Efficiencies of Scale in Call Centers

We've all heard of the concept of Efficiencies Of Scale, but many call centers miss opportunities to maximize those efficiencies. Most operations split their call load into several (often dozens!) of separate mini-call centers, in the interests of specialization, and are surprised when expected savings don't materialize.

In our consulting over the past decade, we've helped clients time and again to consolidate small, specialized groups of agents into larger pools, resulting in massive improvements in operational efficiency. Of course, efficiency and effectiveness are two separate things - but customers on hold will never consider an inefficient call center effective. Efficiency is a necessary prerequisite for effectiveness in our industry.

This article is an in-depth (but fun) look at the math involved, and enables you to quantify the impacts of proposed changes in your own operation.

Consider the following two call centers:

Both centers have the same service level targets and the same handling time per call. The only difference between the two is that the Large center recieves 100 times the volume of calls that the Small center recieves on a daily basis. When Erlang C calculations are performed to determine the staff required to meet the service level target, they tell us that the Large center only needs 25 times as many staff as the Small center, 50 agents compared to 2.

Why is this so? How can 25 times as many people do 100 times the work? It's not magic, and it's not fiction. The answer lies in the numbers above, and in the fact that calls arrive more or less at random into any call center.

The Random Arrival of Calls

You've probably seen the famous episode of 'I Love Lucy' where Lucille Ball is at work at a chocolatier's conveyor belt. The chocolates come along the conveyor belt at a nice and even, steady rate, and Lucy is fine. For her first day on the job, she's doing admirably. But when the chocolates start coming a little faster, and at irregular intervals, well, hilarity ensues. Lucy ends up stuffing chocolates into her mouth and pockets, but still misses some.

Many tasks, and many people's jobs, are like Lucy's original environment - the work comes in evenly and goes out evenly. In that environment, twice as many people could do twice as much work, no more and no less. By setting the conveyor belt to just the right speed, the staff could be kept perfectly busy - not sitting idly by, waiting for the next task, and not in the frenzy of motion that made for one of the funniest moments in the history of television.

But an inbound call center cannot control it's flow of work. Customers will call us when they decide to do so - when they get the chance, or think of it, or when it is convenient. When they dial a call center's number, they do not know or care how many other customers are doing the same thing at the same time. Customers do not arrange among themselves when each will call in, in order to efficiently space their calls for the ease of management and staffing in the call center.

The impact that this has on a call center is obvious - there will be busy periods and slow periods, sometimes within minutes of each other. Calls may clump up at times and at other times there may be dry spells. The trick in call center staffing is to cover all of these periods as well as possible, without grossly overstaffing. That is why service levels are so widely used as a measurement of a call center's performance, and why you will probably never see a call center with a target service level of 100% in ANY seconds: because it is the nature of the business that there are peaks and valleys in workload, and it is not always possible (or even reasonable) to staff for the highest peaks.

For more clues as to why it's not always reasonable to staff for the peaks in workload, let's look at some of the features of randomness in small and large groups - whether call centers, lottery draws, or the months in which the members of your family were born.

Randomness in Small Groups

If you look at the different birthdays in your immediate family, you will find that the birthdays are somewhat spread out over the year, maybe with a little clumping. For example, consider my family:

This distribution of birthdays is pretty sparse, and in that sense is very similar to the Small center's workload distribution. One of my family members "arrived" in the same month as another. And overall, there are fewer birthdays than there are months.

Imagine if we didn't know when these birthdays were coming up. We know that there could be as many as two in any given month, but we wouldn't know which month until it happened. We'd have to bake two birthday cakes every month and hope that this was 'the' month. And we'd be wrong most of the time. A full 75% of those birthday cakes would not be used (18 of the 24). And that's a waste of time and money.

The Small center is in exactly this sort of predicament. If two callers call at the same time, they need to be answered with minimal delay. But the rest of the time, most of the time, 2 agents aren't needed.

