Hire math

Sep 01, 2005 9:30 PM  By

Sharpen your pencils, dust off your calculator, and get ready for a math lesson: When running a contact center, the most important rule to remember is that numbers matter. And the most important number of all is the number of agents who are in their seats each hour and available to respond to customer contacts.

More than two-thirds of contact center operating expenses are related to personnel, so getting the right number of customer service representatives in place is critical in terms of both service and cost. What follows is a step-by-step process to figure out your resource requirements and evaluate the most important service, productivity, and cost tradeoffs.

  • Calculate workload

    With a call volume forecast and some assumptions about the average handle time (AHT), you can perform a straightforward calculation to arrive at staff workload. It’s simply the number of forecast calls for an hour multiplied by the average handle time of a call. The AHT is made up of two components: actual 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, and so forth.

    This handle time will likely vary by time of day as well as by day of week. It’s best to use numbers that reflect actual time-of-day or day-of-week patterns. You then use this workload number to determine how many base staffers you need to handle the calls.

  • Apply a mathematical model

    Assume that your contact center employees are getting 400 calls and that each call takes an average of three minutes to handle — two minutes of conversation and another minute of after-call work. Therefore, we have 1,200 minutes, or 20 hours, of workload within that hour. 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 only 16 calls in progress, meaning that four of our staff are idle. The work is random, not sequential. Therefore, you must have more staff hours in place than hours of actual work to do.

    So how many extra agents do we need? For 20 hours of workload, will we need 21 CSRs? 24? 30? The answer depends on the level of service we wish to deliver. Determining what happens with a given number of resources to accomplish a defined amount of work requires a mathematical model that replicates the situation at hand. Contact centers typically use a model called Erlang C that takes into account random workload as well as the queuing scenario of the calls.

    Let’s take a look at Erlang C predictions based on the 20 hours of workload we defined earlier. The table “Staffing for a random workload” (top right) applies the Erlang C model to predict that with 24 agents in place, 30% of callers would be delayed and that they would wait an average of 45 seconds in queue. With those 24 reps, we’d be able to meet a common contact center service goal — particularly for catalog sales — of 80% of calls handled in 20 seconds or less.

  • Establish service goals

    There’s really no such thing as an “industry standard” for what a service goal should be, but customers have certainly become much more demanding when it comes to speed of answer. Obviously, delay times increase as agents are subtracted, and service improves as they are added. But service is not affected to the same degree each way. Look at the “Staffing for a random workload” table again. If you adjust the staff numbers up or down, there are two very different effects. If you add a 25th agent, the average speed of answer (ASA) improves from 13 seconds to eight seconds; add a 26th, and you get down to four seconds. Adding staff yields diminishing returns, with less and less improvement as the staff numbers get higher.

    Conversely, by taking staff away, service worsens, and it does so dramatically at some point. You can see especially big jumps as our staff number gets closer and closer to the hours of workload.

  • Determine staff shrinkage

    Unproductive time, referred to as staff shrinkage, is defined as any time for which operators are being paid but are not available to handle calls. Included are breaks, meetings, and training sessions.

    In most contact centers, staff shrinkage ranges between 20% and 35%. To calculate shrinkage, divide 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 the shrinkage factor is 30%, then 24 divided by 0.70 yields a requirement of 34 shifts.

  • Consider agent group size

    Another factor that has a major impact on staffing is the size of the contact center or the agent group. Thanks to economies of scale, facilities handling large volumes of calls will naturally be more efficient than low-volume contact centers.

    As shown in “Effect of call volume on efficiency” (middle right), doubling call volume does not require twice the number of staff to meet the same service goal of 80% in 20 seconds. With a higher volume of calls, each person processes more calls each hour and spends less time waiting for a call to arrive. Since each agent handles more calls, we don’t need as many agents.

  • Measure staff occupancy

    While you want staff to be busy processing calls, keeping them too busy (in other words, with no “breather” between calls) isn’t such a good idea either.

