Who Can Figure This One Out!!

[remy]

Here i have some data which we often use here to let people see that a bigger Callcenter is more efficient:

Call volume AHT # Agents Servicelevel Occupancy
10 200 3,6 70% 62%
100 200 26 70% 85%
1000 200 229 70% 97%

Number of agents are calculated with an Erlang-calculator, occupancy is workload/ number of agents.

Hope that this helps to get the pictue clear about the difference in occupancy between a big and a small Callcenter.

[JoeB]

Remy,

First, I am not sure I understand your statement “AHT for the big Callcenter is aimed at 250 seconds en the AHT for the small Callcenter is aimed at 550 seconds” – AHT is a property of the call. You can strive to improve it but you can’t control it directly. For the purpose of this discussion we will assume AHT of 200 seconds in both call centers.

More importantly, I ran your numbers (AHT=200, target SL=70/20) on my software and verified the results using other Erlang calculators. The results are different:

CPH --- Agents --- ASA ---- Occupancy
10 --- 2 --- 17 ---- 28%
100 --- 8 --- 21 ---- 69%
1000 --- 60 --- 20 ---- 93%

As you can see, the ASA is pretty constant, but the utilization increases. (The reason for the more pronounced difference in ASA in the very low call load is that agents (and telephone trunks) are integers, so in a very small call center adding/removing an agent causes a significant change.)

Did you use a commercial Erlang C tool for your calculations or was it developed in-house? For example, your formula for occupancy doesn’t seem right. What is “workload” in your definition “workload/ number of agents”? Occupancy rate is “net” traffic/number of agents. Using my calculations above for 100 CPH occupancy rate for 8 agents is 100/18/8=69%.

Using your number of agents (26) you get 100/18/26=21% which is inconsistent with the 85% you have calculated.

You may want to try another tools (e.g. www.DiagnosticStrategies.com/EasyErlang.htm) to check the numbers and verify that you are still seeing the (significant) discrepancy in ASA.

Interesting discussion!

Joe

[remy]

Well

I can't really say that proves everything. There must be way to have some theoretical prove of the whole problem. I for one would like to see if this is in fact right. If you reason that occupancy goes down to compensate for waiting time I agree, however the chance wil still be bigger of having a free agent in the big call center as opposed to the small call center.

It's too bad that we can't post any graphs. That would make it a lot easier to explain as well. If one would draw the curves for the small and big call center in one graph. (the one with occupancy on the x-axis. Then every point on the servicelevel curve you take would amount to an ASA for the call centers and in both cases they would have to be exactly the same for all possible levels.

Try and do this at home and see what you think about that

[JoeB]

My point was only that the numbers you use to demonstrate your argument seem incorrect and may have led to the wrong conclusions...

As for the occupancy rate, I have posted two graphs showing occupancy rate as a function of call center size.

1. Staffing relative to call volume, i.e. increase in size reflects increase in number of calls http://www.diagnosticstrategies.com/erlang/fig1.jpg. The graph clearly shows increase in utilization.
2. Adding more agents to handle the same call volume (overstaffing) http://www.diagnosticstrategies.com/erlang/fig2.jpg. The result is decrease in utilization (but improvement in service level etc.)

ASA if a far more complex issue. I wasnÂ’t sure if it appropriate to get to this level of detail, but here it is anyway. ASA as a function of agents in NOT a monotonous function and looks like this http://www.diagnosticstrategies.com/erlang/fig3.jpg. What it means is that as you add agents in response to increase in call volume, ASA starts improving, but at a given point, because of the statistical nature of cal arrival (Poisson process), too many calls are queued and ASA increases. You add another agent, ASA improves until the added capacity of the new agent is insufficient and ASA increases again (try this on your Erlang calculator!). As this figure shows, ASA is more STABLE in large call centers.

I hope this provides the empirical proof you were looking for. The math functions describing the theory, and especially how the % of queued calls changes relative to call volume (the famous Erlang C formula) can be found in http://www.diagnosticstrategies.com/...c_modeling.htm

Joe

[mikael]

The link Joe has provided is definitely worth the reading. While the math may seem daunting, it's worth a manager's while to dig into it. You don't have to be a math whiz in order to understand the basic concepts and how they very definitely affect your center's operation.

