Formula to calculate number of calls to regain Grade of service in a call centre

[JONESI]

Hi,

*NB: This is not homework. I am 50 years old and have suddenly acquired an interest in maths (UK) as a hobby. I have started at the beginning (GCSE - UK) and am slowly working my way up.

Question/scenario: GOS (grade of service) in a call centre might be defined (simply) as 85% of all calls answered within 15 seconds. 10 calls answered within 15 seconds out of a total of 20 calls - GOS = 50%. If we assume there is no limit to resources available (i.e. calls centre agents to answer the calls) and that there is an infinite and steady flow of calls, how many calls are now needed to raise the GOS back to SLA (service level agreement) of 85%?

(I am currently revising/re-visiting algebra) This is how I have tried to answer it:

a+x/b+x = 85/100
(multiply both sides by (b+x) ) a+x = 85/100 * (b+x)
a+x = 85b+85x/100
(multiply both sides by 100) 100a + 100x = 85b +85x
100x-85x = 85b - 100a
15x =
x = 85b-100a\15

I have translated this into a spreadsheet and it seems to be correct but I am not advanced enough to prove it. a). Is it correct? b). Is there an easier way to answer "how many calls need to be answered in GOS to get back to GOS?

How it all makes sense and thanks in advance.

Ian

 

[JONESI]

Hi,

*NB: This is not homework. I am 50 years old and have suddenly acquired an interest in maths (UK) as a hobby. I have started at the beginning (GCSE - UK) and am slowly working my way up.

Question/scenario: GOS (grade of service) in a call centre might be defined (simply) as 85% of all calls answered within 15 seconds. 10 calls answered within 15 seconds out of a total of 20 calls - GOS = 50%. If we assume there is no limit to resources available (i.e. calls centre agents to answer the calls) and that there is an infinite and steady flow of calls, how many calls are now needed to raise the GOS back to SLA (service level agreement) of 85%?

(I am currently revising/re-visiting algebra) This is how I have tried to answer it:

a+x/b+x = 85/100
(multiply both sides by (b+x) ) a+x = 85/100 * (b+x)
a+x = 85b+85x/100
(multiply both sides by 100) 100a + 100x = 85b +85x
100x-85x = 85b - 100a
15x =
x = 85b-100a\15

I have translated this into a spreadsheet and it seems to be correct but I am not advanced enough to prove it. a). Is it correct? b). Is there an easier way to answer "how many calls need to be answered in GOS to get back to GOS?

How it all makes sense and thanks in advance.

Ian

To clarify, in the formula above:
a - is the number of calls answered within GOS
b - is the total number of calls
The formula is to find x, the number of calls required to regain the GOS.

Hope that makes sense, and again thanks in advance, Ian

 

[stapel]

To clarify, in the formula above:
a - is the number of calls answered within GOS
b - is the total number of calls
The formula is to find x, the number of calls required to regain the GOS.

Hope that makes sense, and again thanks in advance, Ian

And you're wanting to raise the ratio from the current 50% back up to 85%...?

If so, then I suspect that your formula is fine, if you know the values of "a" and "b". Do you have this information? Thank you!