A practice-oriented overview of call center workforce planning
AA practice-oriented overview of call center workforceplanning
Ger Koole & Siqiao LiCCmath bv & Vrije Universiteit AmsterdamJanuary 26, 2021
Abstract
We give an overview of the practice and science of call center workforce planning,where we evaluate the commonly used methods by their quality and the theory by itsapplicability. As such this paper is useful for developers and consultants interestedin the background and advanced methodology of workforce management, and forresearchers interested in practically relevant science.
Call centers are a fascinating area for stochastic modelling. In manufacturing most pro-duction is being done before the demand occurs, the product is lying on a shelf in a shop ora distribution center waiting for customer demand. In (non-urgent) health care productionis smoothed in time to meet capacity: a patient makes an appointment with a health careprovider at a moment that suits above all the provider. In aviation and hospitality demandis pushed by financial incentives towards low-demand time slots. Inbound call centers havein common with emergency health care that demand has to be met almost instantaneouslyby supply. And while a hospital has at least 15 minutes to prepare for the arrival of atrauma patient, a call center often has to answer a call within 20 seconds. And it can belife-saving, as is the case of an emergency call center.To be able to deliver this type of service planners have to deal with fluctuations, un-foreseen (such as the variability of the Poisson process, or illness of employees, often calledagents) and foreseen (such as intra-day and intra-week seasonality in demand). Call centerscannot react instantaneously to all fluctuations, and therefore have to schedule overcapac-ity. Designing the call center in such a way that little overcapacity is needed, and planningthe right amount and types of overcapacity is the essence of workforce planning.Nowadays many call centers handle contacts through different communication channels ,such as chat and email. However, inbound calls is often the most prominent channel. Togive credit to the different channels the term contact center has been introduced. Few1 a r X i v : . [ c s . C Y ] J a n uarterly Time
Frequency Steps Output Name of the process monthlyweeklyweeklymultiple times per day ? X + 1Y? X + 1Q? X + 2M? X + 1M? X to X + 1M forecastingforecastingforecastingforecastingforecasting capacity planningcapacity planningcapacity planningagent schedulingintra-day management budget planhire & fire training agendavolume to BPOagent schedulesadaptations to schedules & tasks budget planningcapacity planning operational planning & scheduling
Figure 1: The WFM processespeople however use it, thus a call center is most of the time a contact center mixingcontact from different channels. A notable exception are call centers dedicated to outboundmarketing campaigns. Through predictive dialing they deal with fluctuations in the fractionof calls that are answered and the speed at which this is done. Quite a number of patentsfor algorithms can be found on Google Scholar.Will there still be call centers in say a decade? We see a tendency for offering automatedcustomer service by using for example AI in chat bots and call avoidance by for exampleimproved web sites. Indeed, there is evidence that making calling unnecessary is thebest customer service (Dixon et al. [46]). And if people call, avoid that they have tomake another call later on. Avoiding calls is also cheaper, and as most call centers areseen as cost centers, there is a strong incentive to reduce costs. However, there is noevidence that the call center market is shrinking, on the contrary (Mazareanu [97]). Apossible explanation is the popularity of shared service centers which operate effectivelyas call centers (e.g., the human resources department at our university). As such, we seea tendency across industries, from decentralised service to centralised service (operated asa call center, potentially offshored to a country with lower wages) to self-service.This overview focuses on the practice of workforce management (WFM). (A bettername would be workforce planning, but we will stick to the commonly used terminology.)As framework we use the different steps in the WFM processes. The three central planningprocesses are: budget planning, capacity planning, and agent scheduling. See Figure 1.“x” refers to the day of execution, “x+1Q” for example means 1 quarter before the day ofexecution. Note that many companies use business process outsourcers (BPOs) to handle(parts of) their call volume. To allow them to prepare for their job forecasts or requiredstaffing levels are communicated at multiple moments in time.As can be seen from the figure every step starts with forecasting. An exception isintra-day management: the forecast is rarely updated after the agent schedule is made,2lthough that would likely result in an increased accuracy. There are three processes:- the long-term budget process, which is input for the corporate management which setsthe financial boundaries;- the tactical capacity planning process, where decisions concerning the agent pool aremade, mostly the hiring of new agents and the training of new skills;- the short-term operational planning process, which starts with deciding which volumegoes to the external partners, and then consists of agent scheduling (which need to becommunicated a few weeks in advance) and finally intra-day management which is doneat the day itself.Depending on the particular call center the situation might be slightly different, andsmaller call centers with stable volumes might not execute the long-term steps explicitly.Note also that this scheme is biased towards the European situation with its strict laborlaws forcing call centers to schedule carefully and publish schedules well in advance.Next to the three processes from Figure 1 call centers have two more less explicitprocesses: a long-term, ad-hoc process which is about improving the overall design of thecall center: the shift structure, the way forecasts are made, opening times, channels thatare offered, etc. This process also designs all underlying processes. Finally, there is thereal-time routing, the assignment of customer