The Modern Call Center: A Multi- Disciplinary Perspective

24 Pages·2008·0.16 MB·English

PRODUCTION AND OPERATIONS MANAGEMENT POMS
Vol.16,No.6,November-December2007,pp.665–688 doi10.3401/poms.
issn1059-1478(cid:1)07(cid:1)1606(cid:1)665$1.25 ©2007ProductionandOperationsManagementSociety
The Modern Call Center: A Multi-
Disciplinary Perspective on Operations
Management Research
Zeynep Aksin (cid:127) Mor Armony (cid:127) Vijay Mehrotra
CollegeofAdministrativeSciencesandEconomics,KocUniversity,RumeliFeneriYolu,
34450Sariyer-Istanbul,Turkey
LeonardN.SternSchoolofBusiness,NewYorkUniversity,West4thStreet,KMC8–62,NewYork,
NewYork10012,USA
DepartmentofDecisionSciences,CollegeofBusiness,SanFranciscoStateUniversity,1600HollowayAvenue,
SanFrancisco,California94132-1722,USA
[email protected](cid:127)[email protected](cid:127)[email protected]
Call centers are an increasingly important part of today’s business world, employing millions of
agents across the globe and serving as a primary customer-facing channel for firms in many
different industries. Call centers have been a fertile area for operations management researchers in
several domains, including forecasting, capacity planning, queueing, and personnel scheduling. In
addition,astelecommunicationsandinformationtechnologyhaveadvancedoverthepastseveralyears,
the operational challenges faced by call center managers have become more complicated. Issues
associated with human resources management, sales, and marketing have also become increasingly
relevanttocallcenteroperationsandassociatedacademicresearch.
Inthispaper,weprovideasurveyoftherecentliteratureoncallcenteroperationsmanagement.Along
with traditional research areas, we pay special attention to new management challenges that have been
causedbyemergingtechnologies,tobehavioralissuesassociatedwithbothcallcenteragentsandcustomers,
andtotheinterfacebetweencallcenteroperationsandsalesandmarketing.Weidentifyahandfulofbroad
themesforfutureinvestigationwhilealsopointingoutseveralveryspecificresearchopportunities.
Keywords:callcenters;staffing;skill-basedrouting;personnelscheduling;outsourcing
SubmissionsandAcceptance:SubmissionsandAcceptance:ReceivedApril2007;revisionreceivedOctober
2007;acceptedOctober2007.
1. Introduction phone calls (also known as “agents”) typically com-
Virtually all businesses are interested in providing prising 60–80% of the overall operating budget. In-
informationandassistancetoexistingandprospective bound call centers may be physically housed across
customers.Inrecentyears,thedecreasedcostsoftele- several different locations, time zones, or countries.
communications and information technology have Inboundcallcentersmakeupalargeandgrowing
made it increasingly economical to consolidate such part of the global economy. Although reliable in-
informationdeliveryfunctions,whichledtotheemer- dustrystatisticsarenotoriouslyhardtocomeby,the
gence of groups that specialize in handling customer Incoming Call Management Institute (ICMI), a
phone calls. For the vast majority of these groups, highly reputable industry association, regularly
theirprimaryfunctionistoreceivetelephonecallsthat tracks published industry statistics from several
have been initiated by customers. Such operations, sources (www.incoming.com/statistics/demographics.
known as “inbound” call centers, are the primary aspx). By 2008, various studies cited by ICMI predict
topic of this paper. the following:
Inbound call centers are very labor-intensive oper- (cid:127) The United States will have over 47,000 call cen-
ations, with the cost of staff members who handle ters and 2.7 million agents.
665
Aksin,Armony,andMehrotra:TheModernCallCenter
666 ProductionandOperationsManagement16(6),pp.665–688,©2007ProductionandOperationsManagementSociety
(cid:127) Europe,theMiddleEast,andAfricatogetherwill that results in automatic callbacks to customers once
have 45,000 call centers and 2.1 million agents. an agent is available.
(cid:127) CanadaandLatinAmericawillhaveanestimated Also, as call centers now serve as the “public face”
305,500 and 730,000 agents, respectively. for many firms, there is increasing executive consid-
Meanwhile,thedemandforcallcenteragentsinIndia eration of their vital role in customer acquisition and
has grown so fast that the labor supply has been retention. Similarly, the managerial awareness of call
unable to keep up with it: by 2009, the demand for centers’ potential to generate significant incremental
agents in India is projected to be over 1 million, and revenue by augmenting service encounters with po-
more than 20% of those positions will be unfilled tential sales opportunities has also been growing rap-
because of a shortage of available skilled labor. idly: for example, a recent McKinsey study revealed
When a customer calls an inbound call center, var- thatcreditcardcompaniesgenerateupto25%ofnew
ious call handling and routing technologies will at- revenue from inbound call centers (Eichfeld, Morse,
tempttoroutethecalltoanavailableagent.However, and Scott 2006). However, for call center managers,
there is often no agent available to immediately an- there is significant additional complexity associated
swer the phone call, in which case the customer is
with managing this dual service-and-sales role with-
typically put on hold and placed in a queue. The
outcompromisingresponsetimes,servicequality,and
customer,inturn,mayabandonthequeuebyhanging
customer satisfaction.
up, either immediately after being placed on hold or
Finally, every call center manager is acutely aware
afterwaitingforsomeamountoftimewithoutreceiv-
that phone conversations between customers and
ing service. Once connected to an agent, a customer
agents are interactions between human beings. This
willspeakwiththatagentforsomerandomtime,after
suggeststhatthepsychologicalissuesassociatedwith
whicheitherthecallwillbecompletedorthecustomer
the agents’ experience can have a major impact on
will be “handed off” to another agent or queue for
both customer satisfaction and overall system perfor-
further assistance. The quality of the service is typi-
mance. Although these types of issues have been re-
cally viewed as a function of both how long the cus-
searched extensively by behavioral scientists, opera-
tomer must wait to receive service and the value that
tions management researchers have only recently
thecustomerattributestotheinformationandservice
begun to explicitly include such factors in richer ana-
that is received.
lytic models.
