# Calculation of the number of operators and optimization of the call center

**Initial data**

As an example, let’s take an average call center in terms of the number of employees, which operates from 9:00 to 18:00 and receives 3,000 calls per work shift. For modeling, we use Erlang X formulas – this is a mathematical model developed in the 60s of the XX century for the queuing theory, which takes into account the percentage of missed calls. In more detail about the formulas for calculating the load of voice channels, Agner Erlang himself and Erla as units of measurement there is a lot of information on the Internet, for example, on Wikipedia… We will not duplicate theoretical calculations here, but let’s go straight to practical calculations.

Assumptions:

- number of calls per shift: 3,000 (or 6 per minute);
- average talk time (Average Handling Time – AHT): 2 minutes;
- required time to answer a call: no more than 20 seconds (Service level – SL);
- number of external lines: unlimited (never busy);
- the subscribers, after 5 minutes of waiting in the queue, end the call, and the call is considered lost.

**Scenario 1**

Condition: not to allow a single lost call.

The number of employees required to fulfill the condition: 23 operators per shift (excluding breaks).

SL: 99.9% – this number of subscribers will receive an answer within 20 seconds.

Operator occupancy: 52%.

**Scenario 2**

Condition: the number of lost calls – no more than 1% (or 30 lost per shift).

The number of employees required to fulfill the condition: 17 operators per shift (excluding breaks).

SL: 95.7% – this number of subscribers will receive an answer within 20 seconds.

Operator occupancy: 70%.

**Scenario 3**

Condition: comply with SL 80/20 (80% of subscribers must receive an answer from the operator in 20 seconds), while about 60 calls (2%) will be lost per shift.

The number of employees required to fulfill the condition: 15 operators per shift (excluding breaks).

SL: 80% – that many subscribers will receive an answer within 20 seconds.

Operator occupancy: 78%.

Thus, a slight decrease in performance indicators can lead to significant savings due to the number of call center operators, while the personal efficiency and workload of each employee will increase. Call center managers can figure out the requirements themselves and prioritize, for example, whether a 30% increase in costs is worth one percent of missed calls.

In this case, the customer decided to follow the path of the least expenses and chose the third scenario. Moreover, since the project was developed using software from 3CX, this scenario allowed additional savings on the choice of a license.

The 3CX communication platform is licensed not by the number of subscribers, but by the number of simultaneous calls. Basically, for the call center discussed in the example, a license for 24 simultaneous calls in all three scenarios is sufficient. However, in the third case (as the customer decided in the end), you can get by with a license for 16 OB: so, if all 15 operators are talking at the same time, then there is only 1 free line for the queue. There is a certain risk in this, but the call center management decided to start with a smaller license, and if in the process of work there is an obvious shortage of lines, switch to a larger number (especially since 3CX only pays for the difference between licenses without fines and overpayments).

The 3CX platform contains a tool for tracking the current service level (SL) and lost call center calls by sending notifications to interested parties. So in the process of work, you can quickly assess the load of the call center and make a decision on expansion if necessary. In addition, the customer had to choose from two editions – Pro and Enterprise. The latter provides additional redundancy and increases fault tolerance, and also offers more options for customizing interfaces. Here it was also decided not to overpay at the first stage and to limit ourselves to a sufficient minimum.

Of course, most of the savings in choosing one of the three scenarios come from reducing the number of operators and jobs, not the license. In our example, the difference between the most expensive and the cheapest of the considered license options for the customer was about 50,000 rubles per year. This is less than the “cost” of one operator per month.

In some cases, a larger license size may be required (for example, when an outbound scenario appears or an increase in the number of calls during a peak period). On the other hand, for some types of business, it is acceptable to have a scenario where customers can be in a queue for a long time. Due to the flexibility of licensing and upgrading with 3CX, you can easily solve such. Licensing based on the number of calls and not the number of subscribers is an important advantage of 3CX in this regard.

*Experts shared their thoughts on their project by OmniLine…*