    The measure of how busy agents are is called agent occupancy. It’s the percentage of logged-in time in which an agent is actually busy talking or wrapping up a call. It is calculated by dividing the amount of workload by the staff hours in place. Looking at the same chart, with 12 reps handling 8.33 hours of workload, agent occupancy is only 69%. At double the call volume, with 21 operators in place, twice the workload is handled without doubling the workforce, so each person is busier. In this case occupancy has increased to 79%. Most contact centers aim for occupancy of 85%-90%, since rates higher than that lead to undesirable call handling behaviors as well as burnout and high turnover.

  • Evaluate cost and service concerns

    A final staffing issue has to do with the relationship of personnel to service and cost. All contact centers these days are being asked to cut costs and do more with fewer resources. It is all too common to think of layoffs as a way to respond to the call from senior management to tighten belts. But before you write up the pink slips, make sure you understand the implications of staff cuts.

Let’s assume that yours is a fairly small contact center with fewer than 50 agent seats. Most days you’re meeting your service level goal of 70% in 30 seconds. The table “High occupancy, low service” (page 63, bottom right) depicts a scenario with varying numbers of agents during a half-hour in which you’re getting 175 calls.

As you can see, staffing with 33 agents would enable you to meet your service level fairly consistently. But the loss of one person would decrease the service level from 74% to 62% (and increase the average speed of answer from 30 seconds to 54 seconds). Reducing staff by three would make the service level plunge to 24%, resulting in an average delay of 298 seconds!

And service isn’t the only thing that suffers. With 33 operators in place to handle the call workload, agent occupancy is in a good range at 88%. Taking one person away raises occupancy levels to 91%; taking two agents away results in 94% occupancy; and taking three away means the staff will be busy 97% of the time during the hour. In other words, there will be only 3% (108 seconds) “breathing room” between calls for that entire hour — a level of occupancy that can’t be maintained for long.

There’s another point to consider. The labor cost savings might be outweighed by the increased telephone costs associated with the longer delay times. In this example, with 33 reps in place, the average delay is 30 seconds per call. Multiply that by 350 calls per hour: That’s 10,500 seconds (or 175 minutes) of delay. If we apply a fully loaded telephone cost of $0.05 per minute to the queue time, the total is $8.75. If we try to staff with 30 agents, remember that our average delay increases to 298 seconds. Multiply that by 350 calls and that’s 1,738 minutes of delay, priced at $0.05 for a total of $86.90 for the queue time during that hour. In other words, by eliminating three agents to save money, we’ve just increased our telephone bill by over $78 for that hour!

This situation is even more dangerous in a revenue-producing center such as a catalog operation. If the value of a contact is $50, and agent salaries are $20 per hour, it is easy to see that putting another agent on the phone will pay for itself even if the agent answers only one call per hour that would otherwise have abandoned the queue.

So from three perspectives you can see that a simple staff reduction may not save you any money. In fact, it may cost you more in terms of poor service, high occupancy levels, and increased telephone charges.

Note: The tables used in this article were generated using a software tool called QuikStaff. This tool is available as a free download from http://www.thecallcenterschool.com.


Penny Reynolds is a founding partner of The Call Center School, a Nashville, TN-based educational services company.

Staffing for a random workload
No. of agents Delayed portion Delayed callers’ waiting time (seconds) Avg. speed of answer (ASA) (seconds) Service level (% of calls answered in 20 seconds)
21 76% 100 137 32%
22 57% 90 51 55%
23 42% 60 25 70%
24 30% 45 13 81%
25 21% 36 8 88%
26 14% 30 4 93%
27 9% 26 2 96%
28 6% 23 1 97%
Effect of call volume on efficiency
Calls per hour Workload hours Staff required Staff-to-workload ratio Staff occupancy (workload/staff)
100 8.33 12 1.44 0.69
200 16.67 21 1.26 0.79
400 33.33 39 1.17 0.85
800 66.67 74 1.10 0.90
1,600 133.33 142 1.06 0.94
High occupancy, low service
No. of agents Avg. speed of answer (ASA) (seconds) Service level (% of calls answered in 20 seconds) Staff occupancy
30 298 24% 97%
31 107 46% 94%
32 54 62% 91%
33 30 74% 88%
34 18 82% 86%
35 11 88% 83%