It concerns me that so few contact center managers seem to have any understanding of basic forecasting and staffing tools & calculations. I was literally stunned at a recent HDI local chapter meeting to hear a Director of a large bank help desk tell the group about how she'd just discovered that "there was this thing called an Erlang calculator or some such that would help you with staffing." She hadn't had the time to use it herself, she admitted, but somebody had told her that it was a good thing. A *Director!*

A common complaint of contact center managers is that they "can't get no respect." I have to suggest that if you want to be respected as a professional, then you need to *be* a professional -- which includes knowing the basics of your chosen profession and being able to communicate them effectively.

[JoeB]

Thanks Mikael!

Your note is very important and IÂ’d like to suggest that we start a new thread to discuss this topic. I share your concern about contact center managers that run their operation and make critical decisions by the seat of their pants. This pertains not only to the theoretical background, but also to the role that key performance indicators serve in ensuring that the contact center meets its business objectives as part of the companyÂ’s overall business strategy.

A phenomena I am sure Mikael and I are not the only ones to confront is the search for the elusive “industry averages” and “golden standards”. Performance indicators and the relationships between them are very case-specific and relaying on an “average” posted by someone on the Web without sufficient understanding how this number was obtained and their business specifics is risky. Partly to blame are the publishers of benchmark data that is based on self-selecting and self-reporting individuals, and do not have enough specifics and business context to make them useable.

Which really gets us to the realization that although we have a common language to describe the various performance metrics (and hopefully a common understanding as of their meaning), the relative importance of each performance indicator as a measurement of business performance is business specific. We must select key performance indicators and set our performance targets so that they reflect our business strategy!

Joe

[mikael]

Accordingly, I'll start two new threads here.

1. Are you a Professional?

2. The Standards Game

[remy]

http://www.cs.vu.nl/~koole/ccmath/book.pdf

See this piece for more information about what we're saying. If you have a look at page 25 you can see the difference between a bigger and smaller call center if you have occupancy on the x-axis and servicelevel on the y-axis.
The same sort of curves are created when plotting asa and occupancy, however the curves are flipped upsidedown and are not limited (ie asa can increase till infinity).

The graphs you were trying to show me don't seem to work, only the fourth works.

I'm going to try and post some graphs in another website. I 'll send the link if this works

[JoeB]

Thanks for the reference – a very good writeup, although may be a bit too theoretical for some to apply in real-world situation.

Yes, we are all in agreement that that a larger call center has higher utilization, as in http://www.diagnosticstrategies.com/erlang/fig1.jpg I hope that there is no confusion between occupancy [rate] (sometimes called utilization) and the number of agents – x-axis in Fig. 4.3 on page 25 is utilization, not headcount.

If you increase headcount to improve service level, the utilization decreases as shown in http://www.diagnosticstrategies.com/erlang/fig2.jpg

For call center planning purpose, plotting the number of agents on x-axis is more useful because it reflects the impact of changes in staffing on the call centerÂ’s KPIs. http://www.diagnosticstrategies.com/erlang/fig3.jpg shows how ASA changes as function of staffing. It shows that as agents are added in response to increase in call volume, ASA starts improving, but at a given point, because of the statistical nature of call arrival (Poisson process), too many calls are queued and ASA increases. Adding an agent, ASA improves until the added capacity of the new agent is exceeded and ASA increases again. Pure math may not show it, unless the calculations take into consideration that agents must be added as integers.

Given that we have established that utilization increases as the size of the call center increases, the same behavior in http://www.diagnosticstrategies.com/erlang/fig3.jpg should apply if you want x-axis to denote utilization.

You can replicate this graph using the online Erlang calculator the authors of this wrtiteup offer in http://www.cs.vu.nl/~koole/ccmath/ErlangC.php (or use http://www.diagnosticstrategies.com/easyerlang.htm, which allows you to save the results to Excel). Run multiple call volume/agent combinations to see how ASA changesÂ…

[remy]

Well,

I have just received an answer from the author of the piece sent in by me in the last post. He tells me that (he is a call center mathematician) indeed if you increase the size of the call center the ASA will start improving even if you keep aiming at a certain servicelevel.
If you use the Erlang Calculaor they have produced you will see that this is correct. However in the call center becomes too big the ASA will start increasing again. So it looks like this is a economics of scale advantage, where the ASA will improve if you increase call center size whilst maintaining the same servicelevel, however at a certain point increasing the call center won't decrease the ASA anymore and it will even start increasing (this wille happen only with really big call centers).

