ceter. The call ceter provides assistace to the compay s customers. Customers call the compay wheever they eed assistace, ad their request is addressed by a set of agets (or customer represetatives). I the settig of this paper, we assume that the call ceter is operated i such a way that all agets have the same skill. Therefore, assistace to the customers ca be provided by ay aget. I other words, all agets are idetical (statistically) i the sese that they ca aswer all questios comig from the customers with the same efficiecy, both quatitatively ad qualitatively Curret Orgaizatio Mode The call ceter is operated i such a way that at ay time, ay call ca be addressed by ay aget. So wheever a call arrives, it is addressed by oe of the available agets. If oe is available, the call

4 Jouii, Dallery, ad Nait-Abdallah: Team-Based Orgaizatios i Call Ceters Maagemet Sciece 54(2), pp , 2008 INFORMS 403 is placed ito a queue ad will be addressed as soo as possible. There is a sigle queue, ad waitig calls are aswered o a first-come, first-served (FCFS) basis. For simplicity, we assume that the queue has o capacity costrait ad that customers do ot abado while waitig. Uder this orgaizatio, the agets have a give efficiecy. The quatitative efficiecy is measured by the distributio of the processig times, which represets the time it takes for a aget to aswer a call. Note that the radomess of the processig times comes i particular from the variety of questios asked by the customers. The qualitative efficiecy is measured by the probability of successfully aswerig the customer s questio. We assume that if the call has ot bee addressed i a adequate maer, the customer will call back to get assistace from aother aget. This cocept of call resolutio probability was argued by de Véricourt ad Zhou (2005) i a call-routig problem. As for the global efficiecy of the call ceter uder the curret orgaizatio, its positive side comes from the poolig effect. Its egative side is i terms of HR maagemet, give that it is usually difficult to have a efficiet maagemet of a large set of agets i a large call ceter New Orgaizatio Mode The set of agets is split ito a set of idepedet teams i the ew mode. The teams are homogeeous i the sese that they have the same umber of agets ad that all agets have the same skills. I other words, there is o specializatio. Let be the umber of idepedet teams. I the ew orgaizatio, i additio to the partitioig of the total umber of agets i a set of autoomous teams, there is also a partitioig of the customers ito a set of customer portfolios. Agai, this partitioig is doe i such a way that the portfolios are homogeeous. I other words, the overall requests comig from the differet customer portfolios are statistically idetical. So wheever a call arrives from a customer of a give portfolio, it is routed to the correspodig team. The behavior at the team level is the exactly idetical to that described above for the origial large call ceter. This ew orgaizatio is equivalet to idepedetly operatig smaller call ceters, with each call ceter havig its ow customer portfolio. Agai, it is importat to emphasize that uder this ew orgaizatio, all teams ad customer portfolios have the same behavior (statistically). I the research study we performed with Bouygues Telecom, the size of the origial call ceters (total umber of agets) was o the order of 2,000, ad the compay was cosiderig team sizes ragig from 40 to 100 agets. Because all agets are ot always preset, this would mea that the umber of agets simultaeously preset i the call ceter would be o the order of 1,000, ad the correspodig umber of agets preset i each team would rage from 20 to 50. The reaso to move to this ew orgaizatio was alog the lie of the world class maufacturig literature amely, that the HR maagemet could be performed i a much better way at a small team level tha at the global call ceter level. Agets motivatio ad resposibility would icrease. Performace measures, both quatitative (processig times) ad qualitative (rate of calls successfully addressed), could be examied more appropriately ad could be used for iteral team maagemet. Because of the team-portfolio oe-to-oe lik, a customer ot satisfied with the aswer he got from the aget would call back, ad the additioal burde would fall o the same team. Also, the fact that all teams are homogeeous would allow for performace comparisos betwee the differet teams, resultig i a global competitio. Icetives could be give to agets based o the global performace of the team Research Objectives I this research project, our goal is to study the tradeoff betwee the pros ad cos of movig from the origial orgaizatio to the team-based orgaizatio, also referred to as the portfolio orgaizatio. To do that, we cosider a simple