contacts to agents, which has a big impacton the performance. This is automated and part of the telephony/omnichannel switch.Although this could also benefit from updated forecasts and other real-time informationthis is rarely used.Note also that we left out the connections with other departments. Forecasting forexample takes input from marketing and sales to obtain the dates of marketing campaignsand sales forecasts, and the budget plan is used in negotiations with higher management toset the final budget. Furthermore, the processes are not always as linear as they seem: theremight be interaction between forecasting, scheduling and marketing about the feasibilityof marketing campaigns; capacity planning might lead to adaptations to the budget, etc.WFM has a supporting role in a call center. It helps achieve the goals of the threestakeholders, customers, employees and management: give good service by satisfied em-ployees at a reasonable price. Good service is usually defined by service level agreements(SLAs) which serve as constraint in all WFM steps. Employee satisfaction is representedfor example in the types of possible shifts and fairness among agents that routing rulesachieve. The financial side is the main reason for having the budgeting cycle, and budgetis discussed regularly to see if there are any exceptions.In the next sections we discuss one by one the different steps of the WFM processes. Weconclude with a section on overall call center design principles. Papers and other relevantsources of information are cited where appropriate. We do not try to be complete withrespect to the literature, we focus on what we consider to be most relevant to practice.Papers inspired by call centers but of little use to its operations are left out.We end this introduction by citing some general call center WFM references. Thefollowing are academic overviews: Gans et al. [51], Avramidis & l’Ecuyer [18], and Ak¸sin etal. [1]. More practitioner-oriented text books are Cleveland & Mayben [38] and Koole [79].3
Forecasting
Call center forecasting concerns the prediction of call volumes at the interval level, usuallyper quarter. As can be seen from Figure 1, forecasts are needed at all time-levels, from afew intervals in advance to long-term forecasts years ahead. These forecasts should takeall factors that influence volume into account: long-term trend, intra-year, intra-week,intra-day seasonality, and events such as holidays, marketing actions, and IT problems ofproducts and call center systems. An important task of the forecaster is to explain whathe or she predicts, thus it is important that the forecasting method is transparent suchthat the forecaster can say something like: “Next week on Monday we have 2000 calls morethan last week. There is a marketing campaign with an expected impact of 3500, but thebase level is 1500 lower because of the holidays.” Managers won’t allow decisions to bemade on forecasts purely based on black-box forecasting, they want the reasons behind aprediction. Note that, in contrast with the linear processes described in Figure 1, theremight there be interaction between forecasting and planning: events such as marketingcampaigns might be planned on the basis of agent availability.In practice most call centers either use a self-made spreadsheet or judgemental fore-casting. Forecasting is done first at the daily level, for example by a simple decompositionapproach that adds the increase over a year to last year’s volume, in a formula with h historical volumes, ˆ y the forecast, and w and y time periods of a week and a year:ˆ h t = h t − y h t − w h t − y − w . This forecast is adapted using estimations the impact of events on t , t − w , t − y , and t − y − w . It can be made more sophisticated by predicting weekly volumes and intra-weekprofiles and by estimating the yearly increase by averaging over multiple weeks. Somescheduling tools offer forecasting functionality but rarely more advanced. Very few callcenters employ advanced forecasting methods.In the literature many methods have been proposed and applied to call center data.Taylor [112], Jalal et al. [72], Antipov & Meade [7], Weinberg et al. [117], Ibrahim etal. [68] and Huang et al. [65] are some of them. An elaborate overview is given in Ibrahimet al. [70]. All these models, using different (combinations of) algorithms from statisticsand AI, are successful in the context in which they are described, but there is no consensuson which method is preferable in the most common situations. Although various leadtimes (i.e., times in advance for forecasting) are considered when the proposed forecastingapproaches are compared, most works focus on short term forecast such as daily forecastor intra-day forecast without considering intra-year seasonality (impact), which cannot beignorant in practice. Also, most methods lack features that are required to handle alldrivers of call center volume. Especially event handling is often lacking. Some exceptionsare Aldor-Noiman et al. [6], Antipov & Meade [7] and Soyer & Tarimcilar [107], whichincorporate the effect of events (e.g., marketing strategy and special calendar effects) asexogenous variables in their mixed-Poisson arrival count models. A good method to dealwith all aspects is described in Hyndman [66], using smoothing methods as described4n Hyndman & Athanasopoulos [67] and a separate regression for events using dummyvariables. Also a regression model with a polynomial for the trend and events modeled inthe same way works quite well (Koole [79]). Because call center actuals are multiplicativein their components (Ding & Koole [44]) it is advisable to use Poisson regression, i.e., usethe regression on the logs of the actuals.Decomposition methods, by which we mean methods that determine the factors thatinfluence volume one by one, only work in a multi-pass setting because of the dependencesof the underlying variables. For example, the occurrence of outliers can only be determinedif you know the seasonalities. But the seasonalities can be better estimated if the events andoutliers are filtered out. While some form of decomposition is commonly used by forecastersin practice, multi-pass methods are rarely used and neither studied in the literature.Forecasting errors have to be measured using some criterion. It