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.