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Bouzada, Marco Aurlio C.B.:Dimensioning a Call Center: Simulation or Queue Theory?Journal of Operations and Supply Chain Management 2 (2), pp 34 - 46, C International Conference of the Production and Operations Management Society 35

obtained by analytical methods, but they are usuallyprey close to them. The precept of the Simulationsays that it is beer to have a rough solution fora very realistic model than an exact solution for amodel with several approximations.

As studied by Mehrotra and Fama (2003), and Halland Anton (1998), the call centers are interesting ob-jects for the simulation studies, because: (i) they copewith more than one type of call, where each typerepresents a line; (ii) the calls received in each linearrive by chance as time goes by; (iii) in a few cas-es, agents make calls proactively (especially in tele-marketing or charging calls), or as a return for a callreceived; (iv) the duration of each call is random, aswell as the work that the agent executes aer the call(collecting of data, documentation, research...); (v)the progress on the systems which route the calls for

the agents, groups or locals, make the logics behindthe call center even more sophisticated; (vi) agentscan be trained to answer only one type of call, sev-eral types of calls or all types of calls with dierentpriorities and preferences specied for the routinglogics; and (vii) the great amount of money investedin call centers, on both forms, capital and work, iscapable to justify the use of this so powerful tool.

Thus, this paper intends to describe the handling ca-pacity dimensioning maer of a large brazilian callcenters company in order to approach it using analternative methodology: the Simulation. The objec-tive is to use the case of the highlighted company asan empirical scenario for the theoretical discussionon the adequateness of experimental methods (suchas Simulation) to complex operations (such as mod-ern call centers), in detriment of analytical methods(such as the Queue Theory).

2. LITERATURE REVIEW

2.1 Queue Theory applied to Call Centers

In a call center system, a queue occurs when there isno agent available to handle a client, which waits ona virtual line from which he will leave only when anoperator is set to aend him or when he disconnectsthe call. As observed by Brown et al. (2002), in the caseof call centers, the virtual queue is invisible amongthe clients and among the clients and the operators.

In the call centers scenario, Araujo, Araujo and Adis-si (2004) say that the queues discipline, when wellmanaged, is a strong ally for the call centers produc-tion planning and controlling area, which have as a

goal to achieve the expected results with scarce re-sources, turning this area more and more importantfor these companies. The queues discipline, whenwell managed, can bring a signicant reduction tothe clients waiting time.

A few call center characteristics make it dicult toapply analytical formulas from the Queue Theoryfor its modeling, including: generic distribution forthe handling time, time-varying arrival rates, tem-porary overows and abandonment. The model in-troduced by Chassioti and Worthington (2004) con-sists of a practical approach capable of incorporatingmost of these features.

According to Bapat and Pruie Jr. (1998), the prem-ises adopted by the studies based on Queue Theoryanalytical models are extremely limited when based

on call centers current context because: (i) the incom-ing calls are all of the same kind; (ii) from the mo-ment a call enters a queue, it never leaves it, and thisusually overestimates the labor needed, increasingthe personnel costs for the company; (iii) the aen-dants handle the calls following the FIFO (rst in,rst out) discipline; and (iv) each operator handlesall calls the same way.

These premises rarely work at the environment inwhich call centers are inserted, since, according to thementioned authors depending on the individual tol-

erance for waiting his turn to be handled a client maydisconnect the call, if queued. Furthermore, the opera-tors normally dier in relation to their own skills andto the handling time. Additionally, the clients needsare very dierent and, sometimes, a priorization thatcan oer a beer service might be necessary. Neverthe-less, many companies continue to support the usuallycomplex decisions related to the resources allocationby means of Queue Theory analytical models drivenby the approach easiness and quickness.

Many call centers present a generic distribution

(lognormal, for instance) for their handling timesand not necessarily a negative exponential distribu-tion (BROWN et al., 2002). The exponential formatis used in most of the Queue Theory literature, notonly for the time between clients arrival, but also forthe handling time. This is due to the fact that thereare analytical solutions for the system stationarystate when these times are considered as followingan exponential distribution.

But within the real world call centers, at least the in-coming clients rate varies as time goes by. This vari-

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Bouzada, Marco Aurlio C.B.:Dimensioning a Call Center: Simulation or Queue Theory?Journal of Operations and Supply Chain Management 2 (2), pp 34 - 46, C International Conference of the Production and Operations Management Society36

ation is driven by advertisements, work shis etc..The aendants fatigue can also generate a variationon the handling time as the day goes by, but it is in-signicant when compared to the arrival rate varia-tion. The solutions found in the literature to dealwith the time-varying arrival rates are not so useful

because they involve Bessels functions, of dicultapplication (CHASSIOTI; WORTHINGTON, 2004).