is an important task ofthe forecaster to report and explain forecasting errors to management. Therefore the errormeasure should be easy to interpret. The WAPE (weighted absolute percentage error) is agood candidate, also because it is less prone to outliers in small volumes than the MAPE,and because the WAPE is linear in the intra-day management costs ([44]).Call center arrivals can well be modeled as coming from an inhomogeneous Poissonprocess ([78]), thus we forecast the arrival rate. This gives a minimal error, which is, interms of the APE (absolute percentage error) equal to E | N λ − λ | /λ , with λ the forecast and N λ ≈ Poisson( λ ). A formula is given in Crow [39], the (very good) normal approximationis (cid:113) / ( λπ ). Taking a weighted average of the minimal APE for each interval gives theminimal WAPE for any time period consisting of multiple intervals that is to be forecasted.It has been observed that call center data is overdispersed with respect to the Poissondistribution (see Jongbloed & Koole [73] and Avramidis et al. [17]). However, this simplymeans that there is a considerable error, which might well be largely explained by addingmore features such as events. Evidently, the risk of overfitting is present, but a goodforecasting model taking all relevant features into account can reduce the overdispersionenormously. These features include, next to events such as marketing actions, special days,and IT issues, also the weather and other time series such as sales forecasts. The weather,especially the derivative of the temperature, has an impact on call volume: the first dayof nice weather sees a decrease in calls in countries such as the Netherlands. To forecastcall volume using the weather you need a good weather forecast. Therefore includingthe weather only works for short-term forecasting. A simple implementation would be toinclude the first day with nice weather as a recurring event of which the impact can bedetermined from previous days with nice weather. Depending on the granularity, horizonand characteristics of the call center a considerable WAPE on top of the minimal WAPEmight still remain. Although 5% is considered to be the golden standard, this varies wildlyin practice and is regularly much higher than 5%.In the urge to explain the forecast forecasters, and especially their managers, like toinclude time series such as sales in their forecast. Forecasts made this way are called“ratio forecasts”, because a (known) fraction of new customers calls. However, againa forecast of the external variable is needed, while the trend most of the times show5 resh Arrival Agent 1Agent 2Agent 3
SatisfiedAnsweredAbandoned LostRecallsRetrials
Figure 2: Retrials and recallsconsiderable collinearity with the sales. Furthermore, the fraction might change. Thereforeit is questionable whether including a sales forecast improves the forecast. Testing it is theonly way to find out, and often it is indeed not the case. Adding a variable such as a salesforecast is useful if it contains information not yet contained in the call volumes, such asqualitative opinions. This is often the case with long-term forecasts, made for budgetingreasons or capacity planning. An additional advantage is that it explains the forecasts andalso its errors.Note that these errors will be considerable, especially for long-term forecasting (Makri-dakis [94]). Therefore, the question should not be whether the forecast is reliable, but ifwe have enough flexibility to deal with the inevitable error. Call center managers recog-nise the importance of flexibility, but hardly ever make the connection between forecastingerrors and the amount of flexibility required. This should be part of capacity planning , thelong-term determination of the required capacity.Forecasting is often done for the total number of offered calls. However, this includesretrials: callers who abandoned earlier and called again later, see Figure 2. Data analysisshows that retrials often occur shortly after the first attempt, usually within the same day(Ding et al. [43]). Usually one knows the numbers of connected and abandoned calls, butthe fraction of retrials is not known, unless the callers can be identified. An empiricalstudy of retrial behavior can be found in Hathaway et al. [63]. Ding et al. [43] proposea statistical method to determine the “fresh” volume by using the retrial percentage asa variable in the forecasting model. In practice taking the average between the offeredand handled numbers of call often works well, corresponding to 50% retrials. Note thatthere are also recalls , callers who call a second time to get advice. Recalls add to thecall volume and therefore to the workload, but they are also a very important driver ofcustomer dissatisfaction (Dixon et al. [46]). Reducing it however is outside the scope ofWFM.After determining daily volumes they have to be drilled down to the intra-day volume.6ypically forecasters will base themselves on what they consider to be similar days asthe one they are about to forecast: same day of the week, not too long ago, similarevents. Then they take the average of the profiles , the normalised volumes, and multiplythat with the daily forecasts. However, this method leads to considerable overfitting, theaverage profile often shows quite some variability. Much better results are obtained byusing the fact that you expect neighbouring intervals not to vary that much, by fitting apolynomial or a smoothing spline. This proves to work quite well (Bakker et al. [21], Soyer& Tarimcilar [107], Channouf & L’Ecuyer [34]).In this section we fully focused on forecasting inbound calls, but the same methods applyto other forms of customer contact such as email and chat. Next to that, other parametersneeded for scheduling and capacity planning require forecasting as well. Examples arehandling times and form of shrinkage such as sick leave. There are some differences, andusually not the same granularity is required (sick leave is a parameter at week level), butoverall the same methods can be used. Note that handling times also show fluctuationsduring a day. Aktekin [4] and Tan & Netessine [111] observe that the time of the dayaffects agents’ handling times. For example, they may speed up their service when the callcenter is busy.
