I have a question based on a staffing equation used for a call center.

Its basically call length* calls per month during a 12 hour window (8a-8p)
divided by: 60, then 21.667, then 8, then 0.75

So 8 minutes a call * 5,000 calls = 40k minutes worth of talk for a month during the 8a-8p window
Divided by 60, we have 666.6 hours of talk for a month during 8a-8p
Divided by 21.6667 (business days in a month), we have 30.8 hours of talk per work day 8a-8p
Divided by 8 (the 8 confuses me, why not 12?), we get 3.85 Hours of talk needed per hour (across several agents on the phones)
Divided by .75 (agents are talking or available to talk 75% of the time)
we need 5.12 agents, in theory

Now the question is, why is it they're using 8 there? The window is 12 hours, I was maybe thinking 8 hour shifts but it still should be divided by 12. The only reason I can justify 8 is that a majority of the calls come in during 8a-2p, so diving by 8 instead of 12 is their way of jacking up the number of agents needed, since dividing by 12 would leave the hour by hour average too low most of the day when the volume is the highest.

Also, dividing by .75? They might be available some of that time, but they only are on calls 50% of the time, the other .25 of the .75 is just waiting to take a call.

Have they just messed up or are they trying to compensate for the the fact that we dont have linear call arrivals by hour, by lowering the hours in a day (dividing by 8 instead of 12)

3/11/2010 11:34:30 AM

look at your units

somewhere you have to factor in the number of hours a single employee can work in order to get to # of employees

[Edited on March 11, 2010 at 2:04 PM. Reason : ]

you end up with 30.8[hours of work/day]/8[hrs/employee] = 3.85[employees/day]

[Edited on March 11, 2010 at 2:12 PM. Reason : ]

3/11/2010 2:00:20 PM

Well, this isnt necessarily my model. It's something Ive been tasked with reviewing. And yeah, it doesn't account for the fact that no one works for 12 hours.

Suggestion?

So far my only assumption for their current model is to jack the hours low, which jacks the agents up. We typically use it for more 8a-5p staff, but the call volume total is for 8a-8p. Dumb. Anyways, the latter volume total is not going to change. So my only hope is to try and split up the previous two. Have a volume. Say that 80% of the 12 hour volume comes in 8a-5p, staffing equation for that. Another equation for the 5p-8p. 8p-8a isnt so much a big deal as we combine clients and dont get many calls.

3/11/2010 4:07:45 PM

^^ they'd be understaffed in that situation. As soon as someone got up to take a piss, they'd be behind.


That's where the .75 comes in. Nobody works 100% of their shift. And any realistic management doesn't expect it. Whether it's built in via allotted breaks, or simply recognizing that people don't work 100% of the time. Or maybe you simply feel that if they have to talk more than 75%, they'll get worn out and the extra time they're talking will be inefficient. Either way, say your goal is 75%. Whether they're talking 75% of the time or less, you'll be covered up to 75% if you take that into account when figuring out how many employees you need.

And that's actually very realistic in a 9-5 situation. - 1hr for lunch. maybe a couple of 15 minute breaks (which you'll often find in employee handbooks whether they're advertised or not) and you're down to 6.5hrs of work. Then maybe 30 minutes of whatever spread throughout the day, bathroom, checked out mentally for a few minutes, whatever. That's 6/8 = 75%.


Is this an actual formula that a call center is using? Or something out of a textbook? Are you assuming the majority of the calls are from 8am-2pm, or do you know that? Do you know how long the shifts are or what times they run?



This is how I would do it:

8 * 5,000 = 40k
convert to hrs = 666.6 hours/month
divide by business days in avg. month = 30.8hrs of actual talk/work
Now, I expect that to cover 75% of the time my employees work. So what is that 75% of? = 41.07 hrs/day.
assuming 8hr shifts, 41/8 = 5.13 eight-hour shifts.

Then, if you had the data for when most calls came in, you make your schedule while taking that into consideration. And you also decide if you want 5 full-time employees and one part-timer or 6 full-time employees. Or 5 full-time employees and ask them to exceed your goal of 75%.


If you have 9hr workday (-1hr lunch),, you have either 2 full-time shifts or some combination of full-time and part-time. Let's say 2 full-time shifts, an 8-5 shift and an 11-8 shift. If you do the math using the numbers you have, it gives you about 5-6 employees mid-day. Then 2-3 employees for both 8-11 and 5-8pm. Or if most of your calls are in the morning, maybe you have 4 from 8-5. And 2 from 11-8pm. They'd get there in time to cover lunch breaks.

[Edited on March 11, 2010 at 4:34 PM. Reason : ^ had the window opened too long and didn't see the new post]

3/11/2010 4:33:26 PM

What I was saying was in response to your question of why they divided by 8 instead of 12. It seems to me because an employee only works 8 hours a day. I mean if you have 30 hours of work that needs to be done in one day, you can't expect 2 people on a 8 hour work day to get that done (16<30).