stochastic model of the origial pooled orgaizatio. This model captures the origial behavior of the call ceter whe all agets are pooled. Uder this situatio, the call ceter has a omial behavior i terms of efficiecy (quatitative ad qualitative efficiecies). It achieves a give quality of service (QoS). We actually cosider two differet QoS measures: the average waitig time ad the 80/20 rule, which is a idustry stadard for telephoe service (Gas et al. 2003). Uder the 80/20 rule, at least 80% of customers must wait o loger tha 20 secods. I this work, we study the icrease of efficiecy required for the team-based orgaizatio to achieve the same QoS as the pooled system with the same total umber of agets, i.e., o cost icrease. We successively cosider the case where the improvemet comes oly from the icrease of the quatitative efficiecy (decrease of the average processig time) ad the the case where the improvemet comes oly from the icrease of the qualitative efficiecy (icrease i the average rate of successful aswer). To perform the differet aalyses described above, we cosider a geeric model that captures the importat features eeded for the compariso betwee the pooled orgaizatio ad the team-based orgaizatio. As is ofte the case i call ceter modelig, our aalysis is based o the use of a statioary queueig model

5 Jouii, Dallery, ad Nait-Abdallah: Team-Based Orgaizatios i Call Ceters 404 Maagemet Sciece 54(2), pp , 2008 INFORMS Figure 1 Geeric Model Team of agets Arrival process of ew calls Waitig lie Departure process of calls successfully aswered Arrival process of calls ot successfully aswered Departure process of calls ot successfully aswered Delay before callig back (Gas et al. 2003). We use stadard assumptios o the ature of the uderlyig processes: Poisso arrival processes ad expoetial service time. These assumptios are plausible for Bouygues Telecom ad for may other call ceters, especially for the arrival processes. I additio, we assume that calls ot successfully satisfied occur radomly, ad therefore the splittig of the output flow follows a Beroulli process. Moreover, delays before customers call back are assumed to be i.i.d. radom variables. This allows us to use simple results from stadard queueig theory. The geeric model uder cosideratio (for both the pooled orgaizatio ad the team-based orgaizatio) is illustrated i Figure 1. The results of our study are preseted i Out-Portfolio Flow There was aother importat feature i the Bouygues Telecom call ceter. Not all the calls received at the call ceter could be idetified as belogig to a give portfolio of customers. Therefore, the actual situatio was that i additio to the flow of calls comig i for each portfolio, there was a additioal flow of idepedet calls, referred to as out-portfolio calls. I the origial pooled orgaizatio, the calls were treated with lower priority. For the team-based orgaizatio, all out-portfolio calls are set to a sigle queue. These calls ca be served by ay aget of ay team, but portfolio calls have (opreemptive) priority over out-portfolio calls. This meas that whe a aget becomes available, he deals with a call from his portfolio first (the first call i lie). If the queue is empty, this aget provides service to a call from the out-portfolio queue (the first i lie). Uder this more geeral settig, we also ivestigate the improvemet i either quatitative or qualitative efficiecy that would be required to couterbalace the upoolig effect. The results of our study are preseted i Aalysis of the Efficiecy of the Team-Based Orgaizatio We restrict our attetio to the situatio where there is o out-portfolio flow. I 4.1, we preset the relevat queueig models ad determie the performace measures of iterest. I 4.2 ad 4.3, we aalyze the required icrease i terms of quatitative or qualitative efficiecy that must be achieved to couterbalace the reductio of the poolig effect. Fially, i 4.4, we provide some further isights o the advatages of the team-based orgaizatio Modelig ad Performace Aalysis Cosider first the queueig model of the origial call ceter. The model cosists of a sigle ifiite queue ad a set of s idetical servers represetig the agets. Service times are assumed to be expoetially distributed with rate. The arrival process of first-attempt calls (primary calls) is assumed to be Poisso with a arrival rate of a. There is a probability that the customer is ot satisfied with the aswer he got ad therefore will call agai. Thus, 1 represets the probability that a call is successfully aswered. Delays before customers call back are assumed to be i.i.d. radom variables with a geeral distributio. For tractability purposes, we assume idepedece betwee successive calls, both i terms of service times ad probability of success. Let be the overall arrival rate to the queue, i.e., the sum of the primary calls ad the feedback calls. Uder stability coditios, = a / 1. This simple model falls ito the class of product-form etworks aalyzed by Baskett et al. (1975). As a result, the statioary behavior of this queueig model does ot deped o the distributio of the call-back delays. They ca thus be igored. The resultig model is show i Figure 2. It is equivalet to a simple M/M/C queue with C = s servers, a Poisso arrival rate = a / 1,