Agent scheduling concerns the construction of schedules such that, amongst other objec-tives, SLAs are expected to be met to the extent possible. Commonly used SLAs are 1minus the tail of the waiting time distribution (also referred to as the service level (SL),often taken as 80% answered within 20 seconds) and the expected waiting time (the averagespeed of answer , ASA). With the SLA as constraint the minimum required staffing in everyinterval is determined, sometimes explicitly, or implicitly in the scheduling algorithm. If itis done explicitly, and then given to the scheduling algorithm, then it is often done by theforecasters and even called workforce forecasting . We will call it (safety) staffing , as it en-tails planning overcapacity to deal with fluctuations in workload. Staffing is probably thebest-studied part of WFM, and the starting point of many scientists interested in WFM,explaining why many queueing scientists (used to) work on call centers.We will make a difference between single and multi-channel and single and multi-skilloperations. Staffing is done at the interval-level, usually 15 minutes. Even though agentscan often handle multiple skills and/or channels, they are often scheduled during one ormore interval to work on a single skill and/or channel. We will first look at staffing for thesesingle-skill single-channel operations, starting with inbound. Then we will look at staffingin a blended multi-channel environment and in the presence of skill(s)-based routing , wherein real-time a contact from the optimal channel or skill is being pushed to the agent.It is commonly assumed that arrival rates and numbers of agents are stepwise constantfunctions, constant during each quarter. This is motivated by the fact that arrival rates areexpected to change little during each quarter, and that schedule changes are only possibleat the quarter. In this situation the so-called SIPP approach (Green & Kolesar [56]) is7n obvious choice: you assume stationary in each interval, and use a stationary queueingmodel. The M | M | s or Erlang C model is most commonly used in practice. Allowingfor customers to abandon is a relevant feature that improves the approximation. Themodel including abandonments is commonly written as M | M | s + G , with + G denotingthe generally distributed patience. In the case of exponential patience we call it Erlang A.Seminal work on these models was done by Palm [99] and Baccelli & H´ebuterne [20], Zeltyn& Mandelbaum [121] gives simple formulas for the M | M | s + G using integrals over thepatience distribution. Sze [110] added retrials.Compared to the Erlang C the Erlang A has one more parameter: the patience dis-tribution or its expectation, depending on the exact model used. The waiting time ofa customer is the minimum of its patience and the time to service, thus the patience isa censored variable. The famous Kaplan-Meier method ([77]) can be applied, leading toresults as in Brown et al. [29] who did a thorough analysis of call center data. Note thatin practice patience is usually underestimated because practitioners often only look at theabandoned calls. However, taking an expected patience of 5 or 10 minutes is already muchbetter than applying Erlang C. You can also use the patience as a tuning parameter, butthen you need data on the achieved service levels.A handful of papers focuses on the patience distribution and how it affects call centerperformance and staffing decisions. For example, Mandelbaum & Zeltyn [96] study theimpact of various patience distributions on M | M | s + G queues. They observe approximatelinearity between the probability to abandon and the average waiting time when there isa low to moderate abandonment rate. Roubos & Jouini [105] empirically show that thehyper-exponential distribution is an accurate representation of the patience distribution.Aktekin & Soyer [5] conduct Bayesian analysis built upon different families of distributions.Ye et al. [120] estimate the hazard function of customer patience time with a nonparametricapproach. It is worth mentioning that Whitt [118] show that the patience distribution hasa bigger impact than the service time distribution for the same expectations.Erlang A, compared to Erlang C, gives also the possibility to include the abandonmentrate in the SLA, both separately, the fraction of abandonments needs to stay below forexample 5%, or implicitly in the SL ([76]). It is common in science to use the virtualwaiting time : the time an arbitrary customer would have to wait if her patience were ∞ .However, this measure is not measured in a call center, thus the performance cannot beverified. In practice other definitions are used, for example the fraction of all calls beinganswered within the time to answer . For definitions and ways to compute the SL fordifferent definitions see Jouini et al. [76].It is interesting to note that delay announcements, which provide estimates of the wait-ing time, influence the patience. Psychologically, “uncertain waits feel longer than knownfinite waits” [93]. On the other hand, the delay announcement can also induce some cus-tomers to balk or abandon earlier, leading to peaks in abandonments. This, in its turn,influences the waiting times [48, 11, 74, 69, 71]. Ak¸sin et al. [3], as one of the latest workon this topic, applied a series of Cox regression to a bank call center data with delayannouncement messages every 60 seconds and revealed that both the content (i.e., howdetailed waiting time information is offered) and the sequence (i.e., positively/negatively8hange of the waiting situation) announcement messages, the congestion levels of the callcenter and the characteristics of customers have a statistically significant impact on aban-donment behaviour, however, due to the complexity, no staffing decisions considering delayannouncements have been studied yet.SIPP combined with an Erlang model is the most commonly used method in practice.However, there are a number of problems with such an approach. We will discuss themone by one.In the first place, the queue is not in a stationary situation at the beginning of eachinterval. Depending on the parameters of the previous intervals, you might for exampleexpect a backlog. There are a number of methods available with this, of which, accordingto Babat [19], the stationary backlog carryover (SBC) approach by Stolletz performs best([109]).In the second place, the SIPP predicts expected performance. If you schedule usingSIPP at the level of your SLA, then in roughly 50% of the cases you won’t reach your dailySLA. The error can be quite big (Roubos et al. [106]). In practice, this is unacceptable. Asolution might be to look at quantiles of the distribution of the service level ([106]), butusually the problem is solved by intra-day management.In the third place, on top of the transient effect we just discussed, there is uncertaintyabout the arrival rate, the overdispersion we found in the previous section. Schedulingaccording to the expected rate is suboptimal, Ding & Koole [44] propose a method thatintegrates the intra-day adaptations into the staffing step, leading to a newsvendor-typestaffing method. Whitt [119], Steckley et al. [108], and Liao et al. [90] also