Call center managers are increasingly expected to
Given the size of the call center industry and the
deliver both low operating costs and high service
complexity associated with its operations, call centers
quality. To meet these potentially conflicting objec-
have emerged as a fertile ground for academic re-
tives, call center managers are challenged with de-
search.Arelativelyrecentsurveypaper(Gans,Koole,
ploying the right number of staff members with the
and Mandbelbaum 2003) cites 164 papers associated
right skills to the right schedules in order to meet an
with call center-related problems, and an expanded
uncertain, time-varying demand for service. Tradi-
on-line bibliography (Mandbelbaum 2004) includes
tionally, meeting this challenge has required call cen-
over450papersalongwithdozensofcasestudiesand
termanagerstowrestlewithclassicaloperationsman-
books. In addition, there have been several more spe-
agement decisions about forecasting traffic, acquiring
cializedsurveysassociatedwithcallcenteroperations,
capacity, deploying resources, and managing service
includingthatofKooleandMandelbaum(2002),who
delivery.
focusedonqueueingmodelsforcallcenters;L’Ecuyer
In recent years, the call center landscape has been
(2006),whofocusedonoptimizationproblemsforcall
altered by a wide variety of managerial and techno-
logical advances. Reduced information technology centers; and Koole and Pot (2006) and Aksin, Karaes-
and telecommunications costs—the same forces that men, and Ormeci (2007), who both focused on multi-
contributedsignificantlytothegrowthofthecallcen- skill call centers.
terindustry—havealsoledtorapiddisaggregationof Thissurveyseekstoprovideabroadperspectiveon
information-intensive activities (Apte and Mason bothtraditionalandemergingcallcentermanagement
1995). For call centers, this translated into increased challenges and the associated academic research. The
contractingofcallcenterservicestothirdparties(com- specific objectives and major contributions of this pa-
monly referred to as “outsourcing”) and the disper- per are as follows:
sion of service delivery to locations across the globe 1. To provide a survey of the academic literature
(“offshoring”).Inaddition,advancesintelecommuni- associated with traditional call center problem areas
cations technologies enabled richer call center work- such as forecasting, queueing, capacity planning, and
flow,includingincreasinglyintelligentroutingofcalls agent scheduling over the past few years;
across agents and physical sites, automated interac- 2. To identify several key emerging phenomenon
tionwithcustomerswhileonhold,andcallmessaging that affect call center managers and to catalog the
Aksin,Armony,andMehrotra:TheModernCallCenter
Production and Operations Management 16(6), pp. 665–688, © 2007 Production and Operations Management Society 667
academic research that has been done in response to cause of lead times for hiring and training agents.
these developments; Also, because most call centers have fairly high em-
3. Torecognizenewcallcenteroperationsmanage- ployee turnover and absenteeism levels, models that
ment paradigms that consider the role of the call cen- supportresourceacquisitiondecisionsmustexplicitly
ter in helping firms to attract, retain, and generate account for random attrition and absenteeism.
revenue from customers and to propose some impor- Resource deployment decisions are typically made
tant implications of these new paradigms on future 1ormoreweeksinadvanceofwhenthecallsactually
research; arrive. A cost-effective resource deployment plan at-
4. Tochronicleresearchonpsychologicalaspectsof temptstocloselymatchthesupplyofagentresources
call center agent experience, survey recent operations with the uncertain demand for services. The (highly
management papers that have incorporated some of variable) demand for resources is expressed in terms
these ideas into their modeling, and suggest ways in of call forecasts, which are typically composed of call
which such work can be incorporated into future op- arrival distributions and service time distributions,
erations management research; and both of which vary over time. This variability means
5. Tohighlightgapsinthecurrentliteratureoncall that both forecasting and queueing models play an
center operations management and opportunities ar- important role in modeling resource deployment de-
eas for future research. cisions. From a scheduling perspective, agents can
Theremainderofthepaperisorganizedasfollows.In typically be assigned to a range of shift patterns, and
Section 2, we survey recent work on traditional call the process of determining an optimal (or near-opti-
center operations management problems. Section 3 mal) schedule has a significant combinatorial com-
reviews research that considers demand modulation plexity.
as an alternative to supply side management. In Sec- In addition, as new data about forecasts and agent
tion4,welookattheresearchliteraturethatemerged availabilitybecomesavailableforagivendayorweek,
as a result of technology-driven innovations, includ- thisinformationcanbeusedtomodifyboththenear-
ing multi-site routing and pooling, the design of termcallarrivalforecastsandtheagentschedulesthat
multi-skill call centers, the blending of inbound calls are driven by them. Finally, as calls actually arrive,
with other types of workflow such as outbound calls there may be specific decisions to be made about
and emails, and increased call center outsourcing. In queuing policies or call routing.
Section 5, we examine several key human resources In this section, we begin our survey by looking at
issues that affect call centers and chronicle recent op- recent work on these call center operations manage-
erationsmanagementresearchthatsoughttoincorpo- mentproblems.WefocusoncallforecastinginSection
ratesomeofthesefactorsintotheirmodels.InSection 2.1, resource acquisition in Section 2.2, and perfor-
6,weexploreresearchthatintegratescallcenteroper- manceevaluation,staffing,scheduling,androutingin
ations with sales and marketing objectives, focusing Section 2.3. Next, we consider the basic problems of
on cross-selling and long-term customer relationship staffing, scheduling, and routing when arrival rates
management. In each of the above sections, we sug- arerandominSection2.4.Finally,Section2.5provides
gest specific opportunities for future research. Con- a brief overview of developments in performance
cluding comments are provided in Section 7. evaluation models for call centers, reflecting some of
the newer characteristics of modern call centers.
2. Managing Call Center Operations:
2.1. Call Forecasting
The Traditional View Call forecasts are defined by (a) the specific queue or
Traditionaloperationsmanagementchallengesforcall call type associated with the forecast; (b) the time
center managers include the determination of how between the creation of the forecast and the actual
many agents to hire at what times based on a long- time period for which the forecast was created (often
termforecastofdemandforservices(“resourceacqui- referred to as the forecasting “lead time”); and (c) the
sition”) and the scheduling of an available pool of duration of the time periods for which the forecasts
agentsforagiventimeperiodbasedondetailedshort- are created, which can range from monthly (to sup-
term forecasts for a given time period (“resource de- port resource acquisition decisions) to short time
ployment”). In addition, once initial resource deploy- frames,suchas15-,30-,or60-minuteperiods(tosup-
ment decisions have been made, there may be port resource deployment decisions). Over the years,
additional shorter-term decisions to be made, includ- there have been relatively few papers that focused on
ing forecast updating, schedule updating, and real- forecastingcallvolumes,promptingGansetal.(2003)
time call routing. toassertthatcallforecastingwas“stillinitsinfancy.”