Randomness In Large Groups

Continuing with the birthday example, I can draw a similar chart for 413 of my closest relatives:

There are a couple of interesting differences here, some of them obvious. First of all, since there are far more "arrivals" than months, there is considerable overlap. Every month has at least 27 people celebrating their birthday, with a peak of 39 people in some months. We could bake 27 birthday cakes a month and be sure they'd be used. Even if we went all out, and baked 39 cakes every month, we'd use 413 of the 468 birthday cakes. Only 12% (55) would go to waste in this example.

The Large center is also an example of high-volume randomness. Since there are 1,440 minutes in a day, and this call center is expecting 10,000 calls, there will be a lot of overlap in the call arrival pattern. There is still a possibility that no one will call in some of the minutes of the day, but that possibility is much lower than it is in the Small Call center.

The peaks and valleys in the workload are in much smaller proportions to the heights of the columns in the Extended Family chart. Instead of 50% or 100% spreads from one month to the next, the larger sample has changes of 3% to 30%. Not only do larger centers lead to more efficient staffing, they can actually be easier to schedule for!

Occupancy Rate

Let's look at the Occupancy Rate in the two sample call centers. In the Small center, which has a forecasted Service Level of 93%, the 2 agents are occupied with customer calls only 22% of the time. We know from the definition of Occupancy Rate that they spend the other 78% of their time waiting for calls. That's more than half of the day, so why not put only 1 person on the phones?

Unfortunately, as the chart below shows, 1 person would be forecast to achieve a service level of only 58%. True, the Occupancy Rate would double, because the single agent would be doing twice as much work, but due to peaks in the call volume, the lone agent would not be likely to answer all callers in a timely fashion. And at other times of the day (more than half the time), the agent would still be doing nothing while waiting for callers.

On the other hand, occupancy levels in the Large center are much higher. With 50 agents on the phones and a forecasted Service Level of 85%, the Occupancy Rate is at 86%. In fact, these agents are doing exactly 4 times as much work each as the 2 in the Small center (that's 86.1111% occupancy vs. 21.5278% occupancy).

So it is possible for 25 times as many people to do 100 times as much work: they just have to do 4 times as much work each.

Too tidy for you? Here's the math.

Some people see these examples and think that the relationships above must only apply to this one example. It looks too neat (I mean, come on, with numbers like 2,4,25,50, and 100, it doesn't look too 'real world'). It must be a coincidence or a fluke that the relationship exists.

Other people see the above examples and are left saying "What? What'd he do?".  I didn't do anything: the relationship was there all along, regardless of what numbers you use. Here's the math in detail:

This math works for any period, whether a minute or a year or 71.5 hours or anything else. But to do the math, you have to know what interval (period) you're dealing with.

When an Erlang C calculation tells you you'll need 2 agents to meet the service level target, it means two agents for the whole period. So in our 24-hour period, we need a total of 48 phone hours (2 x 24 = 48). A common mistake is to treat the 2 agents as 2 FTEs and assume that you only need 14 phone hours - that wouldn't even cover the phones for the full day!

The Occupancy Rate is the Workload divided by the Total Phone Time. For the Small center, that's 10.3 hours / 48.0 hours. In the large call center, we have 100 times the number of calls and the same handling time per call, so the workload is 100 times greater. The Erlang C calculation tells us that with 50 agents, the Large center will achieve a service level of 84.7551%, which I have rounded to 85% . Keeping in mind Point #2 above, we know that all 50 agents are required for the full 24-hour period, a total of 1,200 hours of phone time. The Occupancy Rates for the two call centers are easily calculated:

The fact that this example resulted in a simple 25 x 4 = 100 relationship is not the point. If the Service Level target had been 95%, we would have needed 3 agents in the Small center and 54 in the Large center. That's 18 times as many agents in the Large center this time, still doing 100 times as much work. In that example, each agent in the Large center would be occupied 5.56 times as often as each agent in the Small center. Their Occupancy Rates are 79.73% and 14.35%, respectively.

1. Family birthdays are not perfectly random, but serve as a useful example.
2. No birthday cake will ever go to waste as long as I'm around.
3. The examples above do not discuss workload distributions for simplicity's sake.

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