6 Jouii, Dallery, ad Nait-Abdallah: Team-Based Orgaizatios i Call Ceters Maagemet Sciece 54(2), pp , 2008 INFORMS 405 Figure 2 Pooled System s µ α (1 α) ad a service rate. This model will be referred to as the pooled system. Cosider ow the modelig of the team-based orgaizatio with a partitioig of the origial call ceter ito autoomous teams, each oe beig associated with a customer portfolio. It is assumed that is such that s is a multiple of. Recall that all teams ad all customer portfolios are statistically idetical. Uder this orgaizatio, the call ceter ca be modeled as a set of idepedet ad idetical queueig models. I the followig, we focus our attetio o the geeric model of ay portfolio/team subsystem. The assumptios are similar to those above. The model cosists of a sigle ifiite queue ad a set of s idetical servers. Service times are assumed to be expoetially distributed with rate. The arrival process of first-attempt calls (primary calls) is Poisso with a arrival rate of a = a /. The probability that a call is ot successfully aswered is give by. The resultig model is show i Figure 3. It is equivalet to multiple simple M/M/C queues, with C = s servers, a Poisso arrival rate = a / 1, ad a service rate. This model will be referred to as the dedicated system. Note that the pooled system ca be viewed as the particular case of the dedicated system for = 1. I the Bouygues Telecom call ceter, like i most call ceters, the arrival rate of calls varies over time. Therefore, we use queueig models to estimate statioary system performace of half-hour itervals. We assume a costat umber of agets ad costat arrival ad service rates, as well as a system that achieves a steady state quickly withi each half-hour iterval of time (Gas et al. 2003). Cosider the dedicated system. Let W t be the cumulative distributio fuctio of the waitig time i the queue. Let r = / = a / 1 be the Figure 3 Dedicated System. s s µ α α (1 α ) µ (1 α ) traffic itesity ad = r /s be the server utilizatio (proportio of time each server is busy). Note that the coditio for existece of a steady-state solutio is < 1; that is, the mea total arrival rate must be less tha the mea maximal service rate of the system. As i Gross ad Harris (1998), Equatio (1) gives the probability that the waitig time i the queue is less tha t. W t = 1 r s p 0 s! 1 e s t Equatio (2) gives the expressio of the average waitig time i the queue. ( W = r s s! s 1 2 (1) ) p 0 (2) Equatio (3) gives the expressio of p 0, which is the statioary probability of fidig o customers i the system. ( s 1 ) p 0 = r i i! + r s 1 (3) s i=0! 1 The above equatios give performace measures of the dedicated system with teams. The pooled system is a special case of the dedicated system. Performace measures of the pooled system are obtaied by usig = 1, s 1 = s, 1 =, ad a 1 = a i Equatios (1) (3). Because of the variability effect i the arrival ad service processes, the compariso betwee the pooled system ad the dedicated system will always show that, for ay positive iteger 2, the pooled system outperforms the dedicated system uder the same situatio, i.e., s = s/, =, a = a /, ad =. Uder these coditios, it is ituitively clear that the dedicated system is less efficiet because a call may wait for oe server (of oe team) while aother server (of aother team) is idle; such a situatio does ot occur i the pooled system. I this sectio, as i the ext oe, we perform the study of the quatities of iterest as a fuctio of the umber of dedicated pools,. Alteratively, we could have chose to perform this study accordig to the size of the dedicated pools, s/. However, because the total staffig level s is fixed i our study, the two aalyses are totally equivalet ad the coclusios draw i terms of ca readily be iterpreted i terms of s/ Evaluatio of Service Rate Percetage Icrease We start from a pooled system with a give QoS (W t or W ); our purpose is to evaluate the required service rate i a dedicated system with pools to esure the same QoS (W t = W t or W = W ). The total staffig