Resource acquisition decisions must be made sev- However, in the past few years, there have been a
eral weeks and sometimes months ahead of time be- handful of important developments in the call fore-
Aksin,Armony,andMehrotra:TheModernCallCenter
668 ProductionandOperationsManagement16(6),pp.665–688,©2007ProductionandOperationsManagementSociety
casting field, driven by increased availability of his- sionality reduction, and their approach also decom-
torical databases of call volumes and by utilization poses predictive factors into inter- and intra-day fea-
and adaptation of new techniques that have been ap- tures. For the empirical cases presented, the
pliedtosimilarforecastingproblemsinotherapplica- methodology produces forecasts that are more accu-
tion areas. rate than both the (highly unsophisticated) standard
Weinberg,Brown,andStroud(2007)proposeamul- industry practice and the results from Weinberg,
tiplicativeeffectsmodelforforecastingPoissonarrival Brown, and Stroud (2007); the methodology is also
ratesforshortintervals,typically15,30,or60minutes significantly less computationally intensive than the
in length, with a 1-day lead time. In their setting, the Monte Carlo Markov chain methods of Weinberg,
callarrivalrateforagiventimeintervalofaparticular Brown, and Stroud (2007).
day of the week is modeled as the product of the Taylor(2007)presentsanempiricalstudythatcom-
forecasted volume for that day of the week and the pares the performance of a wide range of univariate
proportionofcallsthatarriveinthattimeintervalplus methods in forecasting call volumes for several UK
a random error term. To estimate the model’s param- bank call centers as well as for the Israeli bank call
eters, the authors adopt a Bayesian framework, pro- centerdatafromBrownetal.(2005),consideringlead
posing a set of prior distributions, and using a Monte times ranging from 1 day to 2 weeks. Taylor’s perfor-
CarloMarkovchainmodeltoestimatetheparameters mance comparison includes methods that have ap-
of the posterior distribution. pearedpreviouslyinthecallcenterliterature,suchas
Although computationally intensive, the methodol- seasonal Auto Regressive Moving Average modeling
ogyproposedbyWeinberg,Brown,andStroud(2007) (Andrews and Cunningham 1995) and dynamic har-
is quite valuable from an operational perspective. In monic regression (Tych et al. 2002), as well as several
particular, because the model produces forecasts of other models that have not previously been used for
Poisson arrival rates on an intra-day interval basis, call center forecasting. The latter group includes an
these results can be used in conjunction with perfor- exponential smoothing model for double seasonality
mance models and agent scheduling algorithms. In that was originally developed for forecasting short-
addition, the authors propose a modification of this term electric utility demand (Taylor 2003); a periodic
method to allow for intra-day forecast updating, AutoRegressivemodel;andamodelbasedonrobust
which can in turn be used to support intra-day agent exponentialsmoothingbasedonexponentiallyweighted
schedule updating. The paper includes a forecasting least absolute deviations (Cipra 1992). The empirical
casestudyinwhichdatafromalargeNorthAmerican comparisonshowednoclear“winner,”becausediffer-
commercialbank’scallcentersareusedtotestboththe entmethodsprovedtobemoreeffectiveunderdiffer-
1-day-ahead forecasts and intra-day forecast updates, ent lead times and different workloads.
with very promising results.
Soyer and Tarimcilar (2007) introduce a new meth- 2.2. Personnel Planning: Resource Acquisition
odology for call forecasting that draws on ideas from The call center resource acquisition problem has been
survival analysis and marketing models of customer studied by a handful of researchers. Gans and Zhou
heterogeneity. Specifically, this paper models call ar- (2002) model a process in which agents are hired and
rivals as a modulated Poisson process, where the ar- experiencebothlearningandattritionovertime,dem-
rival rates are driven by advertisements that are in- onstrating that a threshold policy for hiring agents is
tended to stimulate customers to contact the call optimalintheirsetting.Ahn,Righter,andShanthiku-
center.Theparametersforthecallintensityassociated mar (2005) look at a general class of service systems
witheachparticulartypeofadvertisementandfuture anddemonstratethatundertheassumptionofcontin-
time interval are modeled by a Bayesian framework, uous number of agents who can be hired and fired at
usingaGibbssampler(DellaportesandSmith1993)to will, the optimal policy is of a “hire-up-to/fire-
approximate the posterior distributions. The authors down-to”form.Bordoloi(2004)combinescontrolthe-
also test their methodology by conducting numerical ory and chance-constrained programming techniques
experimentsusingcallvolumedatafromacallcenter to derive steady-state workforce levels for different
for which all calls can be traced directly to specific knowledge groups and a hiring strategy to achieve
advertisements, with the forecasts being created for these targets. Bhandari, Harchol-Balter, and Scheller-
single- and multi-day time periods. Wolf (2007) consider both the hiring of regular work-
Shen and Huang (2007) develop a statistical model ers and the contracting of part-time workers along
forforecastingcallvolumesforeachintervalofagiven with the operational problem of determining how
day and also provide an extension of their core mod- many part-time workers to deploy under different
eling framework to account for intraday forecast up- load conditions. Ryder, Ross, and Musacchio (2008)
dating. Their model is based on the use of singular examine the impact of different routing strategies on
value decomposition to achieve a substantial dimen- employee learning in a multi-skill environment in an
Aksin,Armony,andMehrotra:TheModernCallCenter
Production and Operations Management 16(6), pp. 665–688, © 2007 Production and Operations Management Society 669
attempt to understand the connection between rout- itsparametersisanalyzedbyWhitt(2006c),whereitis
ing, learning, and overall staffing needs. demonstrated that performance is relatively insensi-
Given the importance of the resource acquisition tive to small changes in abandonment rates.