incorporateuncertain arrival rates into staffing planning.In the fourth place, there are many factors that influence performance that are notmodeled by Erlang C nor Erlang A, such as the impact of short unscheduled breaks andthe behavior of agents under longer periods of high workload. Only recently the firstattempt to validate the Erlang models based on realized service levels was undertaken(Ding et al. [45]). By studying agent data together with call data it was indeed foundthat breaks have a huge impact on performance. One way to solve this is to move toa statistical/machine learning approach that takes all features into account, as in Li etal. [88]. This is even better than simulation because implicitly the behavior of the agents istaken into account; to use simulation it has to be modeled explicitly which is hard becauseof differences between agents and the lack of knowledge on how and when for examplebreaks are taken.The widely used Erlang97 Excel add-in (Bromley [28]) also has the option to computeabandonments. It is based however on a waiting-time quantile of the Erlang C, therebymaking two errors: it does not model the fact that Erlang A generally has a better SLthan Erlang C because some customers leave the queue, and it assumes the patience is thesame for all customers (van Eeden et al. [47]).It is hard to obtain qualitative insights from the Erlang formulas, for example howthey behave when you increase scale. Square-root staffing does. For λ the arrival rateand β the average handling time, it says that staffing should be at λβ + α √ λβ with α aparameter depending on the SL only. The square root can intuitively be interpreted: if9ou add 2 i.i.d. r.v.s then the standard deviation is multiplied by √
2. The same holds forthe safety staffing, because it is there to handle fluctuations in load. This clearly showsthe economies of scale which is one of the reasons why we want agents to be multi-skilled.It also shows decreasing returns, as λβ + α √ λβ is concave in λβ , which tells us that not allagents need to be multi-skilled. Halfin & Whitt [59] introduced this Halfin-Whitt regime in which the load increases but the delay probability is held constant. Since then manypapers have studied this regime in many different variants, see [102, 60, 27, 50] for recentones. Unfortunately these ideas are very little used in practice.Next to inbound a variety of other channels are used. They can be divided into syn-chronous and asynchronous communication. Email, webforms and old-fashioned mail andfax are asynchronous. Usually the time-to-answer is multiple hours or days, at least multi-ple intervals. This means that fluctuations have to be dealt with by flexibility in scheduling,not by safety staffing. A noteworthy synchronous channel is chat . The difference with in-bound from the point of view of WFM is that a chat agent can do multiple chats inparallel, usually 2 or 3. When all agents are saturated customer wait in the queue, justlike an Erlang system. The parallelism increases the efficiency, when an agents answer onecustomers the other(s) can formulate their responses. However, it makes the total timeper chat longer: sometimes a customer has to wait for a chat to be available. Quantifyingthe durations are challenging, but can then be used to extend the Erlang models for chat.See Koole [79] for more details on an implementation.Moving decisions to a later moment when better information is available is a generalprinciple. One way to do this is to move the decision which type of task to do from theschedule to the routing. In a multi-channel environment this leads to blending , in a multi-skill environment to skill-based routing (SBR). We discuss how staffing can be done in theseenvironments.Blending is usually executed by blending synchronous and asynchronous channels, suchas inbound and email or outbound. When the asynchronous channel can be interruptedto deal with priority with inbound, then staffing is easy: inbound is staffed as discussed,and the overcapacity with respect to the expected load is filled with email. Things getmore complicated when the asynchronous channel cannot be interrupted as in the caseof outbound. This case has been studied in Bhulai & Koole [23] and Gans & Zhou [53].Both the routing policy and, implicitly, staffing has been determined. No papers discussblending of asynchronous channels such as inbound and chat. A simple policy could be toassign an agent to the channel with the longest waiting customer. To use as little agentsas possible for chat, chats should be assigned to agents already handling chats but who arenot yet saturated.Now we move to SBR. Because of the lack of closed-form formulas for the stationarysituation, simulation is the only viable option for SBR, apart from some approximationsbased on models without waiting (Chevalier & Tabordon [35], Pot et al. [101]) and basedon fluid models considering abandonment targets as the Quality of Service constraints(Gurvich et al. [57], Bodur and Luedtke [26], Bassamboo et al. [22]). But why run a long-term simulation to find stationary behavior when it is easier to do a short-term transientanalysis, for example of a day? For this reason most studies tackle right away the scheduling10roblem, resulting in little literature on multi-skill staffing alone. Some notable exceptionsare Cezik & l’Ecuyer [30], Gurvich et al. [57], Harrison et al. [61] and Chan et al. [33, 32].
Agent scheduling is the operational process in which agents get assigned to shifts andactivities during these shifts. Activities include the channel and/or skills they have towork on, but also paid breaks, meetings, trainings, etc. Next to the routing, which is partof the telephony/omnichannel switch, it is the part of WFM that is most often supportedby specialized software. There is a wide choice of software vendors, the bigger ones includeGenesys, Injixo, Nice, Teleopti, and Verint. See for example [114] for a list. However, littleis known about their exact workings, Erlang C and simulation are used, the latter oftenleading to very long run times. Fukunaga et al. [49] give some details about Verint (calledBlue Pumpkin at the time). Smaller call centers, and also the ones with less schedulingissues (for example, because they are only open during business hours), often scheduleusing a spreadsheet. Agent scheduling in its generally is hardly studied in the literature:usually unpersonalized shifts are determined, without activities within the shifts, which isactually shift scheduling.In its simplest form agent scheduling consists of three steps, as illustrated in the toppart of Figure 3: for each interval the required staffing levels is determined (e.g., usingan Erlang formula), the most efficient way to cover the staffing needs by the availableshifts is determined (potentially using integer linear programming (ILP), and these shiftsare assigned to agents in some way (for example, by letting them choose in the order ofseniority). The first to formulate a solution for the covering problem of the second stepwas Dantzig in [41], in which he considered toll booths at a US bridge.There are various reasons why such an approach is highly suboptimal and even infeasi-ble. Often employees have different types