Call Center Staffing Mathematics

By Penny Reynolds

Sharpen your pencils. Dust off the calculator. It’s time for a math lesson.

Running a successful call center operation means managing by the numbers. And the most important number of all is the number of bodies responding to customer calls each hour. Since more than two-thirds of call center operating costs are related to personnel, getting just the right number of staff in place is critical in terms of both service and cost. This article outlines a systematic process for calculating call center resource requirements and evaluating the most important service and cost tradeoffs.

Calculating Workload: The first step in the process is forecasting calls, analyzing historical data, trends and seasonal patterns to arrive at monthly estimates, then using day-of-week and time-of-day patterns to break down the numbers into hourly or half-hourly forecasts.

With these call volume forecasts and some assumptions about average handle time (AHT), we’re ready to perform a simple calculation to arrive at staff workload. It is simply the number of calls forecast for each hour multiplied by the average handle time of each call. The average handle time (AHT) is made up of two components: actual conversation or talk time plus any after call wrap-up time associated with the call. The wrap-up time can include almost anything – filling out a form, updating the customer database, etc.

This handle time will likely vary by time of day as well as by day of the week. For example, you may find that AHT is higher during the evening shift since you may have newer staff working the undesirable hours, or simply have callers who like to talk a little longer during the wee hours of the morning! Most call centers simply use an average number for handle time across the board, which can be dangerous if there is significant variance. Imprecise numbers can contribute to understaffing or overstaffing, so it is best to use numbers that actually reflect time-of-day or day-of-week patterns.

The workload number is then used to determine how many base staff are needed to handle the calls. What makes staffing for a call center different than any other kind of staffing situation is that this workload does not represent typical work patterns. Let’s compare an incoming call center to a group of clerical workers processing mail in the same company. Between 8:00 and 9:00 a.m., the clerical staff has 400 pieces of mail to process and each piece takes three minutes to handle. That is 1,200 minutes, or 20 hours of workload. How many people need to be working to accomplish all the work by 9 a.m.?

Okay, this isn’t the tough math part yet. To process 20 hours of workload, 20 staff would be needed. The reason for the one-to-one ratio is that the mail tasks represent sequential workload. In other words, the staff can process the work as back-to-back tasks and each person can accomplish one hour of work in an hour’s time.

Determining Call Center Staff Requirements: Now it is time to staff the call center. These employees are getting 400 calls and each one takes an average of three minutes to handle – two minutes of conversation and another minute of after-call work. Again, we have 1,200 minutes or 20 hours of workload. How many people are needed?

Unfortunately, we cannot handle the calls with only 20 people. At 8:05, there may be 22 calls arriving, meaning all 20 agents are busy, with another two calls in queue. Then at 8:15, there may only be 16 calls in progress, meaning four of our staff are idle. Those four people won’t be able to accomplish a full hour’s work, simply because of the way the calls have arrived. In an incoming call center, the work doesn’t arrive in a back-to-back fashion. Rather, the work arrives whenever our customers decide to place calls, so we have random workload instead of sequential work. This brings us to the first math rule of call center staffing: You must have more staff in place than hours of actual work to do.

So how many extra do we need? For 20 hours of workload, will we need 21 agents? Twenty-four? Thirty? The number of staff needed depends on the level of service we wish to deliver. Obviously, the more staff we have, the shorter the delay. The fewer the staff, the longer the caller will wait.

Determining what happens with a given number of resources in place to accomplish a defined amount of workload requires a mathematical model that replicates the situation at hand. There are several telephone traffic engineering models available and one in particular is well suited to the world of incoming call centers. We use a model called Erlang C that takes into account the randomness of the arriving workload as well as the queuing behavior (holding for the first available rep) of the calls.

An Example of Erlang C: Let us look at Erlang C predictions based on the 20 hours of workload we defined earlier. The table below shows what would happen with anywhere from 21 to 28 staff (Column 1) in place to handle the 20 hours of incoming call workload:

Number of StaffDelayed Portion  Delay of   Delayed CallersAverage Delay
Service Level
(in 20 sec)
2176 %180 sec137 sec32%
2257%90 sec51 sec55%
2342%60 sec25 sec70%
2430%45 sec13 sec81%
2521%36 sec8 sec88%
2614%30 sec4 sec93%
279%26 sec2 sec96%
286%23 sec1 sec97%

Let’s take a look at each of the columns and measures of service. The second column shows the portion of calls that would find no agent available and go into queue and the third column shows how long those delayed callers would wait, on average. Therefore, with 24 agents in place, the Erlang C model predicts that 30 percent of callers would be delayed and that they would wait an average of 45 seconds in queue.