decision, there is significant need for additional re- Formostinboundcallcenters,themanagementob-
search in this area, including models for long-term jective is to achieve relatively short mean waiting
forecasting,personnelplanningforgeneralmulti-skill timesandrelativelyhighagentutilizationrates.Gans
call centers, and resource acquisition planning for in- etal.(2003)refertosuchanenvironmentasa“Quality
creasingly complex networks of service providers (as andEfficiencyDriven”regime.Inthiscontext,letRbe
described by Keblis and Chen 2006, for example). the system-offered load measured in terms of the
meanarrivalratetimesandthemeanservicetime.The
2.3. Personnel Planning: Staffing, Scheduling,
so-called “square-root safety-staffing rule” stipulates
and Routing
thatifRislargeenoughthenstaffingthesystemwith
The traditional approach to call center resource de- R(cid:1)(cid:1)(cid:2)Rservers(forsomeparameter(cid:1))willachieve
ployment decisions is to attempt to build an agent
both short customer waiting times and high server
schedule that minimizes costs while achieving some
utilization.
customer waiting time distribution objectives. As
This rule was first observed by Erlang (1948) and
such, targeted staffing levels for each period of the
was later formalized by Halfin and Whitt (1981) for
scheduling horizon are typically key inputs to the
the Erlang-C model (i.e., an M/M/s queue). Its prac-
scheduling and rostering problems. These targets de-
tical accuracy was tested for service systems by Kole-
pendonbothhowmuchworkisarrivingintothecall
sarandGreen(1998).Thisrulewasfurthersupported
center at what times (as estimated by the call volume
by Borst, Mandelbaum, and Reiman (2004) and Mag-
forecasts and the forecasted mean service times) and
laras and Zeevi (2003) under various economic con-
how quickly the call center seeks to serve these cus-
siderations. This rule has since been demonstrated to
tomers (estimated by some function of the customer
be robust with respect to model assumptions such as
waiting time distribution). Once the forecasts and
customer abandonment (Garnett, Mandelbaum, and
waiting time goals have been established, queueing
Reiman 2002; Zeltyn and Mandelbaum 2005), an in-
performanceevaluationmodelsareusedtodetermine
boundcallcenterwithacall-backoption(Armonyand
the targeted number of service resources to be de-
Maglaras 2004a,b), and call centers with multiple
ployed. The actual performance obtained from the
queues and agent skills (Gurvich, Armony and Man-
deployed resources also depends on the operational
delbaum 2006, Armony and Mandelbaum 2004),
problemofallocatingincomingcallstotheseresources
which will be discussed in more detail below.
dynamically, known as the call routing problem. Our
Borst, Mandelbaum, and Reiman (2004) have also
reviewfollowsthesamehierarchicalorderthatwould
identified two other operating regimes: the quality
be followed in the resource deployment problem for
driven and the efficiency driven (ED) regimes, which
call centers: we first review staffing problems, then
are rational operating regimes under certain costs
provide an overview of scheduling and rostering
structures. In the ED regime server utilization is em-
problems, and finally demonstrate how the call rout-
phasized over service quality; however, with cus-
ing problem interacts with them.
tomer abandonment, this regime can also result in
2.3.1. Staffing Problems. Simulation models and reasonable performance as measured by expected
analytic queueing models are the two alternatives to waiting time and fraction of customer abandonment
performance evaluation. Mehrotra and Fama (2003) (Whitt 2004b). Whitt has proposed fluid models for
providesanoverviewoftheinputsrequiredforbuild- system approximation under the ED regime (Whitt
ing a call center simulation model, while Koole and 2006a,b) and has shown its applicability in staffing
Mandelbaum (2002), and Mandelbaum and Zeltyn decisions under uncertain arrival rate and agent ab-
(2006) are good sources for a detailed overview of senteeism.
queueing models of call centers. Most of the early literature on staffing deals with
The simplest queueing model of a call center is the these problems in settings with a single pool of ho-
M/M/s queue, also known as an Erlang-C system. mogenous agents (see references in Gans et al. 2003;
This model ignores blocking and customer abandon- Garnett, Mandelbaum, and Reiman 2002; Borst, Man-
ments. The Erlang-B system incorporates blocking of delbaum, and Reiman 2004; Atlason, Epelman, and
customers. The Erlang-C model is further developed Henderson 2004; and Massey and Wallace 2006). Re-
to incorporate customer impatience in the Erlang-A cent literature on staffing models focuses on multi-
system (Garnett, Mandelbaum, and Reiman 2002). skill settings, that is, in call centers where calls of
Performance measures and approximations for the different types are served using service representa-
Erlang-A system are discussed by Mandelbaum and tives with different skills (Pot, Bhulai, Koole, 2007;
Zeltyn(2007b).Sensitivityofthismodeltochangesin Bhulai, Koole, and Pot, 2007; Cezik and L’Ecuyer,
Aksin,Armony,andMehrotra:TheModernCallCenter
670 ProductionandOperationsManagement16(6),pp.665–688,©2007ProductionandOperationsManagementSociety
2006; Chevalier and Van den Schrieck, 2006; Harrison queue of call arrivals and a homogeneous pool of
and Zeevi, 2004, Wallace and Whitt, 2005, Armony, agents,eachwithseveralpossibleshiftandbreakcom-
2005, Bassamboo, Harrison, and Zeevi 2005, 2006). A binations and associated restrictions, the size of the
different setting with homogeneous agents serving mathematicalprogramgrowsveryrapidly.Thisissue
variouscustomertypestowhomdifferentiatedservice is addressed by several researchers, most notably
is provided is analyzed by Gurvich, Armony, and Aykin (1996, 2000), who models flexible break con-
Mandelbaum (2006). Aksin, Karaesmen, and Ormeci straints for each shift and tests the proposed method-
(2007),KooleandPot(2006),andL’Ecuyer(2006)sur- ology with several large test problems.