7 Jouii, Dallery, ad Nait-Abdallah: Team-Based Orgaizatios i Call Ceters 406 Maagemet Sciece 54(2), pp , 2008 INFORMS Table 1 Required Service Rates i a Dedicated System i Order to Achieve W = 0 18 Miutes ad W 20 sec.) = 80% W = 0 18 W (20 sec.) = 80% (%) (%) level, the total arrival rate of first-attempt calls, ad the call-back proportio are all held costat. I the pooled system, the arrival rate of first-attempt calls is a = calls per miute, the call-back proportio is = 10%, the service rate is = 0 2 calls per miute, ad the umber of agets is s = I this system, 80% of customers wait o more tha 20 secods, ad the correspodig average waitig time is W = 0 18 miutes. I the dedicated system, each call ceter has a staffig level s = s/, a arrival rate of first-attempt calls of a = a /, ad a call-back proportio of = = 10%. We vary from 1 to 50. For each umber of separated call ceters, we calculate the service rate so that the average waitig time is W = 0 18 miutes. We repeat the same aalysis for the QoS i terms of the 80/20 rule. The results are preseted i Table 1. Figure 4 shows the curves of the required percetage of service rate icrease, calculated as 100 /, accordig to the umber of pools to reach W = 0 18 miutes ad W (20 sec.) = 80%, respectively. Figure 4 shows that, for both types of Figure Percetages of Service Rate Icrease Accordig to Number of Pools i a Dedicated System i Order to Achieve W = 0 18 Miutes ad W 20 sec.) = 80% W = 0.18 mi. W (20 sec.) = 80% QoS, the required icrease of service rate does ot grow i a dramatic fashio. We otice that for a dedicated system with = 20 separate teams, the required mea service time is about 4 miutes, 25 secods to reach W = 0 18 miutes, ad it is about 4 miutes, 30 secods to reach W (20 sec.) = 80%. I a dedicated system with = 10 separate call ceters, the required mea service time is oly about 4 miutes, 40 secods for both types of QoS. Noe of these values is too far from the actual mea service time (5 miutes). I coclusio, it is possible to eve out the performaces of a pooled system by slightly icreasig the service rate. I practice, a icrease i service rate efficiecy o the order of 10% seems reasoable to achieve because of the competitio created by the team-based orgaizatio Evaluatio of Percetage of Call-Back Proportio Decrease Now we focus o evaluatig the required decrease of the call-back proportio i a dedicated system with separated call ceters, to esure the same QoS (W t = W t or W = W ) as i the correspodig pooled cofiguratio. We cosider agai the same example of the pooled system (with the same parameters s, a,, ad ). Each of the separated call ceters of the dedicated system has a arrival rate of first-attempt calls of a = a /, a service rate = = 0 2 calls per miute, ad a staffig level s = s/. For each, we calculate the required call-back proportio so that the average waitig time is W = 0 18 miutes. We repeat the same aalysis for the QoS i terms of the 80/20 rule. The correspodig results are preseted i Table 2. We choose to vary oly from 1 to 10 so that stays positive. I Figure 5, we plot the required percetages of the call-back proportio decrease, calculated as 100 /, versus the umber of pools to reach W = 0 18 miutes ad W (20 sec.) = 80%, respectively. Oce agai, we see from Figure 5 that the required percetage decrease of the call-back proportio grows with the umber of pools i a ot-sostrog way, ad that the curves for each type of QoS Table 2 Required Call-Back Proportios i a Dedicated System i Order to Achieve W = 0 18 Miutes ad W 20 sec.) = 80% Percet W = 0 18 W (20 sec.) = 80% (%) (%) (%) (%)

8 Jouii, Dallery, ad Nait-Abdallah: Team-Based Orgaizatios i Call Ceters Maagemet Sciece 54(2), pp , 2008 INFORMS 407 Figure 5 70 Percetages of Call-Back Proportio Decrease Accordig to Number of Pools i a Dedicated System i Order to Achieve W = 0 18 Mitues ad W 20 sec.) = 80% Table 3 Assumig a Improvemet of the Call-Back Proportio by 20% = 8% W = 0 18 W (20 sec.) = 80% Percet W = 0.18 mi. W (20 sec.) = 80% are similar. For example, i a dedicated system with 10 pools, we have to decrease the call-back proportio by about 60% with regard to = 10% to reach W (20 sec.) = 80%. Note that it is possible to achieve this required decrease i practice, especially whe the quality of respose withi the pooled cofiguratio is quite poor. The reaso for the improvemet is that the agets i the team-based orgaizatio are more resposible for their ow customers tha i the case of the pooled orgaizatio. Agets will try to provide aswers that are as good as possible to dimiish the call-back flow ad, as a cosequece, improve the performace of their team Sythesis The results of the previous sectios show that migratig toward separated call ceters may ot be as bad a idea as it seems. I additio to the aalysis reported above, we have performed a more systematic aalysis to cofirm the robustess of our coclusios. This aalysis is reported i the olie supplemet (provided i the e-compaio). 