2.2 Simulation in Call Centers

Chokshi (1999), Klungle and Maluchnik (1997), Halland Anton (1998), Mehrotra and Fama (2003), Avr-amidis and LEcuyer (2005), Klungle (1999) and Ba-pat and Pruie Jr. (1998) go beyond a few recent fac-tors that contributed to the increase on the demandfor the use of the simulation tool in the call centerssector: (i) the increasing importance of the call cen-ters for a good number of corporations, due to thefast increase of information, communication andtechnological gadgets, increasing the need to usescientic methodologies on decision makings andtools for its strategic management instead of usingthe intuition, only; (ii) the increasing complexity ofcall trac along with rules more and more viewedon the skill-based routing; (iii) the uncertainty moreand more predominant at the decision problemsusually found on the operational management of callcenters phone desks; (iv) fast changes on the opera-tions and improvement of the re-engineering activi-

ties resulting from the increase of joint-ventures andacquisitions, business volatility, outsourcing optionsand the utilization of dierent channels in order toreach the consumer (telephone, e-mail, chat...); and(v) the availability and accessible price of the com-puters, together with a range of Simulation applica-tions in call centers, available in an everyday marketless and less complex, intuitive and easier to be as-similated and used.

Simulation, according to Mehrotra (1997), explicit-ly shapes the interaction between calls, routes and

agents, as well as the random individual incomingcalls and the also random duration of the handlingservice. Through the use of Simulation, managersand analysts translate the call centers gross data (callforecast, distribution of the handling times, sched-ule hours and the agents abilities, call route vectors,etc.), in handling information on the service levels,clients abandonment, use of agents, costs and otherimportant performance measures of a call center.

According to Chokshi (1999) and Klungle and Ma-luchnik (1997), the use of Simulation to help man-

agement decisions in a call center allows the follow-ing benets: (i) to visualize future processes and beused as a communication tool; (ii) to validate theprocesses premises before its implementation; (iii)to analyze the impact of the changes (scenario stud-ies) in detail; (iv) to foresee the aggregated needs of

resources and to schedule the working team; (v) tomeasure the performance indicators; and (vi) to esti-mate impacts on costs and economies.

One of the usages of the Simulation in a call center,as said by Hall and Anton (1998), is the evaluationwhen one may verify where the call center is. Thekey-question is how ecient is the operation now-adays? The goal of this evaluation is to establish apoint of departure (and reference) for the change.

In accordance to Mehrotra, Profozich and Bapat(1997), Yonamine (2006), Gulati and Malcolm (2001),

Bapat and Pruie Jr. (1998) and PARAGON (2005),a simulation model can be used (and has been usedmore frequently than ever) besides normally al-lowing graphics and animations to contemplatea few other critical aspects of the modern receptivecenters of all sizes and types, such as: (i) a specicservice level; (ii) exibility on the distribution of timebetween incoming calls and of handling time; (iii)consolidation of the central oces; (iv) skill-basedrouting; (v) multiple types of calls; (vi) simultaneouslines; (vii) call disconnect paerns; (viii) call returns;(ix) overow and lling of capacity; (x) waitinglines prioritization; (xi) call transference and tele-conferences; (xii) operators preferences, prociency,time learning and schedule. The outputs model canemerge in shape of waiting time, call disconnectingaverage amount, (both with the possibility of dier-entiation on the call types) and level of the operatorsutilization (with possibility of the operator types dif-ferentiation). And, due to the applicability of this ap-proach to the real and complex characteristics of callcenters, the Simulation can make its dimensioningand management more reliable.

In accordance to Mehrotra, Profozich and Bapat(1997), Steckley, Henderson and Mehrotra (2005),PARAGON (2005), Mehrotra (1997), Klungle andMaluchnik (1997), Pidd (1998) and Tanir and Booth(1999), the traditional methods most oen used tomanage and size a call center (intuitive estimatives,unprepared computations, worksheets and Erlangqueue theoretical models) are becoming signicant-ly limited due to the variability of the incoming calls,routes and handling time, to the operators skills andpriorities, to the call heterogeneity and the interac-

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tion among them and the line trunks, to the dynamicof the call disconnections, to the recent tendencies(such as the skill-based routing, electronic channelsand interactive calls handling) and, in general, tothe sophistication and complexity more and moreevidently noticed in the call centers systems. For

example: analytical models usually assume that theclients arrival follows a Poisson process when, as amaer of fact, the call centers data constantly rejectthis premise. In addition, worksheets and Erlangmodels overestimate the number of agents, besideshaving not much precision for call centers with dif-ferent handling for each kind of client.