veyrecentresearchonmulti-skillcallcenterproblems. Anotherproblemwiththetraditionalmathematical
Typically staffing formulations seek to determine programming approach is that it requires as input a
thenumberoffull-timeequivalentemployeesneeded target agent staffing level for each time interval. This
givenanobjectivefunctionandsomeconstraints.The concept of target staffing level is in turn based on the
most widely used is a staffing cost minimization ob- assumption that all agents are able to handle all in-
jectivewithservicelevelconstraints(see,forexample, coming calls. However, in a multi-queue/multi-skill
Atlason, Epelman, and Henderson 2004; Cezik and environment, this assumption is clearly violated, and
L’Ecuyer,2006;Bhulai,Koole,andPot2007;Jagerman much of the work in recent years has sought to ad-
and Melamed, 2004; Mandelbaum and Zeltyn 2007a), dressthisspecificshortcomingofthetraditionalmeth-
although staffing problems with profit maximization odology. Fukunaga et al. (2002) propose a hybrid
methodthatcombinesschedulingheuristicswithsim-
objectives have also been proposed (Aksin and
ulation to simultaneously solve both the scheduling
Harker, 2003; Koole and Pot, 2005; Helber, Stolletz,
and the rostering problem and discuss a commercial
and Bothe 2005; Baron and Milner, 2006). Armony et
implementation of this method that is used by over
al. (2007) establish convexity properties and compar-
1,000callcenterstoday.Similarly,CezikandL’Ecuyer
ative statics for an M/M/s queue with impatience,
(2006) propose a methodology that combines linear
demonstrating the relationship between abandon-
programming with simulation to determine a sched-
ments and optimal staffing. Koole and Pot (2005a)
ule. Avramidis et al. (2007) develop search methods
showthattheseconvexitypropertiesfailtoholdwhen
that use queueing performance approximations to
thebuffersizeisalsoadecisionvariable.Canonetal.
produce agent schedules for a multi-skill call center.
(2005)formulatethestaffingproblemasadeterminis-
Anotherstreamofresearchintheareaofcallcenter
tic scheduling problem.
scheduling focuses on eliminating approximations
2.3.2. Shift Scheduling and Rostering. Taking
thatresultfromthetraditionalseparationbetweenthe
the results from the staffing problem as inputs, typi-
staffingandtheschedulingproblemsdescribedabove.
cally on an interval-by-interval basis, the shift sched-
Motivated by the dependency of adjacent time inter-
uling problem determines an optimal collection of
vals’ waiting time distributions, which is ignored by
shifts to be worked, seeking to minimize costs while
traditional scheduling algorithms, Atlason, Epelman,
achieving service levels or other labor requirements.
andHenderson(2004)usesubgradientinformationfor
Closely related to the scheduling problem, the roster-
the objective function along with simulation in order
ingproblemcombinesshiftsintorostersandprovides
to determine agent schedules. In a similar spirit, not-
the actual matching between employees and rosters.
ing traditional methods assume that service level
The scheduling problem and the rostering problem
goals are “hard constraints” that must be met during
have been studied extensively, both in the context of each interval, Koole and van der Sluis (2003) instead
call centers (see references in Gans et al. 2003) and in developaschedulingmethodologythatseekstomeet
moregeneralcontexts(Ernstetal.2004chroniclesover only an overall service level objective over the course
700papersonthesetopics).Inthissection,ratherthan of an entire scheduling period (typically a day or a
attempt an extensive survey of the scheduling and week).Ingolfsson,Cabral,andWu(2003)notethatthe
rosteringliterature,weinsteaddescribeseveraldiffer- traditional staffing methods use steady-state staffing
entapproachestotheseproblems,alongwithillustra- models for individual intervals and seek to eliminate
tive recent papers and some fruitful directions for errors induced by this approximation by using tran-
future research. sient results on a period-by-period basis, which they
Thetraditionalapproachtotheschedulingproblem refer to as the “randomization method,” along with
is to formulate and solve a mathematical program to integerprogrammingtocreateagentschedules.Moti-
identify a minimum cost schedule. Although variants vated by the potential impact of understaffing on call
ofthisapproachhavebeenwidelyutilized,bothinthe abandonment, Saltzman (2005) and Saltzman and
researchliteratureandinindustrialapplications,over Mehrotra (2007) develop and test a scheduling meth-
theyearsseveralissueshavealsobeenidentifiedwith odology that combines linear programming, tabu
this basic method. For large call centers with a single search, and simulation while including costs to staff,
Aksin,Armony,andMehrotra:TheModernCallCenter
Production and Operations Management 16(6), pp. 665–688, © 2007 Production and Operations Management Society 671
waiting times, and abandoned calls in the objective andKooleandPot(2006),andfurtherinteractwiththe
function. flexibility design problem (Aksin and Karaesmen
The separation of shift scheduling from the actual 2003; Aksin, Karaesmen, and Ormeci 2007). The hier-
rostering process presents another potential problem archical dependency, as well as the close interaction
with the traditional approach. In practice, the mis- between staffing and routing, make these problems
match between the (ideal) optimal shifts and the (ac- challenging from an operations research perspective
tual) assignment of shifts to individual agents can (Cezik and L’Ecuyer 2006; Harrison and Zeevi 2005;
have a major negative impact on the overall perfor- ArmonyandMaglaras2004a,WallaceandWhitt2005;
mance of the call center, and this impact is often Bhulai, Koole, and Pot 2007; Gurvich, Armony, and
exacerbatedbyupdatestocallforecastsandschedules Mandelbaum 2006, Bassamboo, Harrison, and Zeevi
thatresultfromnewinformationbeingobtainedafter 2006; Chevalier and Van den Schrieck 2006). Even
the initial schedule has been created. Because of the when treated in isolation and ignoring important in-
complexity associated with the coordination of indi- terdependencies, obtaining optimal solutions poses a
vidual agents’ preferences and restrictions, many challenge. Deterministic linear programming, diffu-
large call centers and multi-site call center operations sion, or fluid approximations have been proposed to
require agents to “bid” on particular shifts sequen- overcomethisprobleminlarge-scalecenters(Armony
tially,withtheorderofbiddingbasedonfactorssuch and Maglaras 2004a,b; Armony and Mandelbaum
asseniorityandpreviousqualityofservicedelivered. 2004;HarrisonandZeevi2004,2005;Bassamboo,Har-
rison, and Zeevi 2006; Whitt 2006a,b; Tezcan and Dai
Building on this practice (known in the call center
2006;GurvichandWhitt2007).Otherpapersusesim-
industry as “shift bidding”), Keblis, Li, and Stein
ulation in combination with optimization (Atlason,
(2007) investigate an auction-based approach to the
Epelman,andHenderson2003;Atlason,Epelman,and
problemofmatchinglaborsupplywithlabordemand
Henderson 2004; Cezik and L’Ecuyer 2006), loss sys-
in a call center, allowing agents to bid competitively
tem, or other approximations (Koole and Talim, 2000,
for different shifts. In particular, this type of bidding
Chevalier and Tabordon, 2003; Koole, Pot, and Talim
mechanismsuggestsamethodforpricingservicesfor
2003; Shumsky 2004; Chevalier, Shumsky, and Tabor-
part-time “work at home” agents, while also facilitat-
don2004;KooleandPot2005b;ChevalierandVanden
ing real-time schedule adjustments as a result of up-
Schrieck 2006; Franx, Koole, and Pot 2006; Avramidis
dated call forecasts. The issue of real-time schedule
et al. 2006) to enable analysis.