1 It shows that the qualitative results discussed above are valid for a large rage of parameters typical of those that would be ecoutered i real situatios. I additio, it would be realistic to assume that the better team maagemet eabled by the ew orgaizatio implies a improvemet of both parameters, i.e., a icrease of the service rate ad a decrease of the call-back proportio. To see the combied improvemet of the two factors, we perform the same aalysis as that i 4.2 by also icorporatig a improvemet o the call-back proportio. We cosider two cases correspodig to two values of : = 8% ad = 5%, correspodig to a 20% ad 50% improvemet i the call-back proportio with 1 A electroic compaio to this paper is available as part of the olie versio that ca be foud at org/. %of %of improvemet (%) improvemet (%) respect to the iitial value of = 10%, respectively. The results are provided i Tables 3 ad 4 for the rage of values of of iterest, i.e., from 20 to 50. The results show that by havig a improvemet i both efficiecies, the required performace improvemet for each oe is ot as high as whe focusig o each oe separately. Let us ow focus o the mix of efficiecy improvemets for a give value of. Table 5 presets the results pertaiig to the case = 10. Whe we migrate to a dedicated system with = 10 separated call ceters, we eed either to icrease the service rate by about 7.11% with regard to = 0 2 call per miute or to decrease the call-back proportio by about 66% with regard to the iitial = 10% to achieve W = 0 18 miutes. Aother solutio is to icrease by 3% ad decrease by about 37% at the same time. I such a case, it should come as o surprise that we improve the performaces i the dedicated systems rather tha deteriorate them. Team maagemet effects may chage both parameters ad may go beyod the simple fact of outweighig the icrease of variability. Figure 6 shows the variatio of the percetage decrease of accordig to the percetage icrease of. The graph suggests that improvig is liear, accordig to improvig. However, it is ot the case i geeral. I fact, let us take the particular case of a dedicated system with a collectio of separated M/M/1 queues (s = 1). I this case, the average waitig time is give by W = (4) 1 Table 4 Assumig a Improvemet of the Call-Back Proportio by 50% = 5% W = 0 18 W (20 sec.) = 80% %of %of improvemet (%) improvemet (%)

9 Jouii, Dallery, ad Nait-Abdallah: Team-Based Orgaizatios i Call Ceters 408 Maagemet Sciece 54(2), pp , 2008 INFORMS Table 5 percetage icrease Percetages of Call-Back Proportio Decrease Accordig to Percetages of Service Rate Icrease i a Dedicated System with = 10 i Order to Achieve W = 0 18 Miutes percetage decrease where is the server utilizatio, = /. Because = a / 1, we deduce from Equatio (4) that = 1 W W a (5) If W ad a are held costat, Equatio (5) shows that is ot liear, accordig to. However, we obtai a almost-liear behavior whe the umber of pools is ot very large ad the umber of servers per pool s is therefore ot very small, which is the case i our call ceter. It is a iterestig result, because, if we ca assume liearity betwee these two parameters, we are able to approximate them through simple formulas. Aother advatage of the team-based orgaizatio is its robustess with respect to errors i the estimatio of the arrival rate of primary calls. For example, cosider agai the pooled system, = 1, described i 4.2 ad the dedicated system, = 10, obtaied by icreasig the service rate to esure the same QoS as a real i the pooled system. We deote by the real first-attempt arrival rate. Figure 7 plots the average waitig time W versus a real for the pooled system ad for the dedicated system. We observe that the Figure 6 Percet Percetages of Call-Back Proportio Decrease Accordig to Percetages of Service Rate Icrease i a Dedicated System with = 10 i Order to Achieve W = 0 18 Miutes W = 0.18 mi Percetage of service rate icrease Figure 7 Miutes Average Waitig Time of a Pooled System = 1 ad a Dedicated System = 10 Accordig to the Total Arrival Rate of First-Attempt Calls = 1 = ,real QoS of the pooled system is much more affected tha the dedicated system by a uderestimatio of the first-attempt calls arrival rate. Let us give a explaatio. Uder the origial expected first-attempt arrival rate, the server utilizatio i the pooled system, 98.53%, is much closer to 1 tha the oe i the dedicated system, 91.99%. If the first-attempt arrival rate is uderestimated, the deterioratio of the quality of service icreases faster whe the server utilizatio is closer to 1, because the queue becomes less ad less stable. For example, assume that we uderestimate the total arrival rate of first-attempt calls (which is ow a = calls per miute for both systems) by oly 1.41%. The the real server utilizatio of the pooled system becomes 99.92% ad the oe of the dedicated system becomes 93.28%. As a cosequece, the average waitig time of the first system goes beyod 5 miutes ad the oe of the secod system is oly 0.27 miutes. This shows that the team-based orgaizatio is more robust tha the origial pooled orgaizatio. This is a very attractive feature that gives aother strog argumet i favor of the team-based orgaizatio. 