The Simulation enlarges the capacity of the analyticaltools and consists of a superior approach when thereis no workable theoretical model capable to providea reasonable system representation and when the

means are not sucient, the accuracy is important,the operation is detailed, the demand varies toomuch, bolenecks and processes design changingneeds must be identied, or else an animation is nec-essary to improve the communication of a changeto the companys board. The industry recent tenden-cies demand more sophisticated approaches and theSimulation provides the necessary techniques to ac-quire the insights about these new tendencies andhelps to shape its present and future designs, con-sisting in the only analysis method able of modelinga call center eciently and accurately, throughout

an approach much more practical, exible in termsof inputs and outputs, and capable of allowing theinclusion of important details, of representing muchbeer the reality (without great needs of simplica-tions as theoretical models do), of enabling a bet-ter and deeper understanding concerning the callcenter processes and of generating much more ro-bust results regarding the call center performance,allowing its optimization in a more reliable way(PARAGON, 2005; RILEY, 2005; MEHROTRA, 1997;KLUNGLE; MALUCHNIK, 1997; TANIR; BOOTH,1999; SALIBY, 1989; HILLIER; LIEBERMAN, 1995;

HERTZ, 1980; MEHROTRA; PROFOZICH; BAPAT,1997; BAPAT; PRUITTE JR., 1998; CHOKSHI, 1999;KLUNGLE, 1999; WORTHINGTON; WALL, 1999;RAGSDALE, 2001; MEHROTRA; FAMA, 2003).

3. THE CASE

3.1 The company

Contax emerged by the end of the year 2000 as anatural extension of Telemars business, in a branch

of the economy which did not invest much in tech-nology and qualication of the customers service,in order to help its clients on their operational man-agement, aggregating value on the relationship withnal customers (CONTAX, 2006).

Presently in Brazil, Contax is the largest growingcompany in this industry, with a growth of almost60% in 2005, when it invoiced R$ 1.129 millions. It isknown as the largest enterprise of this branch basedon the number of aending service positions, and thesecond largest in terms of sales and work force, in-side the national territory (OUTSOURCING, 2005).

The Contax capital is 100% national and today itoperates with more than 22.000 positions at the cus-tomer service, almost 50.000 employees and morethan 40 clients, with Telemar being the largest one(representing approximately 60% of the sales). The

main products related to this client are: (i) Velox; (ii)103; (iii) technical support and repairs; (iv) Oi; and(v) 102, which receives calls of customers that needinformation from the telephone directory.

3.2 The current dimensioning process of handling

capacity

The dimensioning consists of the analysis that maycustomize physical, technical and personnel struc-tures of a call center towards the objectives of thecustomer service operation that begins with the

forecast of the demand within the days.

The 102 product was chosen to illustrate the dimen-sioning problem, since its demand is the most fore-seeable and, therefore, being possible to measure thequality of a dimensioning process independentlyi.e., departing from the premise that the input de-mand forecast presents a good quality.

The service level for this product is related to the wait-ing time of the nal client at the telephone line, fromthe moment the incoming call arrives to when it is an-

swered. In other words, it is the time which the clientremains waiting in line, listening to the backgroundsong and waiting for the operator. More precisely, thelevel of the service consists of the percentage of calls amongst the completed ones, only that wait nomore than 10 seconds to be answered.

As only the calls answered count in the computa-tion of the service level, the disconnections are notaccounted (and, therefore, not punished), for eectsof the service level. Nevertheless, they are measuredthrough another indicator (abandonment rate) and

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Contax pays nes when this rate exceeds 2% in amonth. As this may happen, to avoid the disconnectis seen as a priority, to the detriment of the servicelevel, as long as this is maintained above a minimumvalue. The service level does not involve formal re-quirements of the contract (as the abandonment rate),

but does inuence the commercial relationship anddignity; i.e., it is interesting to not prioritize only theabandonment and, as a consequence, not worry withthe maintenance of the service level in decent values.

The dimensioning routine isolated for each product(basic and plus due to the priority of the last overthe rst) begins by computation of the daily needs ofoperators, departing from the forecast amount of calls,the average handling time (AHT) and the average timethat operators are busy per day. Aer that, the need ofoperators (converted to the 6-hours-operators paern)

is compared to todays resources availability, discount-ing the losses concerning vacation and absence. Theresult of this comparison is the balance or the decitof the labor for each day of the planned month. Theoutput of this rst step is the amount of operators thatneed to be hired or dismissed in the referred month sothat the required numbers can be achieved.

From the moment the contract decision is taken, orthe dismissal is decided and implemented, the plan-ning team can look forward to a more detailed anal-ysis daily dimensioning. This must be done for oneday only, and this paern format must be repeatedto the other days of the period, since the scheduledhours of each employee must be the same on every-day of the month.