The third column represents the average delay of all calls, including the ones that are answered immediately. So, with 24 staff in place, 30 percent of calls would go to the queue and wait there 45 seconds, while the other 70 percent would be answered immediately. The average delay, or average speed of answer (ASA) is the weighted average of both these groups [(45 x .30) + (0 x .70)] = 13 seconds. It’s important to understand that this ASA number is not the average queue experience for the callers. Either they wait (and do so for an average of 45 seconds), or they don’t wait at all. The ASA isn’t a “real life” number – it’s a statistic to represent the average of the two other numbers.

The fourth column represents service level. Service level represents the percentage of callers that are handled in a specified amount of delay time, measured in seconds. This table shows the percentage that are handled within a specified 20 seconds of wait time. A common call center service goal is to have 80 percent of all calls handled in 20 seconds or less. To meet this goal, we would need 24 staff in place, yielding a service level of 81 percent in 20 seconds.

Staffing to Service Goals: So what should your service goal be? While there are some common goals seen often in call centers, there is no such thing as an industry standard for service level goals. Setting a speed of answer goal depends upon many different factors. Call centers need to consider enterprise goals and marketing strategies, competitor standards, and most importantly, the expectations of customers. We often find that call center management marches toward the same service goal year after year without ever considering whether the goal should be higher or lower based on the business environment or customer demands.

Customer attitudes have certainly changed when it comes to speed-of-answer expectations. More and more callers are basing their perspective and judging your service on their last, best service experience. Taking a look at your call center’s ACD reports and looking at when callers begin to abandon calls will give you some idea about a worst case delay scenario. But setting the best case goal should involve getting feedback from senior management, customers, competitors, and other centers – and then evaluating cost and service tradeoffs to determine the impact of raising or lowering the goal.

Relationship of Staffing and Service: Let’s take one more look at our staffing table and review the impact on service as staff numbers change. Obviously, delay times increase as agents are subtracted, and service improves as staff are added. Although service is not affected to the same degree each way, this is a terribly important phenomenon to understand call center staffing.

Let us say we have decided we need to have 24 staff in place to handle the 20 hours of telephone workload in order to meet an 80 percent in 20 seconds service level goal. If we adjust the staff numbers up or down, there are two very different results. First, if we add a person or two, the ASA improves from 13 seconds to eight seconds with 25 staff, and then to four seconds with 26 staff. The first person added yielded a five-second improvement, with the next person gaining us only a four-second improvement, and a third person would result in an ASA of two seconds, a two-second improvement. Adding staff results in diminishing returns, with less and less impact as the staff numbers get higher.

Now let us look at the effect of subtracting staff from our 24-person requirement. When we subtract one, two, and three agents our ASA increases to 25 seconds, 51 seconds, and 137 seconds respectively. The first person out resulted in an increase of 12 seconds, the second in another 26-second decline, and the third in a jump of another 86 seconds! By taking staff away, service worsens, and it does so dramatically at some points. There are especially big jumps as our staff number gets closer and closer to the hours of workload.

You can view this as both good news and bad news. The good news is that if you’re delivering poor service in your call center, you can improve it dramatically by adding just one more person. On the other hand, when service levels are mediocre to bad, one more person dropping out can send service into such a downhill slide that it’s nearly impossible to recover.

Calculating Shrinkage and Scheduling Requirements: The numbers we’ve discussed so far are purely “bodies in chairs” numbers. These numbers assume that all agents are always available to handle call workload.

But we all know that agents are not available much of the time. So, we must factor this reality into our scheduling requirements so that we end up with enough staff to man the phones.

In calculating staff requirements, a final adjustment needs to be made to factor in all the situations that make staff unproductive. We refer to this unproductive time as “staff shrinkage” and define it as any time for which agents are being paid but are not available to handle calls. We include such activities as breaks, meetings, training sessions, off-phone work, and general unproductivity.

In most centers, staff shrinkage ranges from 20 to 35 percent. We account for this shrinkage factor in our staff requirement by dividing the Erlang C staff requirement by the productive staff percentage (or one minus the shrinkage percentage). In our example, if 24 agents are needed and our shrinkage factor is 30 percent, then 24 divided by seven-tenths (70 percent) yields a requirement of 34 schedules.

Next Steps: In a future article, we’ll help you understand a few more of the numbers associated with call center staffing, including the effect of arrival rate, calculation of staff occupancy, and impact of size on call center efficiencies. We’ll also discuss how workload calculations and staffing models are different when planning resources for handling other channels of communications, such as outbound calls or emails.

Penny Reynolds is a Founding Partner of The Call Center School, a Nashville, Tennessee based consulting and education company. The company provides a wide range of educational offerings for call center professionals, including traditional classroom courses, Web-based seminars, and self-paced e-learning programs at the manager, supervisor, and front-line staff level. For more information, see or call 615-812-8400.

[From Connection MagazineMarch 2003]

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