of contracts, therefore in step 2 different groupsof shifts should be identified, otherwise no match between agents and shifts can be made.Furthermore, many agents have personal preferences. Satisfying as much as possible iscrucial for employee satisfaction, making that the schedule should be made at the individ-ual level, integrating step 2 and 3, as in the middle part of Figure 3. Dealing with thesepersonal preferences is evidently part of WFM software, but hardly studied scientifically.A much better studied subject is the integration of step 1 and 2, as in the lower partof Figure 3. The reason for combining them is that the staffing levels of step 1 are hardto cover with shifts, leading to considerable overstaffing. Often SLAs are formulated atthe daily level, thus SLs are allowed to fluctuate a bit, certainly if that leads to moreefficient schedules and if the daily constraints are met. Integrating step 1 and 2 makesthe optimization problem highly non-linear. It can be rewritten as ILP but a the cost ofhaving many binary variables. Add to this the fact that we should schedule at the weeklylevel (necessary because of constraints on the schedules related to numbers of working daysper week and start times), then we are stuck with heuristics such as local search. In multi-skill settings we need simulation to get reliable evaluation of possible solutions, leading us11 taffing Shift scheduling Shift assignment ScheduleStaffing SchedulingShift assignmentStaffingScheduling Shift assignment ScheduleSchedule
Figure 3: Short-term operational planning processto simulation-optimization with stochasticity on the SL constraints, problems which areknown to be notoriously difficult.In a single-skill situation, Koole & van der Sluis [80] uses SIPP and shows that undera very simple shift structure, a suitable local algorithm can find optimal schedules. In atransient single-skill setting, Atlason et al. [14] use simulation to generate cutting planesused in the shift optimization module. Liao et al. [91] also use simulation. They combinestochastic programming and robust optimization to work out scheduling with uncertainarrival rates. Robbins & Harrison [103] solve a stochastic scheduling problem to minimizethe combined cost of agents and missing QoS targets. Later, Gans et al. [52] considered atwo-stage scheduling problem which allows adding and removing agents based on updatedforecasts at midday.In a multi-skill situation, Pot et al. [101] & Bhulai et al. [24] use an overflow approxi-mation for SBR, similar to Chevalier & Tanbordon [37], to build a multi-skill schedulingalgorithm. Bodur and Luedtke [26] also replace the abandonment level by the approxi-mating formula and solve a two-stage stochastic programming for scheduling with Bendersdecomposition. A main drawback of these approximations is unrealistic assumptions ofidealistic fluid routing policy. Moreover, service levels cannot be approximated.Again leveraging on simulation, Cezik & l’Ecuyer [30] extends the approach of Atlasonet al. [14] to multi-skill staffing. Avramidis et al. [16] extends the cutting plane method tosolve scheduling problem over a day (i.e., multiple periods). Running times however arevery long.The current state-of-the-art is Li et al. [89] which uses machine learning (ML) to speedup the simulations. This makes it possible to solve industrial-size weekly multi-skill multi-12hannel problems in several minutes. Solving the same problem without using ML takesmuch longer, see Li et al. [87]. Note that it is inevitable that the SL fluctuates, becauseof our daily SL objective. In call centers planners spend long hours adapting schedulesmanually to get smooth service levels, evidently a useless and expensive practice.Note that all these problems consider shift scheduling: they determine shifts, but do notdetermine the activities within the shifts. This adds a layer of complexity far beyond thecurrent state-of-the-art, but it is required in the operations and done by WFM software.On the other hand, it can be argued that the activity assignment should be done at therouting level, although some activities (such as meetings) need to be planned in advance.The fact that these methods are not at the level of agents but at best at agent group levelmakes them better suitable for capacity planning, which is the subject of the next section.
Capacity planning is the holy grail of WFM. To be able to do long-term planning you haveto take into account how you all the shorter-term processes, thus all decisions at all levelsimpact capacity planning. On the other hand, it does not have to be done at the samelevel: while agent schedules need to be determined at the quarter level, capacity planningcan often be done at the week level.Let us first consider capacity planning used for budgeting. The long-term forecast is anessential element for this process. Based on the forecast schedules could be made, just asfor agent scheduling. Then the costs of these schedules could be determined leading to thebudget. However, apart from some practicalities such as the lack of information on agentsstill to be hired, runs are often too long to compute the multi-year horizon needed for thebudget, especially because Excel has to be used as the planning tool is not appropriate forthis kind of calculation. A simple fast calculation is to estimate the budget proportionalto the volumes: if the volume increase by x % then the costs will also increase by x %. Ofcourse we make an error: costs are not linear in the forecast, but for small changes theerror is expected to be small, probably much smaller than the forecasting error. Moreadvanced methods, such as an ML model to estimate costs based on the forecast and otherparameters, have been successfully used in practice.More complicated are decisions related to the hiring (and perhaps firing) of agentsand decisions about the training of new skills to existing agent. Hiring and training newagents is a lengthy process that can easily take 3 months or more, thus the capacity hasto be planned well in advance. In the simplest case it is just deciding how many agentsare needed, but often there are choices in types of contract and initial skill sets. Todetermine which types of agents to hire shift scheduling has to be done, over a longerperiod, starting from the current pool of agents, taking agents resignations and shrinkage into account. Shrinkage are all activities that avoid agents from being available for phonework (or other types of contacts), from holidays and illness to meetings and paid breaks.The operational schedule should take activities like meetings and short breaks into account,capacity planning all of them. Note that they are sometimes unpredictable, such as illness,13nd sometimes planable, such as when agents go on holidays or when meetings take place.Both types complicate capacity planning. Many call centers do capacity planning in agrossly simplified way by replacing all randomness and advanced calculations by fractionsas explained in the previous paragraph on budgeting. Probably even more call centers useno calculations at all but make rough estimations, potentially making big errors in theoptimal amount of agents and especially in the optimal contract and