Call Center Mathematics

Call Center Mathematics

To manage call centers, or more generally, contact centers, effectively, one needs to have
multiple skills. Roughly speaking there are those skills which are unique to the product
that is delivered, and there are those skills that are needed in virtually any call center.
Some of these latter skills are soft, such as training and motivating people. Other skills
are of a more quantitative nature, and are related to service level and an efficient use of
the main resource, the people that work in your call center. Mathematics can play an
important role in getting the best out of the service level/cost trade-off. In a simple singleskill
call center we see that the Erlang formula is used to determine the occupation level
at any time of day. Scheduling algorithms are then used to determine shifts and to assign
employees to shifts. In more complex environments mathematics is used to route calls, to
decide how and when call blending is done, and so forth. Mathematics are an essential
part of call center management.

Why should a call center manager know about mathematics?

Let us first put you at ease by stating that we do not think that managers in call centers
should know the mathematics themselves. We do think that managers should know about
the implications of mathematical theory for call centers. But if the mathematics are already
implemented in the software, why know anything about it? Why should we understand the
Erlang formula if it is readily available in many decision support systems? The answer to
this lies in the name decision support system. No computer-based system can completely
automate the complex scheduling and planning tasks in a call center. Human interaction
is always needed, and this is only possible if the user understands the software. In this way,
learning about call center mathematics increases the effectiveness of the available software.
On the other hand, certain tasks within a call center, such as call routing, are completely
automated. But here the crucial decision was taken at the moment the routing algorithm
was implemented. Again, only an understanding of the dynamics of call centers can help us
to implement the right routing machanisms. Thus again, an understanding of call center
mathematics will help us make better decisions. The same holds for long-term decisions
about the structure of a call center. Mathematics can help us understand and quantify
decisions related to the merging of call centers, call blending, multi-channel management,
and so forth.
A better understanding will also improve the communication with other people, not in
the least with the consultant who is trying to sell a model-based solution.

Two ways to call center improvement

Any business change raises questions about the effectiveness of the proposed change. Will
it really work out the way it is foreseen? Given our understanding of call centers we often
have an idea what the type of effect will be of certain changes. Direct implementation of the
proposed changes, on-line experimentation, has the advantage of simplicity and low costs.
But these costs remain only low if the effects of the changes are positive! For this reason one
often likes to experiment first in a “laboratory” setting. Mathematics offers such a “virtual
laboratory”. The important aspects of reality are described in a mathematical model and
this model can be analyzed using mathematical techniques. This way different scenarios
can be analyzed, hence the term scenario analysis. But mathematics can do more. It
can generate solutions for you. This is what a workforce management tool does when it
generates an agent schedule. This solution can be of varying quality, depending on the
model that is implemented. In theory mathematics can generate solutions that are better
than those that are thought of by a human, and in much less time. The mathematical
model however is constructed by humans, and everything depends on its quality.
Merging two call centers leads to economies-of-scale advantages. However, the physical
costs of such a merger can be high! Calculations based on the Erlang model can quantify
the expected cost reduction. This way a reasonably accurate cost trade-off can be made.
There are in principle two ways to use mathematics to improve the performance of a
call center. There is a ‘minimal’ approach in which the insights obtained from this book
and other sources are used to give rough estimates of consequences of possible management
decisions. This type of ‘back-of-the-envelope’ calculations take little time, probably
involve the use of a spreadsheet and one or more call center calculators, some performance
indicators that are already known, and perhaps contact with an in-house OR professional
or mathematician. It is mainly to equip the manager or planner with the skills to execute
this type of task that I wrote this book.
The second approach is the ‘standard’ Operations Research approach, but not necessarily
the best. It consists of building a mathematical model of the call center, estimating
Chapter 2 — What is Call Center Mathematics? 5
all relevant parameters, and drawing conclusion from a thorough analysis of the model.
This analysis often involves simulation of the whole system. This approach is time consuming,
usually performed by external consultants, and whether it really gives good results
is sometimes doubtful. It works best for operational problems of a repetitive nature.
Whatever approach is taken, improving your call center does not end with modeling
(parts of) it once. Improving your call center is a continuous process in which the subsequent
modeling steps (model construction, data collection and analysis, running scenarios,
implementation) are followed again and again.

What to expect from call center mathematics ?

Mathematics can help you manage your call center. However, you should not expect
miracles. Every modeling exercise implies simplifying the real situation first to fit it in the
framework of the model. With this modeling step certain approximations are introduced,
requiring a careful use of the outcomes. Modeling everything simply isn’t possible, because
of time constraints and because for example human behaviour cannot be modeled in all
details. Sometimes you won’t even be able to get all the information you want out of the
ACD! This doesn’t make modeling useless, but it requires an attitude in which outcomes
of modeling studies are tested thoroughly before being implemented. Never implement a
proposed solution until you are completely confident that it will work out the way it is
intended!