Who Can Figure This One Out!!

[remy]

Me and some colleague's of mine (all of us studied Operations Research) can't figure out which of the following statement is true.

Imagine two call centers
1) a big call center
2) a small call center

Both their targets are (for example) a servicelevel of 70% in 20 seconds, They have to be the same

If both call centers, with respect to the other variables, are completely the same (ie handling time etc)(minus occupancy of course) which of the statements will be true.

The asa of the bigger call center will be lower than the one from the smaller call center
The asa of the bigger call center is equal to the asa from the smaller one.

In real life the difference between the two seems to be there, however we can't prove this, even after trying to use the formula's in Hillier and Lieberman's Introduction to Operations Reasearch we couldn't really figure it out.

Hope one of you can help !!!!

[mikael]

Two call centers, of different sizes, but both facing the same AHT, the same incoming volume levels *relative to their staffing* and the same distribution pattern -- and are set up to meet the same service level. If the planners have done their calculations properly, why should there be a difference between the two in terms of ASA? What would cause such a difference to occur?

[remy]

Well this is because of the fact that if you want to meet the servicelevel goals the two call centers will have to have a different occupancy. Ie the smaller call center can only obtain a servicelevel equal to the bigger one by reducing the occupancy. So there could be a difference between ASA and Servicelevel and probably even should be.

[mikael]

I'm afraid that you've lost me a bit.

Let's say that both centers have an AHT of X minutes per call.

Both have a Service Level target of 80% of all incoming calls picked up in 30 seconds or less.

The LargeCenter has a staff of 100 scheduled to be on deck and available, and the SmallCenter only has 30.

Between 0900 and 1000 on Monday morning, each center will receive a total number of incoming calls that matches their forecasted load (i.e. that will enable them to meet their target service level).

If the staffing calculations were done effectively, perhaps even using the same tool for both schedules and both set to hit the target SL *exactly*, why would there necessarily be any difference in the ASA between the centers?

Minor variances could occur in the call patterns, of course, but either center could be favored by such from moment to moment.

In my experience, OR calculations tend to impress the OR folks -- who unfortunately are usually not the ones that authorize the budgets. I have enough trouble when I have to explain the basic concepts of call center managment or what an Erlang calculator is to center managers and to their company's Senior Mgmt teams. If I hit them with the full suite of OR tools, their eyes would glaze over in about two nanoseconds.

[remy]

If you draw the graph consisting of occupancy on the x axis and servicelevel on the y-axis and asa on the second y-axis you would find four different curves for the two call centers (two each)

Do you know the graphs I'm talking about?

That will show you that to get to the 70% servicelevel point one would need a lower occupancy for the smaller call center and thus this will probably result in a higher asa.

[mikael]

" That will show you that to get to the 70% servicelevel point one would need a lower occupancy for the smaller call center and thus this will probably result in a higher asa."

There is no question about the fact that the smaller center will need less "cheeks in seats" to meet their target SL. They take fewer phone calls, so they need less people.

But unless they deliberately overstaff for that SL, there shouldn't be any real difference in the ASA's between the small and large center.

You began the thread by noting that there seemed to be a difference in the real data you analyzed. I suspect that if there really is, that there are other factors in play that should be taken into consideration. Once you eliminate all other factors, however, by assuming them to be equal, the remaining points don't seem to give you anything upon which to hang the assumption that the ASA's would be different. -- At least, I'm certainly not seeing anything that would support the idea.

I know that there are some real data-daemons that haunt the forum; perhaps one of them will jump in. Joe? Dr. Fred?

[Karsten Fuhrmann]

Hi all,

I think that the ASA of the bigger call center is lower. It has to do with the "economy of scale". With more agents, the change of catching one free agent is higher than for the small call center. That's because the likelihood that one agent will end his call within the next let's say 5 seconds is bigger for 100 agents than for 20.

[JoeB]

Yes, there are differences in ASA and utilization between small and large call centers, but one has to be careful how the question is phrased.

For the SAME call volume, the larger call center will show faster ASA because there is a greater probability that there is a free agent to take the call. Your can figure it out intuitively without any queuing theory. If the number of agents relative to the number of calls (considering AHT etc.) is VERY large, there is a very high likelihood that calls will be answered after a short delay, even during peak traffic. As you reduce the number of agents the likelihood of this happening decreases.

It gets confusing when talking about utilization (occupancy rate). We feel that if we staff optimally (relative to the call volume), the utilization should be independent of the size of the call center.. We also know that as we add agents beyond the required number (i.e. we overstaff), the utilization decreases, because there are more free agents at any point in time. So intuitively we assume that the more agents there are the more idle time they have and therefore the lower the utilization rate.