skill mix. Very fewutilise more advanced technology, finding the optimal agents pool and determining whichagents can best be added to the current pool is hardly done.There are no papers solving the pool optimization problem completely. Some papers,such as [16, 24, 87], as discussed in the previous section, solve the shift scheduling problemfor a week or a day, but methods have to be found to extend this to longer periods or tosomehow aggregate weekly results to say a year. Furthermore, all forms of shrinkage haveto be added. In our opinion, this is the biggest remaining challenge in WFM, and the onlypossible solution method we see is a time-consuming simulation-optimization procedure,possibly sped up using ML as in [89].A simpler solution to the pool composition problem might be to use some rule ofthumb. Chevalier et al. [36] studies, using approximations based on networks of overflowqueues, that 80% specialized and 20% fully flexible agents works surprisingly well in manysituations. This holds for the staffing problem, random form of shrinkage will likely makethe need for flexible agents higher in the pool composition problem. Also Wallace &Whitt [115] show, using simulations, that a little flexibility goes a long way, in a situationwhere agents have 1 or 2 skills and a topology that “connects” all skills. Routing in call centers is most of the static: it is entered once in the telephony switch orACD (Automatic Call Distributor) and it does not depend on current service or staffinglevels. Typically, routing is arranged through priorities of agents for certain types of calls,which can be different per agent: agents typically have primary and secondary skills. SLAscan be different for all skills and channels, and priorities which SLAs are most importantto be met can be set. When multiple agents with the same priority can handle a call, thenusually the one with the longest idle time since the last call is selected. (Note that this ruleopens the possibility for the agent to trick the system: by going on a one-second break heor she has again the shortest idle time.) When an agent becomes idle, he or she is assignedto the longest waiting call among the highest priority calls. Nowadays, more sophisticatedrouting rules are supported by ACD like Genesys. For example, threshold policies basedon the queue size or customers’ waiting time. Customer satisfaction can also be consideredby assigning calls to the agent who has the best resolution rate. Although this gives manypossibilities for routing, and many parameters to be set, there is no guarantee whatsoeverthat the best possible performance is achieved. For this reason, intra-day managers oftenchange priorities of agents during the day. Unfortunately, they are not supported bysoftware and cannot oversee all implications of their actions which are therefore often14ighly suboptimal. Systems such as [15] try to improve such situations. But experiencesare mixed due to a lack of understanding and control by the user. Ideally, instead of lettingintra-day managers make last-minute adjustments to the system, the routing rules in theACD should be designed with a full evaluation, validation and optimization.Many routing algorithms have been proposed in the literature, but mainly for a heavy-traffic regime with fixed staffing, such as [95, 98, 12, 13, 10, 116]. Little studies on SBRexist that take various service levels and also fairness between agents into account. Notableexceptions are Chan et al. [31] and Li & Koole [86], both using simulation. [31] considers apolicy that depends through weights on the service and occupancy levels. The weights thatgive optimal stationary performance are obtained requiring full knowledge of arrival ratesand staffing levels. [86] is also based on weights, but introduces a heuristic to obtain thebest performance by the end of a day without explicitly using the system’s parameters butthe service level up to that moment, which is the usual performance measure in practice.Routing between channels is called blending. Most of the studies consider blendinginbound and outbound calls. Bhulai & Koole [23] and Gans & Zhou [53] both show that anon-work-conserving policy is optimal: some agents should be kept free for inbound calls,even though outbound calls are waiting to be handled. Otherwise, the SL on inbound willbe too low. This greatly improves the efficiency compared to separate agent groups, andit is robust to changes in parameters such as the arrival rate. Other threshold policies canbe found in [100, 42, 81], to name a few. Legros et al. [85] develops a threshold policy thatadaptively adjusts the number of agents reserved for inbound calls to achieve the SLA ofinbound calls as well as maximise the throughput of emails.As mentioned in the staffing section, no papers have discussed the blending of asyn-chronous channels such as inbound and chat. While a few papers deal with the routing ofchats (Tezcan and Zhang [113], Legros et al. [25]), they both consider single chat type andidentical agents. Tezcan and Zhang [113] gives a routing rule that minimizes the abandon-ment rate and the staffing level in the long run. Legros et al. [25] considers that customerscan also abandon during the service due to long handling times, and propose a routingpolicy which allows agents to not work up to the maximum number of chats even whenthe queue is not empty. Further relevant references include Cui and Tezcan [40] and Luoand Zhang [92].One may notice that the large body of literature mentioned above focuses merely on callcenter efficiency. Their targets are set to minimize the speed of response, abandonments,SL, and so on. The quality metrics such as call resolution, customer satisfaction and agentpreference are barely taken into account. One of the reasons is that the relevant datacannot be easily retrieved from the call center system, requiring extra processing steps.Some exceptions are Ghareeb et al. [55] and Zhan and Ward [122].Intra-day management are changes made to the deployment of agents during the day ofexecution (or just before). They can be related to the activities they do. Sometimes thisis motivated by the SL: agent priorities can be changed, or for example meetings can becancelled to improve the SL or even scheduled at the last moment when many agents areidle. The changes in activity can also have other motivations, such as the urgent need toschedule a meeting. At all times the consequences to the SL should be taken into account.15ext to changes in activity intra-day management deals with changes in working hours.This starts as soon as the schedule is published by the planners, when for example agentsrequest schedule changes for personal reasons, or when the forecast has changed signifi-cantly and more or less agents are needed. This continues throughout the day of execution,many call centers have a flexible workforce layer through which they can up or downscaleon a short notice, even during the day itself. The management of this is often not basedon SL predictions, and also few papers address this type of issue. An exception is Rouboset al. [104] in which the staffing levels are adapted during the day in an optimal way as toobtain the required SL by the end of the day.