5. Call Ceter Models with Out-Portfolio Flow I this sectio, we address the same issues as i 4 by cosiderig two ew models (a pooled model ad a dedicated model) of call ceters. They differ from the above models by takig a aoymous flow (out-portfolio flow) of calls ito accout. This cosists of calls with which oe caot associate a portfolio whe they eter the call ceter. A aoymous call ca be a call of a customer of Bouygues Telecom who does ot commuicate his phoe umber to the computer-telephoe itegratio, a perso who is ot a customer of Bouygues Telecom etc. I 5.1, we preset the models ad we develop approximatios to estimate the performace measures

10 Jouii, Dallery, ad Nait-Abdallah: Team-Based Orgaizatios i Call Ceters Maagemet Sciece 54(2), pp , 2008 INFORMS 409 Figure 8 Portfolio Pooled System Figure 9 Portfolio Dedicated System PTF: (1 p) 1 α µ µ OPTF: p 1 α of iterest. I 5.2 ad 5.3, we aalyze the required improvemet i terms of quatitative or qualitative efficiecy that must be achieved to outweigh the loss i ecoomy of scale. Fially, i 5.4, we further ivestigate the cosequece of havig a out-portfolio flow o the behavior of the dedicated system. s (1 p) PTF: (1 p) PTF: 1 α 1 α. s µ s 5.1. Modelig ad Performace Aalysis Cosider first the queueig model of the origial large call ceter with two types of customers: idetified customers (portfolio or PTF customers) ad oidetified (aoymous) customers (out-portfolio or OPTF customers). PTF customers have priority over OPTF customers i the sese that agets are providig assistace to PTF customers first. The priority rule is opreemptive, which simply meas that a aget curretly servig a OPTF customer while a PTF customer jois the waitig queue will complete this service before turig to the PTF customer. The model cosists of two ifiite queues ad a set of s idetical servers represetig the set of agets. All agets are able to aswer all types of questios. Each type of customer has its ow queue. Service times are assumed to be expoetially distributed ad idepedet of each other with rate for both types of customers. The arrival process of first-attempt calls (primary calls) is assumed to be Poisso with a total arrival rate of a. The proportio of OPTF first-attempt calls is p. So the total arrival rate of first-attempt PTF calls is a PTF = 1 p a ad that of the OPTF calls is a OPTF = p a. There is a probability that the customer is ot satisfied with the aswer he got ad therefore will call agai. We assume that is the same for both types of customers. We make the same detailed assumptios as those preseted i 4.1. Followig similar argumets, the behavior of this call ceter ca be approximated by a simple M/M/C queue with two classes of customers (PTF ad OPTF), C = s servers, a Poisso arrival rate of PTF customers PTF = 1 p a / 1, a Poisso arrival rate of OPTF customers OPTF = p a / 1, ad a service rate. PTF customers have opreemptive (head-of-lie) priority over OPTF customers. Withi each queue, the disciplie is FCFS. This model, referred to as the portfolio pooled system, is illustrated i Figure 8. Note, however, that i this more geeral situatio, this model is oly a approximatio OPTF: p 1 α of the behavior of the portfolio pooled system. This is because the model o loger belogs to the class of product-form etworks aalyzed by Baskett et al. (1975), because of the priority of the PTF customers over the OPTF oes. Note also that the portfolio pooled system reduces to the pooled system studied i 4 whe p = 0%. Cosider ow the modelig of the team-based orgaizatio with a partitioig of the origial call ceter (with OPTF customers) ito autoomous teams, each oe beig associated with a customer portfolio. It is assumed that is such that s is a multiple of. All teams ad all customer portfolios are statistically idetical. Each team has s idetical servers ad its ow ifiite queue for its ow PTF customers. There is a sigle ifiite queue for all OPTF customers. A OPTF customer is served oly whe at least oe of the agets (of ay team) is idle ad o PTF customers are waitig i the correspodig portfolio queue. The assumptios are similar to those above. The arrival process of PTF first-attempt calls to each PTF queue is a PTF Poisso with a arrival rate of = 1 p a /. The arrival process of OPTF first-attempt calls to the OPTF queue is Poisso with a arrival rate a OPTF = p a. The behavior of this call ceter ca be approximated by a set of idetical parallel M/M/C systems with C = s servers. Each M/M/C system has its ow arrival process correspodig to its PTF customers. This arrival process is Poisso with a rate PTF a PTF = / 1 = 1 p / a / 1. I additio, there is a additioal queue for the OPTF customers. The arrival process to this queue is Poisso with a rate OPTF = a OPTF / 1 = p a / 1. The OPTF customers ca be served by ay server of ay of the parallel M/M/C queues. However, PTF customers have opreemptive (head-of-lie) priority

