The Math of Contact Center Staffing

May 2006 By Penny Reynolds

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Ok, this isn't the tough math part yet. To process 20 hours of paper workload, 20 staff would be needed. The reason for the 1:1 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 timeframe.

Determine Call Center Staff Requirements

Now it's time to staff the call center. These employees are getting 400 calls, and each call takes an average of three minutes to handle - two minutes of conversation and another minute of after-call work. Again, we have 1200 minutes or 20 hours of workload. How many people are needed?

Unfortunately, we can't 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 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 hours 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 staff members, or will we need 24 or even 30? 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 smaller 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. We use a model called Erlang C that takes into account the randomness of the arriving workload as well as the queuing scenario of the calls.

An Example of Erlang C

Let's take a look at Erlang C predictions based on the 20 hours of workload we defined earlier.  Table 1 shows what would happen with when we have from 21 to 28 staff (Column 1) in place to handle the 20 hours of incoming call workload.

TABLE 1 Staffing and Service Comparison

Number of Staff	Delayed Portion	Delay of Delayed Callers	Average Delay (ASA)	Service Level (20 sec)
21	76 %	180 sec	137 sec	32%
22	57%	90 sec	51 sec	55%
23	42%	60 sec	25 sec	70%
24	30%	45 sec	13 sec	81%
25	21%	36 sec	8 sec	88%
26	14%	30 sec	4 sec	93%
27	9%	26 sec	2 sec	96%
28	6%	23 sec	1 sec	97%

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. So, with 24 staff in place, the Erlang C model predicts that 30 percent of callers would be delayed, and 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 agents 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.  

The fourth column represents service level. Service level represents X percent of callers that are handled in a specified Y seconds of delay time. This table shows the percentage that are handled within a specified 20 seconds of wait time. A common call center service goal - particularly for a catalog sales center - is 80 percent of the calls handled in 20 seconds or less. To meet this goal, we'd 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 often seen in call centers, there's really no such thing as an "industry standard" for what a service goal should be. 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 if the goal should be higher or lower based on the business environment or customer demands.

Customer expectations certainly have risen when it comes to speed of answer expectations. More and more callers are basing their expectations and judging your service on their last, best service experience. Looking 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 trade-offs to determine the impact on cost and on service 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 bodies in chairs are added. But service is not affected to the same degree each way, and this is a terribly important phenomenon to understand about call center staffing.

Let's say you decide 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 you adjust the staff numbers up or down, there are two very different impacts. First, if you add a person or two, the average speed of answer (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's look at the effect of subtracting staff from our 24 person requirement.  When we subtract one, two, and three persons 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 another 86 seconds! By taking staff away, service worsens and it does so dramatically at some point. 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.

Penny Reynolds is a founding partner of The Call Center School, a company that provides a wide range of educational offerings for call center professionals. She can be reached at (610) 5812-8410 or by email at: penny.reynolds@thecallcenterschool.com.