adjustments in service operations has also been ad-
dressedbyHur,Mabert,andBretthauer(2004),Easton Despitethelargenumberofpapersdiscussedinthis
and Goodale (2005), and Mehrotra, Ozluk, and Saltz- section, we believe that there are significant research
man (2006). opportunities with these classical problems. In partic-
ular, capturing more of the dependency and interac-
2.3.3. The Call Routing Problem. The routing
tion among staffing, scheduling, and routing is a
problem is a control problem that involves assigning
promising direction for further research.
incomingcallstospecificagentsorpoolsofagentsand
thenschedulingcallswhenseveralarewaitingforthe
2.4. Personnel Planning under Arrival Rate
same agent pool. This problem has attracted a lot of
Uncertainty
attention as a call center application and more gener-
Historically, most of the papers in the call center lit-
ally as a challenging queueing control problem (Or-
eraturehavemodeledthearrivalprocesstobeatime-
meci,Burnetas,andEmmons2002;Ormeci,2004;Gans inhomogeneousPoissonprocessand,thus,forecasting
and Zhou, 2003; Koole, Pot, and Talim 2003; Atar, call volumes is in most cases (implicitly or explicitly)
Mandelbaum, and Reiman 2004a,b; Mandelbaum and equivalent to estimating the time-dependent Poisson
Stolyar, 2004; Harrison and Zeevi, 2004b; Armony, arrival rates. This assumption is in many cases quite
2005;deVericourtandZhou,2006;Bhulai,2005;Koole reasonable. For example, Brown et al. (2005) con-
and Pot, 2006; Bassamboo, Harrison, and Zeevi 2005; ducted an extensive empirical study of historical data
Tezcan, 2005; Atar, 2005a, 2005b; Jouini et al. 2006, from an Israeli bank’s call center operations and con-
Tezcan and Dai, 2006, Gurvich and Whitt, 2007). clusively failed to reject the hypothesis that the call
The problems of staffing, scheduling, and routing arrivals follow a time-inhomogeneous Poisson pro-
exhibit hierarchical dependency. The call routing cess;however,inthesamestudy,afterusingcalltype,
problem in multi-skill call centers is also known as time of day, and day of week to build an empirical
skills-based routing. In multi-skill settings, how well model to forecast the call arrival rates for short time
calls are routed determines the effectiveness of staff intervals, the authors concluded that the Poisson ar-
usage, while the staffing problem constrains the rout- rival rates are not easily predictable.
ingdecision.Theseproblemsinteract,asexplainedvia Because of the difficulty of accurately forecasting
examples in Aksin, Karaesmen, and Ormeci (2007) callarrivalrates,severalresearchershaveexploredthe
Aksin,Armony,andMehrotra:TheModernCallCenter
672 ProductionandOperationsManagement16(6),pp.665–688,©2007ProductionandOperationsManagementSociety
implications of modeling call arrivals with a random a need for research into additional performance anal-
arrival rate. Whitt (1999b) suggests a particular form ysis models under different arrival rate variability
of a random arrival rate for capturing forecast uncer- assumptions, as well as for more validation of such
tainty. Chen and Henderson (2001), Avramidis, assumptions with operational data. Second, reconsid-
Deslauriers, and L’Ecuyer (2004), Brown et al. (2005), ering the scheduling and rostering problems under
and Steckley, Henderson, and Mehrotra (2005) point the more general assumption that arrival rates are
out the randomness of arrivals in real call centers, a random variables is another very promising area that
featurethatisignoredinmostoftheliterature.Steck- is just now beginning to receive attention from re-
ley, Henderson, and Mehrotra (2005), Harrison and searchers. For example, Robbins and Harrison (2007)
Zeevi (2005), Robbins et al. (2006), and Torzhkov and view arrival rate variability as a fundamental compo-
Armony(2007)analyzecallcenterperformanceunder nent of the agent scheduling problem and propose a
randomarrivals.Thompson(1999)andJongbloedand stochasticprogrammingsolutiontodeterminethebest
Koole (2001) provide methods for determining target combination of agents and shifts that explicitly ac-
staffing when the arrival rate is random. Ross (2001, counts for the risk inherent in the arrival rate uncer-
Chapter4)offersextensionstothesquare-rootstaffing tainty.
ruletoaccountforarandomarrivalrate.Robbinsetal.
(2007)considerthequestionofcross-trainingasubset 2.5. Performance Evaluation for Modern
ofagentsfromdifferentqueuestomeetdemandinthe Call Centers
presence of uncertain arrival rates. Other recent pa- As call centers have evolved in terms of size and
pers that focus on planning problems in the presence configuration, and as more empirical analysis has
of random arrivals are those by Steckley, Henderson, shed light on the features of typical queueing model
andMehrotra(2007),Whitt(2006e),BaronandMilner primitives like arrivals, abandonment, and service
(2006), Bassamboo and Zeevi (2007), and Aldor- times in these centers, new performance evaluation
Noiman (2006). models have been developed and analyzed. These
Another traditional call center modeling assump- modelsaremotivatedbydifferentfeaturesofmodern
tionisthatthearrivalsduringonetimeperiodwithin callcenters,aswellasempiricallyobservedcharacter-
a planning horizon are independent of the arrivals in isticsofqueueingmodelprimitives.Thelatteranalysis
the other time periods for purposes of determining hasbeeninitiatedbyaresearchcollaborationbetween
staffing levels and agent schedules. Green, Kolesar, researchers at The Technion and The Wharton School
and Soares (2001, 2003) have dubbed this the station- that has provided a clean source of customer call-
ary, independent, period by period method. However, basedcallcenterdatafromseveralsources,whichhas
several empirical studies have demonstrated that for subsequently been developed into a complete plat-
manycallcentersthereissignificantcorrelationincall form for data-based analysis of call center problems
volumes across time periods. Brown et al. (2005) de- (a description of the DataMOCCA Project can be
velop a non-linear least squares model in which a obtained from http://iew3.technion.ac.il/serveng/
previousday’scallvolumeisanindependentvariable References/DataMOCCA). The important distinction
in predicting the subsequent day’s call volume, pro- of the data provided in this project is that unlike
ducing roughly a 50% reduction in the variability of typical call center data that averages data over time
the forecasted daily volumes. Motivated by empirical intervals, these data are on a per-call basis, thus en-
analysis of a large telecommunication firm’s call cen- ablingdeeperanalysisaswellasamorenaturaltieto
tersthatdemonstratesbothgreater-than-Poissonvari- marketing- or human resource-related analyses. Fur-
ability and strong correlation across time periods ther use of this type of data to explore the links be-
within the same day, Avramidis, Deslauriers, and tween call center operational problems and human
L’Ecuyer(2004)developandtestseveralanalyticmod- resource and customer related issues is a promising
elsinwhichthearrivalrateforeachintervaloftheday direction for future research.
