Saturday, 16 March 2013

What is the best achievable forecast accuracy?

By Ger Koole

The WFM cycle starts with workload forecasting. A good forecast is the first step in good WFM: if the forecast is accurate, then little real-time adaptations have to be done to the schedule. Of course we want an accurate daily forecast, but we need the forecast at the interval (often 15 minute) level, because the right number of agents should be there at every moment of the day.

We define the forecast (FC) accuracy as the relative (percentagewise) difference between forecast and actual. 5% FC accuracy is often used as a target. Everybody understands that exceptions happen, but we would like to stick the the 5% accuracy as much as possible. Thus a target of achieving an accuracy of 5% or better in 90% of the intervals is quickly formulated. But how realistic is this target? To answer this we have to dive a bit into the nature of call arrival processes.

Call volume is determined by many factors, such as day of the week, holidays, the weather, campaigns, and so forth. But in the end it is the customer who calls, and we cannot predict exactly the behavior of every individual customer. Thus, no matter how good we are at forecasting, there will always be some remaining "noise". That noise is quantified by what we call the Poisson distribution, named after a famous French mathematician from around 1800. Without going into the mathematical details, it amounts to the following. When the FC is x, then the deviation from x will be in around 30% of the cases bigger than √x and in 0,3% of the cases even bigger than 3√x, just because of the Poisson noise.

An example: Suppose we have a quarter with a FC of 100. We follow the rule: in 30% of the cases the error is more than √100 = 10, thus below 90 or above 110. 10 of 100 is 10%, thus in 30% of the cases the deviation is more than 10%, just because of the Poisson noise. Any FC error that is made will make the deviation bigger, it is the minimal error. A 5% FC accuracy in 90% of the intervals is unachievable in such a situation, it does not take into account the unpredictable fluctuations.

The situation is very different when we look st daily totals. Suppose that the daily volume is 10000. Only in 0,3% of the cases the deviation is bigger than 3√10000 = 300, only 3% of 10000. The probability of a deviation of 5% is even smaller than 0,3%. Here Poisson noise plays hardly a role, and a 5% accuracy seems like a fair objective. How ambitious this objective is depends on the fluctuations in volume, but the effect of the Poisson noise is only in the tenths of percentages.
We see how Poisson noise can play a big role for forecasting small volumes, and that it is impossible in such a situation to obtain highly accurate forecasts. When volume is bigger this plays less of a role and we can expect a higher forecasting accuracy.

More information on call arrival processes, Poisson noise and forecasting can be found in my book "Call center optimization".