In conclusion, a volume of calls and an average han-dling time (necessary numbers for the dimension-

ing) shall be chosen to be used as a paern for thedimensioning of all days of the month. The chosenday for the paern is, usually, the h day of highermovement. This way, the dimensioning will guaran-tee the desired service level for this day and all thenot-so-busy days, but not for the four days of higher

demand, when there will be a loss in the service lev-el. Nevertheless, this does not represent a problem,because the agreement related to the 102 product in-volves a monthly level service and not a daily level.

Over the day chosen as a paern for the dimension-ing of the month is applied a curve that shall reectthe daily demanding prole, i.e., which daily volumepercentage will happen in the rst half hour of theday, in the second half hour of the day, , and in thelast half hour of the day. This curve is shown basedon the calls report received at each period of half hour

for each day of the week. Concerning the 102 product,the curves of each day of the week are very similar(mainly from Monday to Wednesday, with a lile in-crease of the volume in the aernoon of Thursdaysand Fridays), and on Saturdays and Sundays theyhappen to be a lile dierent. Figure 1, that follows,illustrates the historic curve for Tuesday.

The result of this process is a forecast call demand (vol-ume and AHT for each half hour). With the help of theExcel Supplement Erlang1 formulas, called Turbotab,it is computed the necessary amount of operators thatwill be handling the demand of each period with aminimum pre-established service level (normally 85%of the calls being answered before 10 seconds).

Figure 1 Historic prole for the demand intradaybehavior, Tuesday

0,00%

1,00%

2,00%

3,00%

4,00%

5,00%

6,00%

00:00

01:00

02:00

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10:00

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12:00

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15:00

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Period

%o

fthedailyvolume

Source: Contax

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The last month contingent of operators is then con-sidered. Due to the amount of operators that are ini-tiating their work at each day period and the dailywork load of each one of them (4 or 6 hours), a sheetcomputes how many operators will be available foreach period of half hour. This information is then

compared to the operators need for each period of30 minutes, previously calculated. Such comparisonis summarized in a graphic way as exemplied inthe following gure 2.

Over the actual operators scale, the planning teamwill work on the changing of the operators avail-

ability for each period of the day, in order to achievethe desired service level. The objective is to assurea certain amount of people in each scheduled hour,throughout a trial-and-error process, during whichit will be necessary to analyze several factors, suchas daily working hours load, working laws aspects,

union agreements and available physical space. Inthe case of the 102 product, the balanced scale (al-ternating times with the operational contingent overor under the requirements) can be used, since whatreally maers for commercial purposes is the dailyaverage level service.

Figure 2 Operators need and availability by period, Aug/06

NeededX Available

0

50

100

150

200

250

300

350

400

450

00:0 0 01:0 0 02:0 0 03:0 0 04:0 0 05:0 0 06:0 0 07:0 0 08:0 0 09:0 0 10:0 0 11:0 0 12:0 0 13:0 0 14:0 0 15:0 0 16:0 0 17:0 0 18:0 0 19:0 0 20:0 0 21:0 0 22:0 0 23:0 0

Period

O

Source: Contax

During the stang process, the planning teammakes experiments by modifying the quantity ofoperators that begin to work at each period of time.

These changes consequently alter the quantity ofoperators available in each period of half hour. Thesheet containing the Erlang formulas uses this in-formation then to estimate the service level for eachperiod of half hour and for the day, which dependsalso on the forecast demand.

At this interactive process, the principal motivationof the analyst is to maximize the days average ser-vice level. The level of the service in each hour band,itself, does not present a great concern to the analystwho, nevertheless, tries to avoid great decits of op-

erators assigned in relation to the demanded withinthe hour bands of the day.

The concern about daily decits does exist because,in hours with a higher deciency of operators it ispossible to register a great incidence of abandon-ments. And this could be very bad for two reasons:nes for excess of call abandonments and the pos-sibility that the client le without an answer returnsthe call later on and waits until geing an answer,therefore deteriorating the service level.

This dimensioning eort main goal is to provide abeer adjustment between the demanded and of-fered capacity during the day. An example of the

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changes made in order to achieve a beer dimen-sioning can be visualized on gure 3 that follows.

On the last part of the dimensioning and stangprocesses, the analyst tries to estimate how the op-eration level service will be (percentage of calls an-swered in less than 10 seconds), on all days of themonth (until here the computation was based on the

h day of larger movement, only). The intradaydistribution of operators elaborated during the paststeps is repeated on all days of the month and, alongwith the daily call demanding forecast as well aswith the demand intraday behavior prole, is able,therefore, to estimate through the Erlang Method-

ology

the service levels to be obtained for each dayand hours, within the month in question.

