If i take 5000 calls at 78% service level, how many calls would I need to take at 100% to equal an overall service level of 80%
Please post formula
To find the number of calls needed at 100% service level to achieve an overall service level of 80%, we can use the Erlang C formula. The Erlang C formula is used to calculate the probability that a customer has to wait in a queue because all agents are busy.
The formula is given as:
P0 = 1 / (1 + (A^N / N!) + (A^(N+1) / N!*(N-A) / (N-A+1) + ... + A^(2N) / N!*(N-A) / (N-A+1) / ... / (N-2A+1))
Where:
- P0 is the probability of having zero customers in the system (idle agents)
- A is the offered load (number of calls arrived in a specific time period)
- N is the number of agents available (in this case, the number of calls you're trying to find)
Since we know the service level for the first scenario, we can use the Erlang C formula to calculate the offered load for that scenario. Let's assume the service level is achieved with 5000 calls. So, we set P0 to 0.22 (78% service level).
Now, we can rearrange the Erlang C formula to solve for A:
A = (N * (1 - P0)) / (P0 * (N - A)!)
Now, we can plug in the values:
A = (N * (1 - 0.22)) / (0.22 * (N - A)!)
Since we want to achieve an overall service level of 80%, we set P0 to 0.2:
A = (N * (1 - 0.2)) / (0.2 * (N - A)!)
Simplifying the equation gives:
A = (N * 0.8) / (0.2 * (N - A)!)
To solve this equation, you can use numerical methods like trial and error or iterative approaches. By plugging in different values for N and A, you can find the values that satisfy the equation and give an overall service level of 80%.