11 Jouii, Dallery, ad Nait-Abdallah: Team-Based Orgaizatios i Call Ceters 410 Maagemet Sciece 54(2), pp , 2008 INFORMS Figure 10 Pessimistic Model for the PTF Customers Figure 11 Pessimistic Model for the OPTF Customers (1 p) PTF: p OPTF: 1 α 1 α s µ PTF: (1 p) 1 α OPTF: p 1 α s µ over OPTF customers. The resultig model is show o Figure 9. This model will be referred to as the portfolio dedicated system. Note that this system reduces to the portfolio pooled system whe = 1, ad to the dedicated system whe p = 0%. We ow focus o evaluatig the statioary performaces of the two above models. Exact performace measures of the portfolio pooled system (viewed as a opreemptive priority M/M/C queue) i terms of the waitig time distributio ca be foud i Kella ad Yechiali (1985). However, the exact quatitative aalysis of the portfolio dedicated system is complicated. For that, we developed a set of models that allow us to approximate its performace measures. We preset two approximatios for the portfolio dedicated system. The first eables us to calculate a pessimistic estimate (upper boud) of the waitig times of the PTF customers, ad the secod oe eables us to calculate a pessimistic estimate (upper boud) of the waitig times of OPTF customers. The reaso for choosig pessimistic estimates is that the improvemets i efficiecy that will follow from our aalysis ca be viewed as a lower boud o the improvemets i efficiecy that will actually be required i the exact aalysis. These approximate models are of the same ature as that of the portfolio pooled model. Their performace measures ca the be exactly calculated i the same way. Validatios of these approximatios are preseted i the olie supplemet Pessimistic Model for PTF Customers. The pessimistic model for PTF customers is obtaied from the portfolio dedicated system by splittig the flow of OPTF ito a set of idepedet flows. The resultig model cosists of a set of idepedet ad idetical M/M/C systems with C = s servers ad a service rate. As i the origial model, the arrival process of PTF customers is a Poisso process with rate PTF = 1 p / a / 1. The arrival process of OPTF customers is a Poisso process with rate PTF = p/ a / 1. The OPTF customers ca be served by ay of the s servers from the correspodig team. However, PTF customers have opreemptive (headof-lie) priority over OPTF customers. The model is show i Figure 10. I this model, there is ot a sigle OPTF queue, as opposed to the portfolio dedicated system. The OPTF flow is equally divided ad assiged to each oe of the separate OPTF queues. Thus, it may happe that a OPTF customer has delayed access to a server, while a server of aother team is available. This delay may later o delay the access of a PTF customer to a server because the OPTF customer is beig served ad the priority is opreemptive. Aother way to look at this approximate model is to see it as a upoolig of the OPTF flow, which idirectly causes additioal delays to the PTF customers. Thus, this model provides a pessimistic estimate of the waitig times of the PTF customers Pessimistic Model for OPTF Customers. The pessimistic model for OPTF customers is obtaied from the portfolio dedicated system by mergig the flow of PTF ito a sigle flow ad simultaeously mergig all the servers ito a sigle pool of s servers. This model is similar to the portfolio pooled system. The arrival process to the sigle PTF queue is Poisso with rate PTF = 1 p a / 1. The arrival process to the sigle OPTF queue is a Poisso process with rate PTF = p a / 1. PTF customers have opreemptive priorities over OPTF customers. The model is show i Figure 11. Because of the poolig effect of the PTF customers, the average waitig time of OPTF customers will be loger. I the portfolio dedicated system, a OPTF customer may get access to a server while a PTF customer is waitig i a queue (ot served by this server), which reduces the waitig time of the OPTF customer. I the pessimistic model, this will ever occur because of the poolig of all PTF queues ad all servers. Thus this model provides a pessimistic estimate of the waitig time of OPTF customers. I the followig subsectios, we evaluate the impact of migratig from a portfolio pooled system toward a portfolio dedicated system. We cocetrate o the evaluatio of efficiecy improvemet (both qualitative ad quatitative) required to couterbalace the reductio of the poolig effect of the team-based orgaizatio. We defie a global quality of service QoS global for all types of customers as QoS global = 1 p QoS PTF + pqos OPTF. We oly focus o the QoS measured i terms of the average waitig time. Similar results could be obtaied for the 80/20 rule Evaluatio of Service Rate Percetage Icrease We start from a portfolio pooled system with a give quality of service W global, ad our purpose is to eval-