Figure 3 Changes made during the resources stang, Aug/062

P eriod 06: 00 06: 30 07: 00 07: 30 08: 00 08: 30 09: 00 09: 30 10: 00 10: 30

02:30

03:00

03:30

04:00

04:30

05:00

05:30

06: 00 20

06: 30 20 1

07: 00 20 1 21

07: 30 20 1 21 25

08:00 15 1 21 25 72

08:30 17 0 15 25 72 40

09:00 18 1 20 21 72 40 40

09: 30 20 1 21 24 72 40 40 26

10: 00 20 1 21 24 72 40 40 26 18

10: 30 20 1 21 25 72 40 40 26 18 9

05 "Basic" resources

08 resources

08 resources

05 resources

Source: Contax

For the planning team, the Erlang formula used tocompute the service level is not totally precise, but itis not radically inaccurate to the point of generatingsituations where the actual service level is far fromthe one computed. In fact, a few internal questionscame out concerning this formula, driven by a fewempiric observations, such as in the situation wherethe service level computed for a time band present-ing a decit of 3 agents was 77% and dropped to 0%when the decit went up to 12 agents. Therefore,there is not a common agreement about this meth-odology being the ideal tool to calculate the servicelevel, but the team did not nd any other more ac-curate approach during researches that collected in-formation and analyzed worksheets.

3.3 Suggested methodology for the dimensioning of

the handling capacity

For the real world of call centers, the Queue Theoryis the best analytical methodology to be used, butthere are experimental methods as Simulation, for

instance that should be even more adequate for anindustry with an operational day to day as complexas modern call centers, as suggested by section 2.2 ofthis paper. For example, the methodology current-ly used for the service level computation does nottake into account the hypothesis of clients abandon-ing the call or receiving the busy line signal; i.e., theclients that arrive and do not nd available agents,await indenitely in a queue until being aended.This fact creates a tendency to underestimate theservice level because, in the real operation, some cli-ents will disconnect their calls (if waiting too long),shortening the queue and making the other calls behandled before the expected moment. In addition,the worksheets used to compute the service levelconsider the handling time following an exponentialdistribution. Nevertheless, this rarely occurs eec-tively, characterizing an unreal premise.

The employment of the Simulation allows us to con-template the highlighted characteristics of section2.2, including the abandonment behavior (it is pos-

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sible to consider that a percentage of clients that dis-connected their calls, will return and try a new con-tact in a given amount of time, which can be mod-eled by a statistical distribution) and a exibility onthe denition of the handling time distribution.

In order to verify this beer adequateness, the ideaconsists in simulate by computer and in a few sec-onds, the call centers operation during periods of 30minutes, contemplating more realistically its char-acteristics to obtain more accurate results than theones generated by the analytical methodologies.

This way, it is possible to visualize the operation it-

self (with the calls arriving, being sent to the queues

and handled aerwards) and what would be going

on, in detailed forms (practically as being in loco), in

order to understand why a certain period of the day

presented a service level so low, for instance (insteadof only accepting the number supplied by the analyt-

ical formulas). The following gure 4 illustrates the

dynamic presentation of the performance indicators

that a Simulation soware is capable to provide.

Figure 4 Dynamic indicators of a call center simulation model

Source: Screen captured by the soware during simulation of the model

As it may be seen, several indicators can be followedup while varying dynamically as the simulationis being executed: the amount of clients handled,answered before 10 seconds, the consequent ser-vice level (its value at the moment, in numerical andgraphical forms the level bar, besides its behavioralong the simulation), the number of clients waitingin the queue (in numerical and graphical forms), ofblocked clients as well as of those who disconnected,

the average waiting and handling times (in numeri-cal and graphical forms), and the amount of busyagents (the current value, in numerical and graphi-cal forms, besides an histogram showing its behavioralong the simulation). At the end of the simulation,the reports summarize the consolidated results.

The use of Simulation renders it possible to com-pute empirically (instead of estimate analytically)

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through the use (as inputs) of certain historicalpremises (about clients and system behavior and de-mand forecast) and the amount of agents assigned some important performance indicators, such asservice level, abandonment rate, average waitingtime, agents busy and idle times.

For the dimensioning and stang of the operators tohandle the plus clients of the 102 product, in Augustof 2006, it was used the premise (originated on thedemand forecast) that 586 calls would come to thephone desk with an AHT of 29 seconds in the rsthalf hour of the day (from 00:00 a.m. to 00:30 a.m.). Itwould be necessary, according to the analytical for-mulas, to allocate 12 agents for this part of the day, inorder to achieve a service level of 85%. The stangteam requested then 12 operators and the analyticalformulas forecast 88.04% for the service level during

this period.With the purpose of questioning these numbers, itwas built a model in the soware Arena ContactCenter to simulate how the system would behave inthis period, with the same demand premises (vol-ume and AHT) and with the same operational ca-pacity (12 agents).