It turns out that larger call centers have higher utilization. In other words, in two call centers, each staffed to meet the same service level target, one handling a high call volume and another a lower one, the larger call center will show higher utilization. In a large call center there are many queued calls waiting to be serviced, and there is a greater likelihood of assigning a new call as soon as the agent becomes free. In a small call center the “density” of the calls is lower, fewer calls are queued, and the agent may wait longer for the next call to arrive.

It is important to remember that calls do not arrive in a steady pace. They arrive according to Poison process, which drives this statistical behavior (see more at http://www.DiagnosticStrategies.com/...c_modeling.htm)

I hope this helps.


Joe Barkai
www.DiagnosticStrategies.com

[mikael]

I hoped you'd chime in on this one.

<<"In a large call center there are many queued calls waiting to be serviced, and there is a greater likelihood of assigning a new call as soon as the agent becomes free. In a small call center the “density” of the calls is lower, fewer calls are queued, and the agent may wait longer for the next call to arrive. ">>

However, I'm still not 100% certain on this one. Assuming that both centers were precisely staffed to meet the exact same service level, and *that all other factors about their incoming call loads were the same except for sheer volume,* would you still -necessarily- see a consistent difference in the ASA?

Above, you are assuming that that there are many calls being queued in the large center, but that their greater number of agents allows a greater likelihood of an agent coming free to grab the call -- but doesn't that in fact argue for a lower number of calls being queued? Or, at best, the same percentage of the incoming volume being queued?

Mathematics were never my strong suit, especially theoretical analysis thereof, but something about this question just doesn't seem right to me. I can't put my finger on why not, but there is something there that seems odd.

Can anyone generate some data to use on this? I think that it's a very useful discussion.

[JoeB]

The problem with this type of questions is that we intuitively assume a constant flow of calls whereas they have a random arrival and length pattern (governed by known distributions). I often have to go back to the math and try a couple of examples first to see what the answer is and then try to figure out whyÂ…

First, I was too quick to respond and mixed ASA and utilization, and I apologize for that confusion. As for ASA, if staffed correctly to meet the service level relative to their call volume, there shouldnÂ’t be a difference in ASA between small and large call canters.

However, there will be more queued calls in the large call center and the agents will work harder (utilization will go up). According to Erlang C formula, the probability of a call being queued increases with call volume (everything else being equal). This has to do with the fact that calls arrive at random according to a Poison distribution, which means that statistically speaking, there is a higher probability of experiencing a call rate that is higher than the average CPH (strange, I know), while calls are cleared at a fixed (non random) rate (AHT, which has a normal (sometimes log-normal) distribution).

I tested this with actual dataÂ…

I hope this helps a bit.

Joe Barkai
DIAGNOSTIC STRATEGIES
www.DiagnosticStrategies.com

[mikael]

<<"As for ASA, if staffed correctly to meet the service level relative to their call volume, there shouldnÂ’t be a difference in ASA between small and large call canters. ">>

Thanks for setting my mind at ease on that one, it had me going for a while.

I do find it interesting that agents would have a higher utilization in a larger call center than in a small one. It would be fun to find a "perfect" pair of a large & a small center where we could look at the ACD reports of actual talk times, etc., so that we could dig into this one.

And thanks as well to the starter of this thread for an excellent discussion.

[remy]

We're still not convinced by wat is said here. As to the last reply of Mikael, there is no doubt that a big callcenter can meet a servicelevel with a higher utilization than a small callcenter.

There are scientific articles proofing this statement. I can give you same data from our Callcenters to make our point more realistic:

The following data for our big Callcenter:

Occupancy: 88 89
Servicelevel: 72 73
ASA: 21 28
Call volume: 21614 23349

The following data for our small Callcenter:

Occupancy: 71 64
Servicelevel: 69 70
ASA: 37 43
Call volume: 487 484


We aim at a servicelevel of 70% within 20 seconds. As you can see the servicelevel is almost the same, the occupancy is much higher in the big callcenter, and also the ASA is smaller in the bigger callcenter. So the data seems to tell us that in a big callcenter the ASA is lower than in a small callcenter, and that this has tot do with the difference in occupancy !?

The question is can anybody give a scientific answer to this question ?

[JoeB]

Remy,

I'd like to run your numbers here. I can then give you the "behind the scene" numbers. What is the AHT that you used?Is these call volumes per hour? per day?

Joe

[remy]

Hello Joe,

i don't really understand what you mean by "behind the scene" numbers ?

The call volumes are per day and the AHT for the big Callcenter is aimed at 250 seconds en the AHT for the small Callcenter is aimed at 550 seconds.

The numbers in my previous reply are historical data from our Callcenters. We already built a simulation model with our own data. The results of the simulations also imply that there is a difference in ASA.

So now we like to know if anybody can come up with a scientific answer (in the form of formulas of the M/M/s - model or Waiting queue models)

I'm very intersted in your next reply Joe.

[remy]

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

Call volume