Erlang Formula

Erlang is a mathematical equation used to calculate how many agents are required by any given period to answer the amount of calls forecast within a specified time.

Sounds like gibberish does it not, but if we break this down you will understand further.

Imagine a call centre is expecting to receive 100 calls within an hour and as a call centre your target is to answer 80% of these calls within thirty seconds. As a call centre you could say, well I need 100 people to answer 100 calls, you could be right, but what if you only need 60 agents and the other 40 sit their twiddling their thumbs, that's a huge waste of money. What Erlang will do is review how long your calls are and the time needed by X amount of agents to answer the 100 calls to achieve your target.

Interestingly the Erlang mathematical formula was developed long before the invention of today's call centres and was the brain child of a famous Danish mathematician called Agner Krarup Erlang who was born in Lonborg, Jutland on the first of January 1878.

Agner Erlang designed the Erlang formula while working for the Copenhagen Telephone Company between 1909 and 1929. The Copenhagen Telephone Company (also known as the CTC) gave Erlang a problem to solve as they needed to know how many circuits were needed so they could provide a suitable telephone operator service for their customers.

Erlang being the hardened researcher worked hard and went beyond what they required, he managed to work out a mathematical formula so the CTC could find out how many telephone operators were needed to answer the calls and provide an efficient operator service, thus the Erlang formula was born.

Call Centres across the globe use Agner Erlangs Erlang mathematical formula as part of their staffing process.

The process starts with forecasting how many calls will be delivered for a day then splitting this into half hourly or hourly figures. Once this has been achieved the Erlang formula will be used to determine how many staff are required by half hour/hour to answer the forecast calls efficiently.

Once the Erlang formula has delivered the numbers required an additional percentage will be added for absence, sickness and holiday before the staff are scheduled on shifts that will cover the numbers needed throughout the day.

When you ring and have to wait a few minutes for an advisor this may be due to a "call spike" where a large number of calls come in at the same time or it may be due to calls being above forecast causing extra resource to be required.

I have created a free Erlang calculator so if you work in a call centre you have the ability to work out your staff requirements. This Erlang calculator lets you put in your call requirements for one day then returns the amount of agents required to answer those calls within you agreed service level targets.

To get your free Erlang calculator just click on the link below.

FREE Erlang calculator

This calculator is created in Excel and requires an Excel Erlang plugin which can be found in the .zip file with the calculator. There is a wordpad doc. showing how to install the Excel Erlang addin so the formulas work in the calculator.