As the calls come to the phone desk without anykind of control, this process can be considered a ran-dom one, the conceptual basis suggesting thereforethat the call arrivals rate might be shaped through

a Poisson process. The conceived simulation modelimplemented this process with a mean of, approxi-mately, 0.33 calls arriving per second (or 586 in a 30minute interval).

In relation to the handling time, the Erlang distribu-tion uses to beer shape this process and, therefore,it was used with a mean of 29 seconds. It requiresnevertheless an additional parameter (k) relatedto the variance of the data around the mean. Thestandard deviation of the distribution is equal to itsmean divided by the square root of k. To be able to

consider a moderate variance of the data around themean, the model takes the Erlang distribution with k= 4, resulting on a variation coecient of 50%.

In order to allow a correct interpretation of the cli-ents abandonment behavior, it was necessary toperform a research close to the Contax basis, whichincludes the disconnected calls of the 102 product.The research showed that the waiting time of thecalls disconnected historically present a mean ofabout 2.5 minutes, following a distribution not too

far from an exponential one. It was also necessary tomodel the return behavior of the disconnected calls.To make it possible, it was used the premise that80% of the disconnected calls are recalled between1 and 9 minutes aer the disconnectment happens(uniform distribution).

3.4 Results analysis

The simulation of the call center operation during 30minutes was replicated 100 times in the soware ina period of 142 seconds, and the rst results indicatethat, in average, 595 calls were generated in eachreplication. This number is a lile higher than thatdemand premise of 586 calls, due to the fact that, inthe simulation, a few of the disconnected calls werereplicated and put on the queue again. From thegenerated calls, 579 calls in average were eectivelyhandled by the operators in each replication.

From these calls, 541 were handled before 10 sec-onds, resulting in a service level of 93.31%. Thisvalue is fairly higher than 88.4% (the service levelforecast by the analytical approach). More, this factsustains, at a rst sight, the expectation of underesti-mating this variable by the Queue Theory.

Aer consulting Contax database, it was possibleto recover the information revealing that, on August22, 2006, 12 agents were operating from 00:00 a.m.to 00:30 a.m.. Within this period of time, 592 calls

were handled in 29.4 seconds each, in average. Thesenumbers exceed just a lile the demand premises(volume = 586; AHT = 29 seconds) used for the di-mensioning process via analytical formulas, as wellas in the simulation model presented here. This isthe reason why this day and time band were chosento serve as a comparison base between the resultsobtained by both approaches.

During these 30 minutes, 549 of the 592 calls wereanswered before 10 seconds. In other words, the realservice level in this interval was of 92.74%; i.e., much

closer to the value empirically computed by the simu-lation (93.31%) than the value analytically estimatedby Erlang formulas (88.04%). According to what wassaid, the underestimation of the service level pro-moted by the Queue Theory is mainly due to thenon-contemplation of the call abandonment carriedout eectively by some clients, but not consideredtheoretically by the analytical models.

From the 595 calls generated in each replication, 14.5(in average) were disconnected by the clients, gener-ating an abandonment rate equal to 2.44%. Amongst

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the disconnected 14.5 calls, 11.5 (79.41%) returned tothe queue a few minutes aer the disconnectment.

As may be observed, the Simulation allows severalother performance indicators related to calls be-sides the service level to be computed and ana-lyzed. For example, the AHT was 29,35 seconds, buta client came to be handled in 4,70 seconds, and an-other one in 147,60 seconds! In relation to the wait-ing time, the calls held for, in average, 1,94 secondsbefore been answered. Some clients were answeredimmediately and at least one awaited 38 seconds.

According to the section 2.2 alert, this type of analy-sis involving the variability and the maximum andminimum values of the performance indicators, can-not be made by means of analytical methods (ca-pable of presenting only average values), becomingfeasible only via experimental approaches.

Simulation can also generate indicators related toagents. In the highlighted period, the occupationrate for them was 78.75%, in average. This indicatorcan guide the management towards a sta increaseor decrease, according to the previously determinedoccupation goals.

It is interesting to also notice the experimental ap-proach accuracy during other time periods, with dif-ferent service level platforms.

For the operators stang within the period between02:00 a.m. to 02:30 a.m. (also in August, 2006), it wasused the premise that 196 calls would reach the callcenter, with an AHT equal to 28 seconds. It wouldbe necessary, according to the analytical formulas,to allocate 5 agents for the period, in order to reachthe required service level (85%). Nevertheless, only4 operators were assigned for that period and thisagents decit (-1) made the analytical formulas fore-cast 44.05% for the service level.