isarandomvariablethatiscorrelatedwiththearrival Large call centers have motivated the analysis of
rates of the other intervals. Steckley, Henderson, and heavytrafficlimitsasusefulapproximationsofqueue-
Mehrotra(2005)analyzedatafromseveralcallcenters ing models (see, for example, Halfin and Whitt 1981,
andidentifysignificantcross-periodcorrelationincall Garnett, Mandelbaum, and Reiman 2002, Jennings et
volumes;motivatedbytheseresults,Mehrotra,Ozluk, al.1996,Whitt2004a,b).Motivatedbyrecentempirical
and Saltzman (2006) present a framework for intra- studies demonstrating that service times and aban-
day forecast and schedule updating that utilizes the donment times are not necessarily exponentially dis-
call arrival model of Whitt (1999b) to model cross- tributed (Mandelbaum, Sakov, and Zeltyn 2000;
period correlation. Brown et al. 2005), models with general service times
Webelievethatthispointstoatleasttwointeresting and general abandonment times have been analyzed
andimportantareasforfutureresearch.First,thereis and approximations for their performance developed
Aksin,Armony,andMehrotra:TheModernCallCenter
Production and Operations Management 16(6), pp. 665–688, © 2007 Production and Operations Management Society 673
(Whitt2004b,2005,2006c;Reed2005,ZeltynandMan- tion is also used to reduce operating costs by encour-
delbaum 2005, Jelenkovic, Mandelbaum, and Mom- agingcallerstoobtainservicethroughotherchannels,
cilovic 2004, Mandelbaum and Momcilovic 2007, such as the Internet, that are more scalable or less
Gamarnik and Momcilovic 2007, Kaspi and Ramanan expensive.
2007).MandelbaumandZeltyn(2004)explorealinear Thesimplestformofdemandmodulationthatmay
relationship between the probability to abandon and be used in call centers is call admissions. The most
the waiting time in queue in an Erlang-A model. Al- primitive form of call admission is a busy signal that
thoughsuchlinearityshouldnotexistinthepresence customers encounter every time all lines are busy.
of general impatience distributions, empirical evi- Given costs of infrastructure, such busy signals are
dence by Brown et al. (2005) suggests a similar linear very rare in medium to large call centers and non-
relationship. Mandelbaum and Zeltyn (2004) analyze bursty call volume. A more sophisticated form of call
the problem both theoretically and empirically and admission can be done by selectively admitting calls
demonstratethat,overrealisticparametervalues,gen- accordingtotheirrelativeimportancetotheorganiza-
eral impatience distributions result in performance tion(Ormeci,2004).Thispracticeisalsoveryunusual
that resembles the Erlang-A model. This is an impor- incallcenters.Bassamboo,Harrison,andZeevi(2006)
demonstrate that under some circumstances it is
tant result, supporting the robustness of the Erlang-A
beneficial not to admit less profitable customers so
model, even in settings with non-exponential impa-
astoreducethechancesoflosingmoreprofitableones
tience times. Similarly, as reviewed in more detail in
later on.
Section2.4,Steckley,Henderson,andMehrotra(2005),
Regardlessofwhetheracallcenterregulatesitscalls
HarrisonandZeevi(2005)andTorzhkovandArmony
through an admission control mechanism, one fact
(2007) analyze call center performance under random
that call center managers must face is that callers are
arrivals.
inherently impatient. If a customer call is not an-
Blocked or abandoned calls may redial later, which
swered within a certain time, the customer will hang
isafeatureignoredinmostmodels.Thistypeofretrial
up(abandon)andsubsequentlymayeitherretrylater
behavioranditsinfluenceonperformanceismodeled
or not. Generally, call center managers strive to min-
by Mandelbaum et al. (1999) and Aguir et al. (2004).
imize the number of abandonments, because of the
Approximations, in particular a fluid approximation,
premisethatabandonmentsareassociatedwithaneg-
perform very well for such systems. The use of fluid
ative waiting experience and might lead to loss of
approximations in the presence of time-varying pa-
goodwillandeventochurn.However,abandonments
rametersisalsosupportedbyRidley,Fu,andMassey
alsohaveapositivecomponentassociatedwiththem,
(2003) and Jimenez and Koole (2004). The need to
because they provide a natural mechanism for load
managemulti-skillcallcentershasledtoperformance
balancing. To wit, when the system is heavily loaded
evaluation models for systems with flexible servers
impatient customers tend to abandon, alleviating the
(ChevalierandTabordon2003;Shumsky2004;Stolletz
workload and hence shortening the waiting times of
and Helber 2004; Whitt 2006a; Franx, Koole, and Pot
the more patient callers.
2006).
Because of the importance of abandonment in de-
We believe that performance evaluation will con-
termining staffing levels, there has been a stream of
tinuetoprovideresearchopportunities,particularlyin
literature that focuses on understanding customer
light of the developments described in Sections 3 and
abandonment (Hassin and Haviv 1995; Mandelbaum
4 below.
and Shimkin 2000; Zohar, Mandelbaum, and Shimkin
2002; Shimkin and Mandelbaum 2004) and its impact
3. Demand Modulation
on system performance (Garnett, Mandelbaum, and
Many call centers face highly unpredictable demand Reiman 2002; Mandelbaum and Zeltyn 2004; Zeltyn
that is also time-varying. The time-varying element is and Mandelbaum 2005; Armony, Plambeck, and Se-
relatively easy to handle by adjusting staffing levels. shadri2007;MandelbaumandZeltyn2006;Baronand
PapersbyJenningsetal.(1996),Massey(2002),Ridley, Milner 2006; Mandelbaum and Zeltyn 2007b).
