When such a complex phenomenon as service level is reduced to a few numbers, then it is
unavoidable that certain aspects are ignored.
As an example, take the waiting times of just 4 calls: 0, 10, 30, 100 seconds. Then
the ASA is 35 seconds. However, the sequence 35, 35, 35, 35 has the same ASA. This
shows that the ASA, by its proper definition, does not depend on the variability: is the
ASA caused by many calls having a short waiting time or by a few calls having a very long
waiting time? Both are possible!
This is a good reason to look for other service level metrics. Consider next the TSF,
which is indeed, to a certain extent, sensitive to variability. However, in case of a bad
SL (a low TSF) you can better have high variability, and in the case of a high SL a low
variability! This can be seen from the following examples, each with AWT 20 seconds: 15,
15, 15, 15 (ASA 15, TSF 100), 0, 30, 0, 30 (ASA 15, TSF 50); 25, 25, 25, 25 (ASA 25,
TSF 0), 15, 35, 15, 35 (ASA 25, TSF 50).
Another disadvantage of the TSF is that does not take into account the waiting time in
excess of the AWT: the sequences 0, 10, 30, and 100 seconds and 0, 10, 24, and 30 seconds
give the same TSF of 50, although there is a clear difference between the situations! The
difference shows up if we vary the AWT. This however would lead to a SL metric consisting
of multiple numbers, which has the disadvantage that it is harder to interpret and to
compare.
Thus we find that neither the ASA nor the TSF represents the SL well. Focusing on one
of these can lead to consequences that go against common sense: it motivates managers to
take decisions that decrease the common perception of SL.
A call center has two types of calls: calls with a negociated SL in terms of a TSF that has
to be met, and ”best effort” traffic where the revenue depends on the SL. Under high traffic
conditions the TSF of the first type of calls cannot be met, even when priority is given to
these calls. Therefore, the rational decision, given the contract, is to give priority to best
effort calls in case of high load and to give priority to fixed TSF calls when traffic is low to
catch up with the SL. This is in complete contradiction with the intentions behind the SL
contract. (Source: Milner & Olsen, Management Science, 2006.)
It is common practice in call centers to answer the longest waiting call first. If the SL
is only measured through the TSF, then this is not a good solution: calls waiting longer
than the AWT should not be answered at all, instead the call that waits the longest among
those that wait less than the AWT should be helped. Thus the TSF stimulates wrong
behavior.
For the ASA the order in which calls are answered does matter at all. A possible solution
would be to report both the ASA and the TSF. Still priority is given to calls waiting a
little less than the AWT, but long-waiting calls eventually get served. An alternative SL
metric consisting of a single number that motivates us to help long waiting calls first is
as follows. It takes the AWT into account, and it penalizes waiting longer than the AWT
by measuring the time that waiting exceeds the AWT. We call it the average excess time
(AET). For the 0, 10, 30, 100 sequence the waiting times in excess of 20 seconds are 0, 0,
10, and 80, giving 90/4 = 22.5 seconds as AET. For 0, 10, 24, 30 it gives 3.5, and for 35,
35, 35, 35 the AET is equal to 15. When using the AET is it clear that those calls that
wait longer than the AWT get priority.
A discussion of service level metrics
Service level and abandonments
A phenomenon that occurs in every call center is that callers abandon (or renege) while
waiting in the queue. In general, this is considered to be something to avoid, although
some callers abandon in less than the AWT. One way to deal with abandonments is by
setting a separate service level constraint on abandonments, e.g., on average not more than
3% abandonments.
If the TSF is used, then there is also the possibility to integrate the abandonments in
this way of choosing the SL. For this, we first have to decide how to count abandonments. It
is clear that callers who abandon after the AWT have received bad service, and therefore
these calls are added to the number of calls for which the service requirement was not
met. For callers that abandon before the AWT there are different possibilities. The most
reasonable is perhaps not to count these calls at all. This leads to the following definition
of service level:
SL =Number of calls answered before AWT
Number of calls answered + Number of calls abandoned after AWT
× 100%.
Another possibility is to count them as calls for which the SL was met.
A call center receives 510 calls during an hour. The AWT is set equal to 20 seconds.
A total of 460 receive service, of which 410 are answered before 20 seconds. Of the 50
abandoned calls 10 abandon before 20 seconds. Therefore the service level is 410
460+40×100% =
82%. Not taking abandonments into account when computing the SL would lead to a SL of
410
460 × 100% = 89%!