Again, a model was built, this time to simulate thesystem behavior at this second time period, withthe same demand premises (volume and AHT) andwith the same capacity dimensioned (4 agents). Thecalls arrival and the handling time were modeled inaccordance to these average premises and follow-ing the exponential and Erlang (k = 4) distributions,respectively; and the abandonment behavior wasmodeled the same way as before.

In average, 209 calls were generated in each repli-cation; from these, 193 (in average) were actuallyhandled by the operators, 144 from which before

10 seconds. It was obtained a service level equal to74.44%, a value lower than the goal (85%), but ex-tremely higher than the 44.05% forecast by the ana-lytical formulas that, as a maer of fact, seem to haveunderestimated this variable.

In accordance to Contax database, in August 29,2006, 4 operators handled 192 calls between 02:00a.m. and 02:30 a.m., with an AHT equal to 27.6 sec-onds. These numbers are very closer to the demandpremises used for the dimensioning process via Er-lang formulas, as well as in the simulation modelpresented here. Within this interval, 136 calls wereanswered before 10 seconds, generating an actualservice level equal to 70.83%.

As it happened in the original scenario (from 00:00a.m. to 00:30 a.m.), this value was closer (this time,even closer) to the service level computed by the

simulation. Thus, it seems to happen an even higheraccuracy gain for the service level forecast in sce-narios with low values for this variable. One shallnow evaluate the behavior of this accuracy when theservice level is very high (more dimensioned agentsthan the amount needed).

In the period between 05:30 a.m. and 06:00 a.m., dur-ing August of 2006, it was considered that the callcenter would receive 253 calls, with an AHT equalto 31 seconds. According to the analytical formu-las, it would be necessary to allocate 7 aendants

for this period, in order to achieve the service levelgoal. Eleven agents were assigned (balance of 4) forthis time band and the Erlang formulas had forecast99.78% for this period service level.

With the objective of questioning this estimated ser-vice level, a model was built considering the samedemand premises (volume and AHT) and the samedimensioned capacity (11 operators), this time forthis third period.

The calls arrival and the handling time were mod-

eled in accordance to these average premises andfollowing the exponential and Erlang (k = 4) distri-butions, respectively; and the abandonment behav-ior was modeled the same way as before

The simulation of the operation during this periodof time was replicated 100 times. In average, 253.31calls were generated, 253.27 answered and 253.22 be-fore 10 seconds, in each replication. Abandonmentsalmost did not happen, and this is not surprising dueto the over dimensioning table done for this scenar-io. The resulting service level was equal to 99.98%,

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an extremely high value (even when compared tothe goal of 85%), and very similar to the one forecastby Erlang formulas for this scenario (99.78%).

Contax database reveals that in August 15, 2006,11 agents were handling calls during the period be-tween 05:30 a.m. and 06:00 a.m., when 249 calls werehandling with an average time equal to 31.5 seconds.These numbers are very close to de demand prem-ises used for the analytical and simulation models.

Within this period, 248 calls were answered before10 seconds, generating an actual service level equal

to 99.60%. This time, the values forecast by both ap-

proaches (analytical and experimental) were very

similar to the real value. It seems there is no accu-

racy gain for the service level forecast in scenarios

with very high values for this variable achieved by

the usage of the experimental approach.

At last, it is possible to present a more complete

comparison. The accuracy gain behavior achieved

by the usage of the Simulation approach in rela-

tion to the service level platform can be summarized

in the following Table 1.

Table 1 Service level actual and estimated by Erlang formulas and Simulation, estimation errors and accu-racy gain for dierent service level platforms

Period 02:00 - 02:30 00:00 - 00:30 05:30 - 06:00

1 less (out of 5) 1 less (out of 13) 4 more (out of 7)

-20% -8% +57%

Actual service

level70,83% 92,74% 99,60%

Erlangformula 44,05% 88,04% 99,78%

Error 26,78% 4,70% 0,18%

Simulation 74,44% 93,31% 99,98%

Error 3,61% 0,57% 0,38%

4,13% -0,20%

Operators

balance

Accuracy gain 23,17%

Source: Table elaborated by the author

4. CONCLUSIONS

It was possible to verify, along this research and viathe use of simulation models to deal with the han-dling capacity dimensioning problem faced by thestudied companys call center, some advantages ofthe experimental approach when compared to theanalytical ones, mainly in more complex operations:(i) it is possible to include more details of the opera-tion, to use statistical distributions more compatible

with the input data and to have the model closer toreality, assuring the collection of more accurate re-sults; (ii) the service level computed by Erlang for-mulas is usually underestimated, mainly becausethese formulas ignore the calls abandonment; (iii)other performance indicators (not available whileusing analytical approaches, as the abandonmentrate) can be evaluated, presented and analyzed;(iv) minimum and maximum values of each impor-tant indicator can be obtained, the analyst not be-ing restricted to the average values as when usingthe Queue Theory; (v) a beer understanding of the

operation is achieved with the adoption of the ex-perimental approach, which provides the possibilityto dynamically follow up the system behavior andits performance indicators behavior and, therefore,understand why the queues are being formed andthe reason why the waiting time is high, for exam-ple, while throughout the Erlang methodology it ispossible to see only the generated outputs (numericindicators) in relation to the provided inputs, mak-ing more dicult the complete comprehension of

the operation; (vi) the communication can becomeeasier via the use of graphic animations.