12 Jouii, Dallery, ad Nait-Abdallah: Team-Based Orgaizatios i Call Ceters Maagemet Sciece 54(2), pp , 2008 INFORMS 411 Table 6 Required Service Rate Icrease i a Portfolio Dedicated System i Order to Achieve W global = 0 18 Miutes p = 0% p = 5% p = 10% p = 20% (%) (%) (%) (%) uate the required service rate i a portfolio dedicated system with idetical teams to esure the same global average waitig time W global = W global. The total staffig level, the total arrival rate of firstattempt calls, ad the call back proportio are all held costat. I the portfolio pooled system, the arrival rate of first-attempt calls is a = calls per miute, the call-back proportio is = 10%, the service rate is = 0 2 calls per miute, ad the umber of servers is s = The server utilizatio is the = 98 53%. We choose the same parameters as i the pooled system that we studied i 4. I additio, we vary the proportio of OPTF customers, p = 0%, p = 5%, p = 10%, or p = 20%. As expected, W global does ot deped o p. I fact, the portfolio pooled system is a workcoservig system. It is ot the case that oe server is idle while a customer (PTF or OPTF) is waitig for service. If we vary p, the order of service of a give customer may chage, but the overall average waitig time remais uchaged. We give the mathematical explaatio i the olie supplemet. Here, W global = 0 18 miutes for all values of p. For each value of p, we ow cosider the correspodig portfolio dedicated system. We vary from 1 to 50. For each, we evaluate the required service rate (usig pessimistic models) so that the global average waitig time is W global = W global = 0 18 mi. We preset the results i Table 6. Moreover, we calculate by simulatio the exact values of 20 for p = 5%, 10%, ad 20%, to get some idicatios of their deviatios regardig the values give by the proposed models. Recall that for p = 0%, the portfolio dedicated system behaves like separate Erlag-C models. So the correspodig 20 is obtaied by a exact umerical result. For p = 5%, the required service rate give by simulatio is 20 = istead of 0.221, as give by our approximatio models; for p = 10% it is istead of 0.217; ad for p = 20% it is istead of This shows Figure 12 Percet Percetages of Required Service Rate Icrease Accordig to Number of Pools i a Portfolio Dedicated System i Order to Achieve W global = 0 18 Miutes W global = 0.18 mi. p = 0% p = 5% p = 10% p = 20% us that the costs of partitioig give by our models are ot too far from those give by simulatio, at least for the reasoable parameters of the portfolio dedicated system we have chose. I Figure 12, we plot for each value of p the curve of the percetage of required service rate icrease, calculated as 100 /, i the portfolio dedicated system accordig to the umber of pools, i order to reach a global quality of service of W global = 0 18 miutes. We otice that for a give p, we have the same qualitative results as i 4.2. The required icrease of the service rate is ot very importat, ad it is feasible to reach i practice. This is because of the competitio elemet of the team-based orgaizatio. The ew iterestig isight here is that the ecessary icrease of the service rate to compesate the loss of poolig effect decreases whe the proportio of OPTF customers icreases. Particulary, migratig toward a portfolio dedicated system (with ay p>0%) is always less costly tha migratig toward a dedicated system p = 0%. For example, cosider a portfolio dedicated system with = 10. If the OPTF proportio is p = 5%, we eed to icrease the service rate by 4.91%. However, with a proportio p = 20% we oly eed to icrease the service rate by 1.17%. We explai this advatage by the fact that the OPTF flow is used to reduce idle periods of servers while customers are waitig i the portfolio dedicated system. Idle times would ot exist i the case of p = 100% (pooled system). This will be explaied i more details i Evaluatio of Percetage of Call-Back Proportio Decrease Let us agai start from the portfolio pooled system of 5.2. We aim to evaluate the call-back proportio for a portfolio dedicated system with idetical teams to get W global = W global = 0 18 miutes as i the Portfolio Pooled System. We agai vary p (p = 0%, p = 5%, p = 10%, or p = 20%). For each p, we vary from