The 75% just seems like a fudge factor to me, a way for accounting for that one day where you might need 50 hours of work (30 hours is the average meaning some the days will require more than that) which would also account for mandatory breaks and meals.

EDIT:^I left out the 75% part on purpose trying to show him where the 3.85 came from

Quote :

"we get 3.85 Hours of talk needed per hour (across several agents on the phones)"

[Edited on March 11, 2010 at 4:43 PM. Reason : ]

3/11/2010 4:38:57 PM

yeah, you can look at the 75% as the amount of time the company expects the person to actually talk. The rest of the time could be filling out reports, meetings... whatever. That's something you have to decide on upfront though to figure out what you really need.


^ i gotcha now. The way he has it written out is weird to me and is not written out in a sensible way, even though it works out the same (which i realize was probably given to him).

I just went about it in a way that made was more sensible to me when written out.

I have no confusion about where numbers are coming from in this:
8 * 5,000 = 40k
convert to hrs = 666.6 hours/month
divide by business days in avg. month = 30.8hrs of actual talk/work
Now, I expect that to cover 75% of the time my employees work. So what is that 75% of? = 41.07 hrs/day.
assuming 8hr shifts, 41/8 = 5.13 eight-hour shifts.

[Edited on March 11, 2010 at 5:11 PM. Reason : .]

3/11/2010 4:49:04 PM

nm, both way are pretty much exactly the same and no more sensible than the other. I just did the conversion at a different point.

Ehh, at least it kept me occupied for the last few minutes of the work day.

[Edited on March 11, 2010 at 5:35 PM. Reason : .]

3/11/2010 5:30:38 PM

Well the 75% is the time someone is ready to work or working. 25% of the time is used for the bathroom, email, etc -- any time that theyre not on the hook with respect to their phone.

Most calls come in 8-2 as a fact. The question is that when we take an average over 12 hours, were going to be over staffed a lot and understaffed a lot. BUT, ignoring that. We're just trying to find a starting point with this. It's almost always adjusted.

The .75 is going to be adjusted because honestly, theyre only actually answering calls for 40% of the day, the other time is spent waiting for calls (we have really strict speed-to-answer contracts with clients).

Divided by 21.6667 (business days in a month), we have 30.8 hours of talk per work day 8a-8p
Divided by 8 (the 8 confuses me, why not 12?), we get 3.85 Hours of talk needed per hour (across several agents on the phones)
Divided by .75 (agents are talking or available to talk 75% of the time)
we need 5.12 agents, in theory

Theyre dividing by 8, presumably assuming that youve got 8 hour shifts and youre getting 6 hours of on phone service from them. But the model never addresses the fact that the volume is coming from a 12 hour, 8a-8p window. The model is too limited, but because we tweak afterwards because every contract is different, is merely a jumping point for the negotiations. I've just been tasked with giving my input. And to be honest, I think its pretty bad. Id much rather look at the percent of calls by a few intervals within the 12 hours and staff appropriately from there.

But. The 8 hour divison (8 hour shift theoretically, 75% talking or ready to talk) and no acknowledgement of the 12 hour window is what kills me. But I guess multiplying the total volume by the volume coming in that 12 hour window might be sufficient? (e.g. 1,000 calls, 90% occur between 8a-8p, so we multiply average call length by 900 to start with....so is the 12 hour pretty much null/void/accounted for after that?).

btw, thanks for the discussion, anything to get my brain going is more than appreciated after staring at numbers all day

3/12/2010 1:17:37 PM

do you not have data for various time ranges? You can't see how many talk hours are between 8-2 and how many are between 2-8pm?

3/12/2010 4:48:50 PM

Something I haven't seen addressed where you could add value is to bring up the point that one consideration they should have is to minimize time spent on hold in order to provide better customer service. Acknowledging that calls are not dispersed uniformly throughout the day, you can model the calls as a Poisson arrival process, then use the number of staff in order to calculate an expected hold time before a call is taken. If they have a standard for what an acceptable average hold time would be, then you can take that into account.

Iterating on that model, you can use data like ^ suggests in order to model each hour separately; if there are more calls during midday than early in the morning, that would entail an arrival process with a higher rate parameter during midday. You could use that to make suggestions about the shift design since people only work 8 of the 12 hours in a day, to get how many employees should be on staff in the morning versus night.

3/12/2010 9:59:07 PM

Well, I can tell you most everything about number of calls, arrivals, expected ring/talk/work/type of the call. However, they're not interested in something complex. Part laziness, part because the deals we price come from outside clients that really only say 'uhhhh we get about 10k calls a month' but rarely have good data or people to work with.

3/15/2010 4:41:28 PM