This paper also allowed concluding that the accu-racy gain for the service level, promoted by Simu-lation, tends to be higher when this variable showslower values, according to Table 1, already shown.

4.1 Suggestions and recommendations

Much has been done since the complexity inherentto the management of modern call centers was real-

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ized. Obviously, there is much more to be answered,and in a more accurate way, such as questions re-lated to call centers optimization, throughout morediscussions and new studies, and the improving ofa fundamental aspect for the modeling systems: theproximity to the real world.

An interesting research object would be to map the cli-ents post-abandonment behavior (the amount whichtries to call again and the distribution format for thetime period elapsed before the second aempt) andto include it in the model. Additionally, it should alsobe taken into account the fact that aer disconnect-ing the initial call, a client trying a new contact couldbe more impatient and decide to stay less time in thequeue now, before disconnecting again.

The decret number 6523 (july, 2008) states several

issues that must be addressed by brazilian call cen-ters. Some of them are capable to impact this andfuture studies about call centers. For instance, theinitial access to the aendant will no more be subjectto the prior provision of data by the consumer; thesedata may have to be provided during the service,increasing the handling time and impacting the per-formance measures.

In addition, specic regulations will address themaximum time required for direct contact with op-erators; this new need will you force brazilian call

centers to improve their performance not only dueto commercial reasons but henceforth driven by le-gal issues. These and other kinds of impact may beexplored by future and similar works, maybe study-ing call centers fully adapted to this decree.

Finally, future Simulation works to be applied to thecall centers industry could explore other peculiari-ties present on this kind of operation, which are notused to be well approached via analytical method-ologies, such as, for instance: (i) the call transferenceprocess during a client aending operation before

being handled by the correct agent; (ii) conferencesamongst the client and more than one operator atthe same time; (iii) conditional call detours towardsspecialized services; and (iv) other queue disciplinesthan the traditional FIFO.

Since most of the Simulation sowares address suchoperational features, it would not be complicated for a researcher interested in these suggestions andwilling to deepen about the used tool functional de-tails to model these peculiarities and reach interest-ing conclusions for the industry being focused here.

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AUTHORS BIOGRAPHY

Marco Aurlio Carino Bouzadais a Production Engineer (UFRJ, 1998), M. Sc. in Business Administration(COPPEAD/UFRJ, 2001) and Ph. D. in Business Administration (COPPEAD/UFRJ, 2006). Currently a profes-sor belonging to the permanent sta of the Estacio de S University M. Sc. in Business Administration Pro-gram, to the Escola Superior de Propaganda e Marketing Graduation in Business Administration Programand to the COPPEAD/UFRJ Finance Specialization Program, with experience on topics like Statistics, Quan-titative Methods, Operational Research and Business Games.

Steckley, S., Henderson, S. and Mehrotra, V. (2005), PerformanceMeasures for Service Systems with a Random Arrival Rate,Winter Simulation Conference, p. 566-575.

Tanir, O. and Booth, R. (1999), Call center simulation in BellCanada, Winter Simulation Conference, p. 1640-1647.

Weinberg, J., Brown, L. and Stroud, J. (2006), Bayesian Forecast-

ing of an Inhomogeneous Poisson Process with Applicationsto Call Center Data (white paper), University of Pennsylva-nia.

Worthington, D. and Wall, A. (1999), Using the discrete timemodeling approach to evaluate the time-dependent behaviorof queueing systems, Journal of the Operational ResearchSociety, Vol. 50, p. 777-788.

Yonamine, J. (2006), O Setor de Call Centers e Mtodos Quanti -tativos: uma Aplicao da Simulao, Dissertation (M. Sc. inBusiness Administration), Rio de Janeiro: UFRJ/COPPEAD.

Endnotes

1 The Queue Theory is used for the agents dimensioning at Contax. The clients that arrive and do not nd available operatorsawait indenitely in a queue until being handled (there is no abandonment or busy line signal), according to the theory. Thewaiting times are forecast: (i) using the premise that the interval between arrivals and the handling time follow exponentialdistributions; and (ii) based on the agents amount, the number of clients in the queue and the average handling time.

2 The available agents amounts highlighted in blue are smaller than those of operators beginning their workday in each pe-riod, due to the break time for part of the employees during these periods.

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