His reasoning is (more or less like mine) something like this. (translation from a piece he wrote me in Dutch).
-small call center
The servicelevel of a small center consists of the number of clients that will be answered immediately, the clients that won't be answered immediately however will wait a substantial time. So the ASA will be around zero seconds or a really long periode of time. Together this will give a relatively high ASA.
-big call center
While size increases the percentage of calls that has to wait longer will increase. However most of them will be answered within the AWT which will result in a lower ASA than the small call center

[JoeB]

I am afraid that we are dealing with two separate phenomena and possibly ignoring some real-world realities.

First, it is true that in general, in two call centers stuffed according to their call volume and for the same SL, the ASA in the larger call center is usually better due to the better utilization as we have already established. This is not because “most of them will be answered within the AWT which will result in a lower ASA” but rather the higher (statistical) availability of agents leads to ASA that can be better than SL.

I will even agree to a rough rule of thumb that says that in small call centers ASA is usually greater than SL and in larger ones ASA < SL, although this highly depends on the specifics.

The other phenomenon is the relationships between staffing and ASA. Stating that “ASA is better in large call centers” is an oversimplification of the situation, as demonstrated in http://www.diagnosticstrategies.com/erlang/fig3.jpg This statement applies only where is “large” call center is significantly larger than the “small” one. The range of data in this plot is from 33 to 250 agents, yet the ASA “improvement” trend is hardly noticeable.

To give you additional food for thought, I reran my calculations on a larger range of call center size range: 25-500 agents and placed it in http://www.diagnosticstrategies.com/erlang/cc.xls

Notice that the “average ASA” (a bad term…) has improved from 53 seconds to 49 seconds, hardly noteworthy…

You will also notice the zigzag nature of ASA caused by adding capacity in multiples of integer “person units”, and that in a smaller call center the ASA range is significantly greater. Still, as the graph sows, a small call center CAN accomplish ASA that is the same or better than the large one, and actual calculation in call centers may not agree with the general statement.

Finally, you will notice that ASA is indeed showing an improvement trend, but at a given point is seems to become worse! This coincide with the area were utilization reaches 0.99. Two points:

1. In my calculations I donÂ’t assume that 100% utilization is practical and force lower utilization if the calculations reach 100%. In actual planning we watch for the number and shoot for a much lower workload. If your math assumes that 100% utilization is possible, your results will be different.
2. The ASA trend line is a second order polynomial, which seems to work, but I havenÂ’t spent any time validating it.

[remy]

The reason however why I started this thread and inquiry is that I wanted to know if (in theory) the ASA from the bigger would or would not be lower. Now that a mathematicain has proven this to me it makes me confident that in fact in theory the ASA should be lower.
Would this happen in real life? I guess so, but I can't prove it. We have a lot of call centers but none of them are exactly the same, and that I think is the major problem. No two call centers are exactly the same and the only way to come to answer in questions like these is mathematical research.

I looked at your figures from the ASA you calculated, and where you say that 4 seconds is hardly noticeable. However if you calculate this in percentages this is about 8%, which I find to be quite a lot.

Indeed the research you did is very interesting but it should also prove to you and the other that indeed ASA decreases as size increases, up till the point where occupancy reaches a level where there's no difference anymore between a big and a small call center (your 99%). However I haven't got an intuitive explanation for this phenomena. Nevertheless the decline of the asa before this happens seems very logical to me. I hope you'll all agree with me on that part by now.

[remy]

By the way

I'm glad to have started a thread which already has had so many reviews. Good to have such a nice discussion on the net. Too bad that there weren't that many people involved and that we had to do everything the three of us :-)... Thanks for that
Hope to get more feedback some time soon to see what other people think about stuff like this or is this too scientific?