Fu, and Massey (2003), Feldman et al. (2005), and Acknowledging that overloaded situations and
Green, Kolesar, and Whitt (2007) are examples of pa- abandonmentswillalwaysexist,researchershavepro-
pers that consider the staffing problem under time- posed that notifying callers of their anticipated delay
varying demand. But when call volume is unpredict- as soon as they call would cause impatient customers
able,limitedflexibilityinadjustingstaffinglevelsmay to leave right away (balk), whereas the more patient
lead to situations of over- or under-staffing, at least customers are likely to wait until their call is an-
temporarily. This section deals with means of modu- swered.Whitt(1999a)hasdemonstratedthattheover-
lating demand as a way of ensuring load balancing allaveragewaitingtimeofallcustomersisreducedif
and higher level of predictability. Demand modula- delay announcement is accurate. Guo and Zipkin
Aksin,Armony,andMehrotra:TheModernCallCenter
674 ProductionandOperationsManagement16(6),pp.665–688,©2007ProductionandOperationsManagementSociety
(2006, 2007a) have identified cases in which informa- tive service channel when the system is overloaded.
tion improves performance, but have also demon- SuchanalternativechannelcouldbeaWebsiteoran
strated that such information can actually hurt the e-mailservicerequest,butcouldalsocomeintheform
service providers or the customers under exponential ofsuggestingtothecustomertocallatalessbusytime
service time and more general phase-type distribu- ortoleaveanumberandbecalledbacklater.Armony
tions. Guo and Zipkin (2007b) noted that the effect of and Maglaras (2004a,b) propose a model in which
informationontotalthroughputdependsontheshape callersaregivenachoiceofwhethertowaitonlinefor
of the distribution describing the customers’ sensitiv- their call to be answered or to leave a number and be
itytodelay.Intheiranalysis,GuoandZipkincompare called back within a specified time. They show that
asystemwithdelayinformationtoasysteminwhich this call-back scheme allows the system to both in-
the decision on whether to join the queue is based on crease throughput and reduce average waiting times.
expected steady-state delay equilibrium. This equilib- Most call center papers consider the call volume to
rium analysis is similar to the approach taken by be an exogenous factor, an external stream of calls.
Whitt (2003), where it is assumed that the balking However,manycallsareinfactredialsofcallerswho
decisionisbasedonexpectedsteady-statedelayequi- havebeenblocked(busysignal)orabandonedorhave
librium, and it is demonstrated how the demand not had their call resolved. A generic name for such
scales with respect to the number of servers. Jouini calls is retrials. Recognizing the significance of call
and Dallery (2006) consider how to estimate callers’ resolutiononoverallcustomersatisfactionandonthe
waiting time and what information to announce to system load, many call centers include in their com-
callers in a multiple-customer setting with a fixed pensationschemestotheircustomerservicerepresen-
prioritysequencingrule.Theabovepapersallassume tatives (CSRs) a number-of-resolved-calls component.
that if a customer has decided to stay given the an- Forexample,deVericourtandZhou(2005)considera
nounced information, he will subsequently remain in system in which agents differ with respect to two
the system until his service ends. quality dimensions: service speed (rate (cid:2)) and proba-
Giventhatdelayannouncementsinastochasticen- bilityofcallresolution(p).Acallerwhosecallhasnot
vironmentareinevitablyinaccurate,itisplausiblethat beenresolvedwillcallthecenteragainwiththesame
callers may abandon the system even if initially they concern. In this paper, the authors consider the prob-
decided to stay and wait for their service. Armony, lem of routing calls to CSRs to minimize the total
Shimkin, and Whitt (2006) propose a model in which number of calls in the system. They show that the
callersmaybalkinresponsetoadelayannouncement, routing policy that routes calls to the CSR with the
but provided they do not balk their time-to-abandon highest product p(cid:2) is optimal under certain condi-
distributionisalsodependentonthesameannounce- tions. Armony (2007) considers this problem for a
ment.Armony,Shimkin,andWhitt(2006)proposesas system with many servers (who are grouped in mul-
a delay announcement scheme the delay of the last tiple pools consistent with their service rate and call
caller to enter service, which is numerically shown to resolution probability) and demonstrates that the
be very accurate in large overloaded systems. A same p(cid:2)policy is asymptotically optimal in the sense
closelyrelatedschemeofannouncingthedelayofthe that it minimizes the queue length and waiting times
first customer in line has been proposed by Nakibly in steady state. Mehrotra, Ross, and Zhou (2007) con-
(2002).SimilartoArmony,Shimkin,andWhitt(2006), sider such an environment with multiple pools of
in a single class setting, Jouini, Dallery, and Aksin agentsandmultipleclassesofcustomersandexamine
(2007b) consider a model where customers are al- several routing policies in an attempt to simulta-
lowed to abandon subsequent to delay announce- neously maximize call resolution rates and minimize
ments.Thepossibilityofannouncingdifferentpercen- customer waiting times.
tiles of the delay distribution is proposed and the Aguir et al. (2004) consider how retrials impact the
relationshipbetweenperformanceandannouncement performance of call centers. They propose a fluid
precision is explored. The paper demonstrates that model to approximate the queue length process,
announcements with higher precision are not univer- which tends to be accurate for large overloaded sys-
sally preferred. Finally, in the context of delay an- tems.Usingnumericalanalysistheydemonstratethat
nouncement in call centers Jouini, Dallery, and Aksin erroneously considering retrials first-time calls can
(2007a) published the first paper to model delay an- lead to very significant distortions in forecasting and
nouncement in a multiple-customer class setting with staffing decisions. In a subsequent paper, Aguir et al.
priorities. In this setting, future arrivals to the higher (2007)demonstratethat,surprisingly,ignoringretrials
priorityclassmayincreasethedelayoflowerpriority byconsideringthemfirst-timecallscanleadtounder-
callers. or over-staffing with respect to the optimal staffing
In addition to abandonment, load balancing can level, depending on the forecasting assumptions.
alsobedonebyencouragingcallerstouseanalterna- Ourdiscussionthusfarwithrespecttoloadbalanc-