We start this section with some general guiding principles on how the workforce should beplanned.Decisions that limit flexibility should be taken as late as possible. That way we canbetter deal with fluctuations, because for all types of fluctuations it holds that over timemore information becomes available, i.e., the variability of the unknown variable decreasesover time. E.g., take a multi-skilled call center. During the scheduling phase skills can beassigned to agents blocking them for other skills, unless traffic management changes theschedule. Letting SBR do the assignment is much more efficient, even a fixed assignmentat the last moment is better because the latest forecast can be used, and availability isfully known, you known for example who is ill. A re-assignment could be part of intra-daymanagement, but we then schedule in the first place?An objection to SBR is that agents have to change skill (e.g., move from one language toanother) often, which can be annoying. Similar objections hold against blending, especiallywhen email handling is interrupted for inbound calls. Good routing however can avoid that:in certain systems you can limit the number of times that an email might be interrupted,and one can think of similar solutions for blending.When the decision is related to something that influences employee satisfaction thenmaking decisions later might be more efficient but at the same time decrease employee sat-isfaction which negatively impacts the performance of the call center. However, flexibilityis not always required at the maximum level, asking a few fraction of the employees tobe flexible might give you the majority of the advantages of flexibility, which is the nextguiding principle.A little flexibility goes a long way. Wallace & Whitt [115] observed this for the numberof multi-skilled agents in an SBR setting, but this holds in general: a few agents withpart-time shifts, a few back-office agents who can help in the front-office (the call center),etc. Another way to state it is that flexibility shows decreasing returns. From this italso follows that you can better have a bit of multiple types of flexibility, than a largeamount of one type of flexibility. However, using all these forms of flexibility together inthe smartest way is a challenging task that requires tooling, nobody can immediately graspthe consequences of one agent less on all skills, even the one he or she does not have. That16rings us to the final guideline.Automated decision making is preferred over manual. Few decisions are fully manualor automated, for most decisions there is some tool (which can be a spreadsheet) thatsupports the decision. The better the tooling, the less human interference is required. Weargue that a higher agree of automation is usually better: advanced knowledge in the formof algorithms can be implemented in software, knowledge that most planners will neverobtain. An important constraint is the outcomes should be transparent, to be able toexplain the outcomes and interact with it. As an example, take an agent who wants theafternoon off. Usually an intra-day manager looks at the current SL, and makes a decisionon the basis of that. It would be much better to have a SL prediction for the rest of the dayto base the decision on, but that requires advanced tooling. From there it is a small stepto an automated system that compares the predicted SL with the SLA and that makesa decision on that basis. Clearly this makes the call center more efficient but also makesthe WFM smaller, leading to additional costs savings which are usually higher than thesoftware costs.When designing a call center WFM is only one of the aspects that have to be taken intoaccount, each decision should also be evaluated from the point of view of WFM: what arethe consequences for the SL, the agent satisfaction, and the efficiency, i.e., the costs? Quiteoften WFM is not in the loop when design decisions are made. E.g., when the decision ismade not to look at AHT anymore to allow agents to give the best possible service, whatare the consequences on the required workforce if the AHT gets much longer? It mightbe customer-friendly to expand the opening hours, but what are the consequences for theSL? There are many questions of this type. The tools described in the previous sectionscan often be used to solve these problems.There are different examples in the literature of designs that are well-built, also fromthe point of view of WFM. We cite a few of them. Jouini et al. [75] studied a multi-skilled situation with different teams where every team has its own customer base. Toobtain flexibility and with that economies of scale unidentified callers are routed to theleast occupied team. This combines motivational incentives, such as being able to compareteams on quality-of-service and up-sell, with WFM aspects. Legros et al. [83] proposeda new SBR architecture for the situation that every agent has two skills per agent. Theefficiency of the proposed architecture is compared to chaining using simulation. Ak¸sinet al. [2] discussed the optimal capacity levels under two different outsourcing contractmodels: volume-based and capacity-based contracts. They observed that no contract typeis universally preferred, and both the operating environments and cost-revenue structuresmatter. Gans and Zhou [54], Hasija et al. [62], and Gurvich and Perry [58] studied theoverflow operating rules in the outsourcing environment. Some call centers offer a call-backoption to smooth the arrival traffic, whereby customers may register a request when allagents are busy. Later the system will call them back within a pre-specified time slot. Inthis way, waiting inbound turns to the outbound task at scheduled moments. The analysisof such systems is conducted in [8, 9, 64, 84, 82].17 cknowledgements
We are grateful to the stimulating environment that CCmath of-fers and that made this paper and its research possible. We are especially grateful toGiuseppe Catanese, Alex Roubos and Wout Bakker for their feedback. CCmath has itsown algorithms for forecasting, staffing and scheduling of which we were not allowed to dis-close the details for commercial reasons. Note that this overview might be biased towardsthe situation found at CCmath’s clients.The second author also wishes to thank the Vrije Universiteit for the hospitality thatwas offered to her over multiple years.
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