These ways of calculating the service level are all easily done on the basis of observed
waiting times of calls: one needs to remember the numbers of served and abandoned calls
that get served or abandon before and after the AWT, in total four numbers per interval
for which we want to know the SL.
Another way of defining the service level is to compute it from the waiting time of ‘test
customers’ who have infinite patience. In general this leads to numbers very close to the
definition in which we ignore customers who abandon before the AWT. This definition is
attractive because it is independent of the patience of a caller. On the other hand, it is
somewhat more complicated to derive from the observed statistics: just the four numbers
as above do not suffice, one should really introduce virtual test customers and look what
their waiting times would have been.
Service levels can be measured in two different scales: between 0 and 100 or between 0 and 1.
We will use both. To go from one scale to the other we simply have to divide or multiply by 100.
Mathematicians often prefer to measure between 0 and 1, because the results can be interpretedas fractions or probabilities. Although it will be clear usually, we will always use the ”%” sign when using the percentage scale.
We should also consider how to incorporate abandonments in the ASA, in case the ASA
is used as service level metric next to or instead of the TSF. Defining the ASA in the case
of abandonments is done by looking at the ASA of test customers with infinite patience.
Service level metrics
We saw that the goal of call center management is to obtain the right cost-service level
trade-off. We also saw by who and by what types of decisions cost and service level can
be influenced. We now go into more detail how this service level can be defined.
The service level (SL) obtained by a call consists of several different aspects. Several
of these aspects are related to the handling of the calls themselves, such as the way in
which the agents attend to the call, and the ratio of calls that need no need further calls,
the first-time-fixed ratio. Others are related to the waiting process, notably the waiting
times and the occurrence of abandonment. We focus on waiting times and abandonments,
although other aspects of the service level can have a large impact on the waiting time and
therefore also on the abandonments.
The help desk of an Internet Service Provider had a considerable rate of callers that phoned
back after their call because the answer was not sufficiently clear to solve their problems.
By improving scripts and documentation and by additional training this rate was reduced
considerable. This not only improved the perceived service level, it also reduced the number
of calls. This had a positive effect on the waiting times, and thus again on the service level.
The common way to define service level is by looking at the fraction of calls that
exceeds a certain waiting time, which we will call the ”acceptable waiting time” (AWT).
The ”industry standard” is that 80% of all calls should be answered in 20 seconds, but other
numbers are possible as well. The SL can simply be calculated by dividing the number of
calls handled before the AWT by the total number of calls.
Often we know the SL for short intervals (often giving by the ACD), and we want
to compute the SL for longer intervals, for example in a spreadsheet to make a monthly
report. The SL of a long period composed of several shorter of which we know the SL can
be calculated be averaging in the right way service levels over the shorter periods. When
averaging over a number of intervals the number of calls in these intervals should be taken
into account. Consider the table below. At first sight the average service level is 75%, by
averaging the four percentages, but now the differences in numbers of calls per week are not
taken into account. The right way of calculating is to compute the fraction of calls in each
interval first. For example, the fraction of calls in the first interval is 2000
17000 , 17000 being
the total number of calls over the four weeks. Using these fractions a weighted average is
calculated in the following way:
200017000× 95 +700017000× 55 +500017000× 70 +300017000× 80% = 68.5%.
Week Number of calls Answered within 20 s. SL
1 2000 1900 95%
2 7000 3850 55%
3 5000 3500 70%
4 3000 2400 80%
This way of calculating averages corresponds to the answer in case the service level was
computed directly for the whole month. Indeed, out of a total of 17000 calls 11650 were
answered in time, thus a 11650
17000 × 100 = 68.5% service level.
The difference between 68.5 and 75% is not that dramatic. This is because the number
of calls in the different weeks are roughly of the same order of magnitude. If the number of
Chapter 3 — On call center management and its goals 11
calls in the intervals over which we average are very different, then the way of averaging can
have an even bigger impact on the result. These big fluctuations typically occur during
days. At peak hours we can easily have ten or twenty times as many calls per hour as
during the night. Then the difference between ways of averaging can run into the tens of
percents.
The percentage of calls that is answered in less than a certain fixed waiting time is
sometimes called the telephone service factor (TSF). Another commonly used waiting time
metric is the average speed of answer (ASA).
